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FORCED-CONVECTION H EAT-TRANSFER MEASUREMENTS WITH A MOLTEN FLUORIDE SALT MIXTURE FLOWING IN A SMOOTH TUBE J. W . C o o k e B. c o x

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

W Contract

NO.

W-7405-eng-26

Reactor Division

MARCH 1973

OAK RIDGE NATIONAL LABORATORY Oak Ridge, Tennessee 37830 operated by UNION CARBIDE CORPORATION for the U. S. ATOMIC ENERGY COMMISSION

iii

coNTms

............................ Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . Description of the Apparatus . . . . . . . . . . . . . . . . . . . . Operating Procedures . . . . . . . . . . . . . . . . . . . . . . . . Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix A -Additional Details of the Experimental System . . . . . Abstract..

Page 1 1 2 11

15 16

24 27

â&#x20AC;&#x2122;

Appendix B .c .

- Experimental Data

Appendix C -Computer Program Appendix D

- Chemical Analyses

................... ................... and Physical Properties of the Salt .

27 29

43 55

bi n

FORCED-CONVECTION HEAT-TRANSFER MEASUREMENTS WITH A MOLTEN FLUORIDE SALT MIXTURE FLOWING IN A SMOOTH TUBE J. W. Cooke B. Cox

ABSTRACT Heat-transfer c o e f f i c i e n t s were determined experimentally f o r a proposed MSBR f u e l s a l t (LiF-BeF,-ThF4-UF4;67.5-20.0-12 .O-0.5 mole 4 ) flowing by forced convection through a 0.18-in.-n> horizontal, c i r c u l a r tube f o r t h e following range of variables: Reynolds modulus Prandtl modulus Average f l u i d temperature Heat f l u x (Btu/hr f t2)

- 30,600 1050 - 1550 22,000 - 560,000 400

4 - 14

(OF)

Within these ranges, t h e heat-transfer c o e f f i c i e n t was found t o vary from 320 up t o 6900 Btu/hr*ft2 OF (Nusselt modulus of 6.5 t o 138). Correlations of the experimental data r e s u l t e d i n t h e equations :

w i t h a n average absolute deviation of

6.gfor

NRe

w i t h an average absolute deviation of 4.1$ f o r 3500

1000;

< NRe < 12,000;

and

with a n average absolute deviation of 6.2$ f o r NRe > 12,000. Keywords: Heat t r a n s f e r , fused s a l t s , forced convection, heat exchangers, f l u i d flow, c o r r e l a t i o n s . INTRODUCTION

The design of molten s a l t reactors requires d e t a i l e d i n f o r m t i o n about t h e t r a n s p o r t properties of t h e proposed f u e l , coolant and blanket mixtures.

Although t h e molten salts generally behave as normal f l u i d s

w i t h respect t o heat transfer,'

t h e p o s s i b i l i t y of unexpected e f f e c t s ,

2 such as nonwetting of metallic surfaces or t h e formation of low-conductance surface f i l m s , indicates that heat-transfer measurements for s p e c i f i c rea c t o r salts are needed.= mole

8).

The technique employs forced convection of

t h e l i q u i d salts through a smooth thin-walled Hastelloy N tube. ance heating supplies t h e tube w i t h a uniform heat flux.

Resist-

This method i s

p a r t i c u l a r l y well suited t o t h e molten s a l t system because t h e e l e c t r i c a l resistance of t h e molten salt i s very large compared with t h a t of the metal tube.

Furthermore, the resistance of Hastelloy N remains nearly

constant over t h e e n t i r e temperature range of the measurements, which simplifies t h e achievement of an a x i a l l y uniform heat flux.

I n addition,

a constant heat capacity of t h e molten s a l t i n t h e observed temperature

range m k e s possible several convenient assumptions i n t h e calculation of local f l u i d bulk temperatures.

DESCRIPTION OF THE APPARATUS

The apparatus f o r studying heat t r a n s f e r with t h e molten s a l t system

is shown schetmtically i n Fig. 1 and i n t h e photograph, Fig. 2.

Molten

s a l t flows by means of gas pressure through a small diameter, e l e c t r i c a l l y heated t e s t section.

The f l o w of molten s a l t alternates i n d i r e c t i o n as

pressure from a n i n e r t gas supply i s added t o e i t h e r of two storage ves-

sels located a t each end of t h e t e s t channel.

Each 6-ga1. salt reservoir

is suspended from a weigh c e l l whose recorded s i g n a l indicates t h e flow rate.

The flow of s a l t reverses a u t o m t i c a l l y by t h e a c t i o n of solenoid

valves that control t h e flow of i n e r t gas t o t h e reservoirs. flow of t h e salt m y be varied from 0.25 t o 1.7 gal/min,

The r a t e of

emptying a

reservoir i n from 3 t o 20 minutes. The weigh c e l l c i r c u i t shown i n Fig. 3 i l l u s t r a t e s t h e e l e c t r i c a l and mechanical systems t h a t control t h e flow of gas and thereby t h e flow of molten s a l t .

A second suspension system maintains tension on t h e t e s t

section, t o prevent it from sagging, by means of counter weights connected by f l e x i b l e cables.

This report describes heat-transfer experiments

w i t h a proposed reactor f u e l of mixed fluoride salts (LiF-BeFsThF4-UF4;

67.5-20.0-12.0-0.5

The t e s t section consists of a smooth Hastelloy N

tube, 24.5 in. long, O.25-in.

outside diameter, and 0.035-in.-wall

ORNL-OWG

66-42942 ARGON

REVERSE

FLOW

CONNECTING

TUBING

VALVE

W MIXING CHAMBER

EELECTRIC

I I

1 1 1 1 1 i 111

*SALT

TANK

SALT TANK -

_.-_. L. (It2

Fig. 1. characteristics

Schematic diagram for determining the heat-transfer of molten salt by forced convection.

HEATERS

Fig. 2. Photograph of t h e apparatus viewed from the same aspect as that of Fig. 1.

ORNL-DWG

MECHANICAL

4 4510

/EL;-------

HONEYWELL RECORDER CONTROL I

72-

i I

SOLENOID VALVE

GAS

1 I I

‘t ,,4

TANK

Fig.

Weigh cell

circuit

for molten salt

heat-transfer

system.

thickness and i s resistance heated with a 60 Hz a c power supply.

d e t a i l of the mixing chambers located a t each end of t h e t e s t s e c t i o n is shown i n Fig. A-1, Appendix A .

The electrodes connecting t h e t e s t section

with t h e power c i r c u i t serve a l s o as end p l a t e s of the disk-and-donut mixing chambers.

The power c i r c u i t t o t h e t e s t s e c t i o n i s shown i n Fig. 4.

The e l e c t r i c a l power t o the t e s t s e c t i o n i s supplied by a 440/25 v, 25 kva transformer and i s measured with a General E l e c t r i c watt transducer, a l s o shown i n Fig. 4.

The t e s t s e c t i o n is insulated with a 3-in.-thick layer

of vermiculite powder contained i n a sheet metal t r a y .

The s a l t reservoirs

and connecting tubes a r e heated by a u x i l i a r y clamshell and Calrod heaters placed i n positions indicated i n Fig. 1. A t y p i c a l t h e a t e r c i r c u i t f o r an a u x i l i a r y heater i s depicted i n Fig. 5 . The i n l e t and o u t l e t salt temperatures a r e measured by four, 40-mildiam, Chromel-Alumel sheathed thermocouples inserted i n t o two wells i n

each mixing chamber (Fig. Arl).

The temperature d i s t r i b u t i o n along the

t e s t s e c t i o n is measured by a s e r i e s of 24 Chromel-Alumel thermocouples (0.005-in.-diam

wire) spot welded a t 1-in. i n t e r v a l s t o t h e outside tube

The scheme f o r attaching these thermocouples i s shown i n Fig. A-2.

wall.

Details of a s a l t r e s e r v o i r can be seen i n Fig. A-3.

The i n t e r i o r

of these tanks as well as the t e s t s e c t i o n and t h e mixing chanibers a r e s t r e s s relieved and hydrogen f i r e d before they a r e assembled. A data a c q u i s i t i o n system provides f o r t h e a u t o m t i c monitoring of

t h e temperatures; record is mde ,by a paper printout and a paper tape punch.

I n t h i s system a multichannel Vidar data recorder reads emf

signals from each thermocouple, from the weigh c e l l s , and from t h e power c i r c u i t i n a sequential switching arrangement known as a "crossbar scanner."

The manufacturer claims a n accuracy of b e t t e r than +O.5"F

f o r the Vidar system.

The data recording equipment is shown schematically

i n Fig. 6 and i n a photograph i n Fig. 7. The weigh c e l l and wattmeter c a l i b r a t i o n curves and a l i s t of pert i n e n t experimental equipment may be found i n Appendix A as Fig. A-4, Fig. A-5,

and Table A-1,

respectively.

ORNL-DWG 72-ttstt

POTENTIAL TRANSFORMER

POWER TRANSFORMER

r-,-T-

7 PANELBOARO FRAME GROUND

.. SIGNAL TO VIDAR

WATTMETER TEST SECTION

FRAME GROUND

Fig. 4. Test-section power c i r c u i t f o r molten salt heat-transfer experiment.

. .-

. ORNL-DWG 72-1 4542 POWER CIRCUIT

145 V AC HOT

NEUTRAL

EVl= VOLTMETER EiI=AMMETER

o-'50v

EiI @O-IOA

RELAY

@-- -< :XF:MENT f I I

TEMPERATURE CONTROLLER

ORNL-DWG 72-14543

t T E REF. JUNCTION

VIDAR DIGITAL VOLTMETER

SEQUENTIAL

TAPE PUNCH

. 1

Fig. 6.

Thermocouple c i r c u i t f o r molten salt heat-transfer system.

Fig. 7.

Photograph of data recording equipment.

I n preparation f o r t h e addition of t h e molten salt mixtures, t h e system including t h e t e s t s e c t i o n is heated t o the desired temperature l e v e l above the melting point of the salt mixture.

Approximately 165 l b

of t h e molten s a l t is then introduced i n t o one of the reservoirs by t h e force of argon gas pressure.

Salt is forced back and f o r t h through t h e

t e s t s e c t i o n as t h e operation of the apparatus i s t e s t e d

- for

blockages, thermocouple and data recording functioning, e t c .

leaks,

After t h e

i n i t i a l checkout procedure, the system is put on a standby mode by venting t h e gas pressure t o the atmosphere and allowing the salt t o siphon t o equal l e v e l s i n both reservoirs.

The standby mode is used t o protect the

t e s t - s e c t i o n thermocouples by minimizing t h e heating of the t e s t section. Before each run, temperatures i n t h e t e s t section a r e r a i s e d t o about

lOOOOF over a period of 45 minutes and t h e salt flow is reestablished.

fixed flow r a t e is established and power t o t h e t e s t - s e c t i o n heater i s increased t o t h e desired heat f l u x .

s t a t e conditions, a l l parameters tures

- are

When t h e temperatures indicate steady-

- power

continuously recorded,

input, flow r a t e , and tempera-

The flow of salt i s reversed when one

reservoir i s nearly empty, and t h e heat f l u x i s momentarily reduced t o about half the operating value t o prevent a temperature excursion i n t h e t e s t s e c t i o n a t the time of zero flow.

The upper range of f l a w r a t e s i s

limited by t h e time required t o empty one of t h e reservoirs.

Whenever

the temperature exceeds the desired l e v e l , the system is allowed t o cool

by reducing the power t o t h e t e s t s e c t i o n and other appropriate heaters. Periodic c a l i b r a t i o n s of radial heat losses were made by measuring t h e power required t o m i n t a i n an empty t e s t s e c t i o n i n a n isothermal condition as a function of temperature l e v e l .

The information furnished

by t h i s c a l i b r a t i o n i s used i n each run, when a n isothermal check of t h e t e s t - s e c t i o n thermocouples i s obtained a t the desired temperature l e v e l

*This

hd I

procedure r e s u l t e d i n s e v e r a l s a l t leaks when a number of power f a i l u r e s occurred during the standby condition. Melting of t h e confined salt was invariably accompanied by rupture of t h e thin-walled tubing due t o the expansion of t h e s a l t upon p a r t i a l melting. A b e t t e r standby procedure would be t o d r a i n the salt i n t o one reservoir, allowing unrestrained expansion of the s a l t during melting if a n unexpected freeze should occur.

12 w i t h the hot salt flowing and only enough heat added t o t h e t e s t s e c t i o n

t o equal the radial heat loss.

I n Fig. 8, t y p i c a l t e s t - s e c t i o n thermo-

couple readings from a n i s o t h e r m 1 run show a scatter band of f4'F about the average outside w a l l temperature.

The sheathed thermocouples i n t h e

mixing chambers read s l i g h t l y higher during isothermal runs and a r e believed t o be more accurate.

Their readings, therefore, provide t h e basis

f o r standardization and t h e tube wall readings a r e corrected t o t h i s standard

Extensive t e s t s were conducted t o insure the r e l i a b i l i t y of the apparatus and experimental procedures.

The f i r s t t e s t - s e c t i o n tube pro-

duced e r r a t i c a x i a l temperature patterns which d i d not improve w i t h more thermal insulation of t h e t e s t section.

Subsequently, t h e anomalous a x i a l

temperature p r o f i l e s were traced t o the t e s t section, i n which a hole had burned through t h e w a l l and had been repaired by welding. Excessive weld material protruding i n t o t h e tube was thought t o have disturbed t h e temperature and velocity p r o f i l e s .

Replacement of t h e t e s t s e c t i o n eliminated

the difficulty. Other possible sources of e r r o r were investigated during t h e search f o r the cause of the temperature i r r e g u l a r i t i e s .

E l e c t r i c a l conduction

through the molten salt would r e s u l t i n a d d i t i o n a l heating of t h e salt, but t h e r a t i o of the r e s i s t i v i t y of the salt t o that of t h e t e s t s e c t i o n

is g r e a t e r than 2500, indicating very l i t t l e heat generated i n t h e s a l t i n t h i s manner.

Additional calculations of the radial temperature d i s t r i -

bution4 confirmed that not more than 0.2$ of t h e power was expended by e l e c t r i c a l conduction i n t h e s a l t . Temperature v a r i a t i o n s due t o f r e e convection a r e believed t o be l a r g e r than those a t t r i b u t a b l e t o i n t e r n a l heating; but according t o t h e c r i t e r i o n of Shannon and DePew,'

f r e e convection i n t h e horizontal t e s t -

section position is insignificant compared with forced convection i n t h e range of Reynolds numbers described i n t h i s work.

A s a n a d d i t i o n a l check of natural-convection e f f e c t s , t h e r e a c t o r f u e l salt experiments were repeated w i t h t h e t e s t s e c t i o n anchored i n a v e r t i c a l position while other equipment arrangements and operational procedures remained unchanged.

The object of the change was t o compare the

e f f e c t s of f r e e convection i n the v e r t i c a l and horizontal positions.

X, dietance

Fig.

Tube wall

thermocouple

from Inlet

readings

(in.)

during

isothermal

salt

flow.

DWG 6g-ncj28

14 crack developed i n one of t h e piping connections t o t h e t e s t s e c t i o n a f t e r 8 runs and repairs were not attempted.

However, t h e r e s u l t s of

t h e v e r t i c a l runs d i d not show any difference i n t h e e f f e c t of f r e e con-

vection as related t o the o r i e n t a t i o n of t h e t e s t section. presented l a t e r i n t h e report and i n Appendix B.

The data a r e

The p o s s i b i l i t y of heat conduction l o s s e s t o t h e electrodes a t t h e ends of t h e t e s t s e c t i o n prompted calculations t o be made based on the conservative assumptions of miximum heat f l u x and a minimum Reynolds number.

The r e s u l t s of these calculations show that t h e n e t heat con-

duction i n t h e a x i a l d i r e c t i o n is less than 0.1% of t h e t o t a l heat generated i n the t e s t s e c t i o n a t a distance of 0.25 i n . from t h e entrance. The e l e c t r i c a l r e s i s t i v i t y of t h e Hastelloy N t e s t - s e c t i o n tube v a r i e s less than 1% i n t h e temperature range of 1000 t o 1500Â°F and the heat capacity of the s a l t v a r i e s less than range.

54 over

t h e same temperature

The v a r i a t i o n of t h e radial heat l o s s along length of tube i s

l e s s than lo$ and t h e heat loss i t s e l f i s less than

54.

A constant a x i a l

voltage drop measured along t h e t e s t s e c t i o n v e r i f i e d t h e uniformity of t h e heat f l u x generated i n the t e s t - s e c t i o n w a l i and provided a check of t h e wall thickness and tube radius v a r i a t i o n as a function of i t s length. Experiments conducted with a well-known heat-transfer salt (â&#x201A;ŹITS)* provided a f i n a l t e s t i n t h e new t e s t s e c t i o n of t h e experimental procedure.

E a r l i e r experiments2 showed that HTS data a r e well correlated

by standard heat-transfer equations.

The experiments with HTS i n t h e

present system demonstrated that t h e outside w a l l temperatures remined p a r a l l e l t o the mean salt temperature over half of t h e t e s t - s e c t i o n length, indicating f i l l y developed flow and a constant heat-transfer c o e f f i c i e n t . I n 11 runs with HTS, t h e experimentally determined values of t h e heat-

transfer c o e f f i c i e n t were compared with those predicted by standard correlations.

Ten of t h e values of t h e heat-transfer c o e f f i c i e n t were

within 134 of that predicted by t h e Sieder-Tate correlation' value w a s within 254.

and t h e other

Before t h e system was charged w i t h r e a c t o r salts,

t h e â&#x201A;ŹITS was removed by extensively flushing w i t h water and drying i n heated vacuum f o r 10 days.

*HTS:

KNO, -NaNO,-NaNO,

(44-49-7 mole

4).

u t

15 CALCULATIONS t

The l o c a l coefficient of forced-convective heat t r a n s f e r i s defined

by t h e equation

where h = coefficient of heat t r a n s f e r , Btu/hr*ft2 OF; Q, a t p o s i t i o n x

along tube; q = heat-transfer r a t e t o f l u i d , Btu/hr;

A = heat-transfer (inner) surface area, f t 2 ;

t = temperature, OF; t m , f l u i d mixed mean a t any position; ts, inner surface of t h e tube a t any p o s i t i o n x; &, outer surface of t h e tube a t any position x. Beyond the thermal and hydrodynamic entrance regions, hX reaches an asymp,

For a constant heat flux, (q/A)x, t h i s l i m i t i n g value w i l l occur when (t t ) reaches a constant value.

t o t i c value.

m X

The inside tube wall temperature is r e l a t e d t o the measured outside tube wall temperature by the equation

where k = t h e r m 1 conductivity of f l u i d , Btu/hr.ft-OF; conductivity of tube;

G, thermal

L = t e s t - s e c t i o n length, f t ;

r = t e s t - s e c t i o n tube r a d i u s , f t ; rS, inner surface; rw, outer surface; t h i s i s t h e s o l u t i o n t o t h e one-dimensional steady-state heat conduction equation with a source term and a heat loss, qL, a t the outside w a l l ? The only variable on the right-hand s i d e of Eq. (2) i s t h e thermal cond u c t i v i t y of the metal wall,

temperature r i s e s along the tube.

which remains nearly constant over small Thus, when the temperature p r o f i l e s

tW and tm a r e p a r a l l e l , t h e f l u i d flow i n t h e tube is e s s e n t i a l l y f u l l y developed.

For most of t h e measurements, t h e heat gained by t h e f l u i d i n

traversing the t e s t section was calculated by t h e equation q=wC(t -t ) p m,o m,i

(3)

i n which = s p e c i f i c heat of f l u i d a t constant pressure, Btu/lb OF, cP w = mass flow rate, lb/hr,

and subscripts

= outlet

= inlet.

For t h e l a t e r measurements (Runs 210 through 220), t h e heat gained by the f l u i d was determined from t h e e l e c t r i c a l heat generation i n t h e t e s t section corrected f o r the calibrated heat loss.

By calculating t h e heat

input i n t h i s manner, t h e influence of t h e uncertainties i n measuring t h e f l u i d mixed-mean i n l e t and o u t l e t temperatures can be reduced. The computer program used f o r reducing t h e experimental data i s given

i n Appendix C. RESULTS

Heat-transfer coefficients were determined experimentally i n 70 runs covering the laminar, t r a n s i t i o n , and turbulent flow regimes.

Ten runs

w i t h HTS t o t e s t t h e equipment are included w i t h data shown i n Appendix B.

The physical properties and chemical analyses of t h e molten s a l t a r e l i s t e d i n Appendix D, Tables D-1 and D-2,

respectively.

The duration of a run usually permitted time f o r three thermocouple scans t o demonstrate thermal steady s t a t e .

Figure 9 shows t y p i c a l outside

w a l l temperatures and mean f l u i d temperatures.

A s t r a i g h t l i n e i s drawn

between t h e mean i n l e t and mean o u t l e t f l u i d temperatures by assuming cons t a n t physical properties of t h e molten s a l t and uniform heat t r a n s f e r over t h e inner surface of t h e t e s t - s e c t i o n w a l l .

These assumptions a r e

supported by the constant heat capacity of t h e molten s a l t i n t h e observed temperature range and t h e constant resistance of t h e Hastelloy N t e s t section mentioned e a r l i e r .

. *

.bd

ORNL-DWG 72-115t7

4300

t200

* *

lee

TUBE OUTER WALL FLUID

1100

R U N ' ~ ~ ~ , N=R5,9 7

to00 1600

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

5 w u

5It 500

RUN 157, N ~ ~ = 2 8 , 1 0 4 I

1400 1200

1400

tow

X, DISTANCE FROM INLET (in.)

Fig. 9. Axial temperature p r o f i l e s f o r molten salt flowing i n a smooth tube a t l a m i n a r (N = 597), turbulent (NRe = 28,104), and t r a n s i t i o n (N = 4277) Re

fEw.

18 Three regions of N Re a r e shown i n Fig. 9 - t h e l a m i n a r , t r a n s i t i o n , and turbulent a t NRe = 597, 4277, and 28,104, respectively. The co-

e f f i c i e n t of heat t r a n s f e r h assumes i t s l i m i t i n g value rapidly f o r X

turbulent flow; b u t i n laminar and t r a n s i t i o n flows, a s i g n i f i c a n t entrance region is evident. when h

This entrance region i s seen more c l e a r l y

is plotted versus t h e distance along t h e t e s t s e c t i o n x as i n

Fig. 10 f o r t h e t r a n s i t i o n flow run.

A f t e r the thermal and hydrodynamic

boundary layers become f i l l y developed, h

decreases t o a l i m i t i n g value.

The t e s t section i s not long enough f o r hx t o reach t h e l i m i t i n g value

i n laminar flow.

Therefore, integrated values of hx over the e n t i r e tube

length, coupled w i t h t h e parameter D/L, are used i n developing t h e l a m -

inar flow correlations; whereas, t h e l i m i t i n g constant h values are used f o r t h e t r a n s i t i o n and turbulent heat-transfer correlations. Standard heat-transfer correlations f o r t h e three flow regimes a r e given i n t h e following discussion of Eqs. (4) through (8).

Heat-transfer

data from t h e 70 runs are then presented i n t h e dimensionless forms of

standard correlations f o r comparison using t h e data l i s t e d i n Appendix B and t h e physical properties i n Table D-1. 1.

For l a m i n a r , forced flow i n t h e absence of n a t u r a l convection,

t h e equations of Sieder and T a t @ and Martinelli and Boelter’ are, respectively:

and NNU = 1.62 CNRe Npr

(D/L)]”

For t r a n s i t i o n region flow beyond t h e entrance region, a modified

form of Hausen equation2 is:

3. For turbulent flow, t h e equations recommended i n Ref. 9 and a t t r i b u t e d t o McAdams and t o Sieder and Tate a r e respectively: 0.8

N~~ = 0.023 N~~

0.8

NNu = 0.027 NRe

0.4

NFY

’

$-”(p/pS)’*l4

(7) f

10 x, distance

Fig.

10.

Axial

variation

15 from inlet

of the heat-transfer

(In.)

coefficient

(NRe = 4277).

where "u

= Nusselt modulus, hD/k, dimensionless,

= Prandtl modulus, C pfk, dimensionless, NPr P %e = Reynolds modulus, pVD/p, dimens ionless,

and V

= mean v e l o c i t y of f l u i d , f t / h r ,

= inside diameter of tube, f t ,

= f l u i d density evaluated a t f l u i d mixed-mean temperature, lb/ft3,

= f l u i d v i s c o s i t y evaluated a t f l u i d mixed-mean temperature, l b / h r * f t ; ps, evaluated a t temperature of the inner surface of

the tube. Equations (4),

(6), and (8)

a r e compared with t h e experimental data

i n Fig. 11. The experimental r e s u l t s a r e i n good agreement i n t h e laminar region but a r e s l i g h t l y below the equations representing t h e t r a n s i t i o n For example, i n t h e range 3500 < N < 30,000, t h e Re data l i e about 13%below Eqs. (6) and (8). The heat-transfer data could

and turbulent regions.

not be correlated i n the t r a n s i t i o n range 2000 < N < 4000because of Re entrance e f f e c t s t h a t p e r s i s t e d over t h e length of t h e t e s t section. The l a m i n a r data do not fit Eq. ( 5 ) as well as Eq. (4),

as shown by comparing

Figs. 12 and 11. Similarly, Eq. (7) provides no s i g n i f i c a n t improvement i n the c o r r e l a t i o n of t h e data f o r NRe > 10,000 over that of Eq. (8) [compare Figs. 13 and 113. The data plotted i n Figs. 11 through 13 suggest t h a t t h e experimental data f o r laminar and turbulent flow can be f i t t e d t o Functions of t h e

form: Ordinate =

n NRe

(9)

where K and n a r e dimensionless constants having d i f f e r e n t values f o r

l a m i n a r and turbulent flows and t h e "ordinate" i s t h e ordinate used i n Fig. 11. Least-squares f i t s of t h e data t o t h e form of Eq. ( 9 ) were c a r r i e d out assuming a constant value (l/3) f o r the Prandtl modulus exponent.

These f i t s were t r i e d with and without a v i s c o s i t y r a t i o cor-

r e c t i o n term.

We found t h a t when t h e v i s c o s i t y r a t i o correction term

was included, t h e values f o r the Reynolds modulus exponent, n, came

c l o s e r t o the commonly accepted values of l / 3 f o r laminar flow and 0.8 f o r turbulent flow.

The r e s u l t i n g equations f i t t i n g the experimental

I ,

io3

to4

lo5

N R ~ REYNOLDS , MODULUS

Fig. 11. Comparisons of the molten s a l t data for E q s . ( b ) , ( 6 ) , and (8).

ORNL-OWG 12-11515

9 I IOZ

IO'

NRa,REYNOLDS MODULUS

Fig. 12.

Comparison of laminar flow data of molten s a l t with Eq. ( 5 ) .

ORNL- DWG 72- 1t516

z 0

W LL

z a U

fW 4

g,1

lo3

2 NRe

io5

REYNOLDS MODULUS

Fig. 13. Comparison of t r a n s i t i o n and turbulent data of molten s a l t w i t h Eq. (7).

data are

= 1.89 [NRe NPr

(D/L)]"'""

w i t h an average absolute deviation of

(P/P~)O'~*

6.6% f o r NR e

with a n average absolute deviation of 6.+

C 1000; and

f o r NRe > 12,000.

Because t h e data i n the t r a n s i t i o n region d i d not follow t h e form of Eq. ( g ) , t h e equation f o r t h e experimental data i n t h i s range of NRe 0

was obtained by adjusting t h e c o e f f i c i e n t i n Eq. ( 6 ) , giving t h e following

re l at ion: "u

= 0.107 ( q e 3

- 135) Npr

(P/Ps)0'14

with an average absolute deviation of 4.1$ f o r 3500 < NRe < 12,000. The heat-transfer measurements mde with t h e t e s t s e c t i o n oriented i n

a v e r t i c a l p o s i t i o n t o t e s t f o r t h e possible e f f e c t s of f r e e convection are i n good agreement w i t h t h e standard c o r r e l a t i o n s , except f o r four higher points (see Figs. 11 and 1 3 ) .

These higher points were obtained

with downflow i n contradiction t o t h e predicted enhancement of heat transf e r w i t h upflow.

Thus, a s y s t e m t i c thermocouple e r r o r i n one of t h e

mixing chanibers i s t h e most probable cause of t h e higher r e s u l t s w i t h downflow. DISCUSSION The r e s u l t s indicate that t h e prQposed r e a c t o r f u e l salt behaves as

a normal f l u i d i n t h e range 0.5 C N < 100 with regard t o heat t r a n s f e r . Pr It should be noted t h a t u n c e r t a i n t i e s i n t h e physical properties of t h e

salts r e f l e c t as g r e a t an e f f e c t on t h e c o r r e l a t i o n s as does t h e unc e r t a i n t y i n t h e heat-transfer c o e f f i c i e n t . Our data l i e below t h e standard c o r r e l a t i o n s i n t h e turbulent and t r a n s i t i o n regions but not i n t h e laminar region.

If t h e deviations i n

our d a t a were caused by low-conductance surface films or entrained gas, one would expect t h e e f f e c t t o be apparent i n a l l t h r e e regions.

An un-

c e r t a i n t y i n t h e v i s c o s i t y of t h e salt might explain the.discrepancies i n

25 t h e turbulent and t h e t r a n s i t i o n regions since t h e heat-transfer function i n t h e l a m i n a r region i s almost independent of t h e viscosity.

I n addition,

t h e lower values i n t h e t r a n s i t i o n regime could be t h e r e s u l t of t h e f a i l u r e

of t h e t h e r m 1 boundary layer t o f u l l y develop over t h e length of t h e t e s t s e c t ion. The problem of boundary-layer development i s most pronounced i n the

N < 4000, where entrance e f f e c t s Re persisted f o r t h e e n t i r e length of the t e s t section. The same e f f e c t

range of Reynolds number 2000

could be produced up t o NRe = 5000 a t higher w a l l heat fluxes.

Figure 1 4 i l l u s t r a t e s t h e apparent effect of heat flux on t h e entrance region length.

A t NRe = 3762 and a w a l l heat f l u x of 2.55 X 10'

Btu/hr.ft2,

there i s no

region of constant heat-transfer coefficient.

I n contrast, temperature p r o f i l e s a t a s i m i l a r Reynolds number, NRe = 3565 and t h e lower w a l l heat f l u x of 0.74 X

lo6

Btu/hr*ft2 show a constant heat-transfer coefficient

over most of t h e t e s t - s e c t i o n length.

Since the v i s c o s i t y of t h e f l u i d

decreases w i t h increasing temperature, heat t r a n s f e r from the tube w a l l m y be exerting a s t a b i l i z i n g e f f e c t on t h e l a m i n a r boundary layer, 9.10 thus delaying t r a n s i t i o n . Future experiments with t h e f u e l s a l t should include system modif i c a t i o n s so that t h e entrance region e f f e c t s i n t r a n s i t i o n flow can be better evaluated.

Possible modifications would be t h e i n s e r t i o n of a n

unheated calming s e c t i o n p r i o r t o heat addition t o permit establishment of t h e hydrodynamic boundary layer before changing t h e temperature profile.

This would separate t h e two e f f e c t s t h a t now occur simultaneously.

Another p o s s i b i l i t y would be t o increase t h e length of' t h e t e s t s e c t i o n while m i n t a i n i n g a constant heat f l u x along the length.

A sufficiently long tube might allow f u l l y developed flow patterns t o be reached before

the test-section exit.

LJ ORNL-DWG 72-11 519

I500

1400 TUBE OUTER WALL I FLUID 0

1 300

a 1200 a a w

NRe=3762,q/A=2.55X405 Btu/hr.ft 2

z W

I-

itoo

1200

t too

I I

h e- 3 5 6 5 , q/A=0.74Xt05 Btu/hr.ft2

io00

X, DISTANCE FROM INLET (in.]

Fig. 14. Comparison of axial temperature p r o f i l e s of t h e molten s a l t a t similar NRe with heat f l u x varied by a f a c t o r of 3.5.

CONCLUSIONS We have found molten f l u o r i d e salt mixtures t o behave, f o r t h e most p a r t , as normal f l u i d s w i t h respect t o forced-convection heating i n a smooth tube.

Although t h e present r e s u l t s average -13% below t h e standard

l i t e r a t u r e heat-transfer correlations, one must r e a l i z e t h a t some unc e r t a i n t i e s e x i s t i n the physical properties of t h e s a l t and t h a t t h e standard c o r r e l a t i o n s themselves are based on heat-transfer data using f l u i d s such as air, steam, water, petroleum, etcb, which e x h i b i t a &20$ s c a t t e r band around t h e standard curves. No evidence of t h e existence or influence of low-conductance surface films, such as corrosion products, gases, or oxides, was found i n t h e

present s t u d i e s .

I n t h e Reynolds modulus range from 2000 t o 5000, w e did

f i n d t h e heat-transfer c o e f f i c i e n t t o vary along t h e length of t h e tube i n a mnner which appeared related t o a delay i n t h e t r a n s i t i o n t o t u r bulent flow. *

We believe t h i s delay i n t r a n s i t i o n is abetted by t h e

s t a b i l i z i n g influence of heating a f l u i d whose v i s c o s i t y has a l a r g e negative temperature c o e f f i c i e n t .

We intend t o make f u r t h e r s t u d i e s of

t h i s phenomenon.

ACKNOWLEDGMENTS The design, construction, and operation of these experiments w e r e

mde possible by t h e a b l e a s s i s t a n c e of J. J. Keyes, Jr., H. W. Hoffman,

R . L. Miller, J. W. Krewson, W. A . B i r d , and L. G. Alexander.

REFERENCES

H. W. Hoffman, Turbulent Forced-Convection Heat Transfer i n Circular Tubes Containing Molten Sodium Hydroxide, USAEC Report ORNL-1370, Oak Ridge National Laboratory, October 1952; see a l s o Proceedings of t h e 1953 Heat Transfer and Fluid Mechanics I n s t i t u t e , m d University Press, Stanford, California, 1953.

H. W. Hoffman and S. I. Cohen, Fused Salt Heat Transfer - P a r t 111: Forced-Convection Heat Transfer i n Circular Tubes Containing t h e Salt Mixture NaNOz-NaN03-KN03, USAEC Report ORNL-2433, Oak Ridge National Laboratory, k r c h 1960.

H. W. Hoffman and J. Lones, Fused S a l t Heat Transfer - Part 11: Forced-Convection Heat Transfer i n Circular Tubes Containing NaK-XI?-LiF Eutectic, USAEC Report ORNL-1777, Oak Ridge National Laboratory, February 1955.

H. F. Poppendiek and L. D. Palmer, Application of Temperature Solut i o n s f o r Forced-Convection Systems with Volume Heat Sources t o General Convection Problems, USAEC Report ORNL-1933, Oak Ridge National Laboratory, September 1955.

R. L. Shannon and C. A . DePew, Forced Laminar Flow Convection i n a Horizontal Tube with Variable Viscosity and Free-Convection Effects, ASME Technical Paper 68-w/m-20.

6. E. N. Sieder and G. E. Tate, Heat Transfer and Pressure Drops of Liquids i n Tubes, Ind. Eng. Chem. 28(12): 1429-1435 (1936).

P. F. Massier, A Forced-Convection and Nuclear-Boiling Heat-Transfer Test Apparatus, JPL-TR-32-47, J e t Propulsion Laboratory, &%arch 3, 1961.

E. R. G. Eckert, A . J. Diaguila, and A . N. Curren, Experiments on

Mixed-Free-and-Forced-Convective Heat Transfer Connected with Turbulent Flow Through a Short Tube, NACA TN-2974, National Advisory Committee f o r Aeronautics, July 1953.

W. M. Rohsenow and H. Y. Choi, Heat, Ivhss, and Momentum Transfer, Prentice-Hall, Englewood C l i f f s , New Jersey, 1961.

10. H. Schlichting, Boundary Layer Theory, 4th ed., McGraw-Hill, New York, 1960.

11. A. R. Wazzan, The S t a b i l i t y of Incompressible F l a t P l a t e Laminar Boundary Layer i n Water with Temperature Dependent Viscosity, pp. 184-202- i n Proceedings of the Sixth Southeastern Seminar- on Thermal Sciences, Raleigh, North Carolina, April 13-14, 1970. 12.

S. Cantor, ed., Physical Properties of Molten-Salt Reactor Fuel, Coolant, and Flush S a l t s , USAEC Report O R N L - T M - ~ ~ ~Oak ~ , Ridge National Laboratory, August 1968.

J. W. Cooke, Thermophysical Properties, pp. 89-93 i n MSRE Semiann. Progr. Rept. Aug. 31, 1969, USAM: Report Om-4449, Oak Ridge National Laboratory.

APPENDIX A ADDITIONAL DFPAILS OF THE EXPERl3LEWXAL SYSTEM

~~~

.... .". .....

. .

".. ..

...

....

.,.

0 R N L- DWG 72-11522

LAVITE WEDGE TO HOLD THERMOCOUPLES AGAl NST WALL

0.040 in. CHROMEL-ALUMEL STAINLESS STEEL SHEATH THERMOCOUPLE

f in. SCH. 40 P I P E

'/4 x

8 HOLES 5/32in.DlAM EQUALLY SPACED ON '346 in. DIAM CIRCLE

0.035 in. TUBES,

in DlAM HOLE

SECTION A-A

Fig. A-1.

Mixing chamber weldment.

. - ..

._.

l_."l_I._.

_ _ _ . l . l l

ORNL-DWG 72-11524

HCERAMIC FIBER INSULATION SLEEVE

36 GA. C. A. B A R E WIRE SPOT WELDED T O TH TEST SECT10

F i g . A-2.

T E S T SECTION

Scheme for the attachment of a test-section thermocouple.

ORWL-OW6 72-1%523

v2 I 0.042 in. DIP LEG TUBE

f l % x0.035 in. THERMOCOUPLE WELL TUBE \

\ \

Fig. A-3.

Detail of a Salt reservoir.

ORNL- DWG 72- 11521

'ii 70 @

80 70

& 4 50 0

60 0 INCREASING WEIGHT . DECREASING WEIGHT

40 30 STANDARD WEIGHT (pounds)

Fig. A-4.

Weigh cell calibration

curve.

w F

ORNL-DWG 72-44520

800

600

e 0

-400

200 c

60 SIGNAL ( millivolts)

Fig. A-5.

Wattmeter calibration curve.

400

36 PERTINENT EXPERIBENTAL EQUIPMENT

Equipment

Capacity or Range

Load Cells BLH electronics Type T3Pl and T3P2B

S t r i p Recorder Honeywell Model BY1532W- (W") - ( I V ) A l (modified)

500 lb ( 1 5 6 overload) 3 mv/v input

+o.o+

L-2 Special

+_0.25$ f u l l s c a l e

Current Transformer Nothelfer windings Labs, Incorporated Model 14388

25 kva (prim. & s e c . ) 48 v prim. 4 x 250 amp sec

D i g i t a l Voltmeter Vidar Model 521

+_lomv t o flOOO v i n 6 decade stages

System Coupler Vidar Model 650-12

Accuracy

full s c a l e (see Fig. A-4)

+o.o~$ of

f u l l scale ( l e a s t count 1.0 pv)

Scanner Cunningham Scannex Control Model O O O l l 3 G Tape D i g i t a l P r i n t e r Franklin Electronics, Inc

Tape Punch Process Tally Corporation Model 1665 Tape Drive Model Pl5O Tape Reader Model 1848 Wattmeter General E l e c t r i c Type 4701 Watt Transducer Thermocouple Reference Junction Cornpensator Universal Compensator Model RJ4801-CS

2.5 - 10.0 i n 2.5 s t e p s

(see Fig. A-5)

fO 75%

6d c

Table B-1. Experimental Data f o r Heat-Transfer Studies Using t h e Salt LiF-BeFo-ThF4-UF4; 67.5-20.0-12.0-0.5 mole $

Run No.

Tin ( OF)

Tout (OF)

6T (OF)

(lb/hr)

1388.3 1362.7 1383 7 1379.1 1418.0

1436.0 1415.8 1438.4 1436.6 1474.4

47.7 53.1 54.7 57.5 56.4

2532.0

1456.2 1488.2 1097 9 1082.7 1081.5

1507 9 1537.8 1156.4 1163.3 1177.1

51.7 49.6 58-5 80.6 95.6

1089.8 logo. 6 1029.6 1036.3 1062.8

1159.9 1160.2 1118.7 1134.8 1117.7

70.1 69.6 89.1

1075.4 1048.2 1064.0 1076. g 1093 5

1135.7

1460.4 1460.6 1469.4 1477.0 1486.7

1482.9 1489.5 1488.4 1501.8 1513.4

1103.4 1115. g 1131.o

1148.3

1387.2 1807.2 1185.0 2191.2

4/A

(Btu/hr*fta x 10-6)

4.07 2.48 3.33

Heat Balancea 1.05

1.12

("q

NPr

15,993 8,345 11,419 7,495 14,917

6.3 6.6 6.3 6.3 5*8

106.1 61.5 78.6

21,647 25,119 738 839

5.5 5.1 13.1 13.5 13.3

134.6 140.4 42.1 8.6

407 381. 357 358 1940

673 760 550 405 4,940

13.5 13.4 15.9 15.3 14.5

8.8 8.3 7.7 7.8 42.2

2200

5,523 5,304 6,026 6,573 7,583

13.8

47.8 46.3 54.7

4882 2831 3617

1.01 1.05

2302

4.16

1.04

4590

2968.2 3206.4 1636.8 250.8 279.6

5-17 5.36 3.23 0.68

1.04 1.00 1.05

6192 6462 1936 396 427

0.54 0.60 0.66

54.9

227.4 256.2 221.4 155.4 1785.o

60.3 55 - 2 51.9 54.1 54.8

1910.8 2007.6 2199.6 2307.6 2506.8

3.87 3.73 3 -85 4.20 4.63

1.04 1.04 1.Ob 1.04 1.03

2129 2513 2727 3068

22.5

1166.4 1700.4 2093.4 2458.2 2784.6

0.89 1.66 l.34

0.94

2230

1.03

3434 3977 4573 5426

98.5

28.9 19.0 24.8 26.7

0.90

0.52

3-30

2.05 2.51

1.02

0.97

0-93 0.93 1.04

1.01 1.oo

1.09

b %t

h e f t *OF)

2.30

f.O1 1 .oo

5,005

8,393 12,260 15,282 18,300 21,235

15.0

14.6 14.0 13.2

5-6 5.5 5.5 5*4 5.6

50.0

99.8

9.2

56.000 3 1 902 41.497 26.270 54.082 74.415 79 762 16-713 3 359 3.563 3.488 3 265 2.821 2.944 16.148 9

66.7

18.56? 17.459 20.984 23.072 26.549

48.5 74.7 86.4 99.5 117 9

27.007 41.743 48.472 56.022 65.520

59.2

w v)

.. .

. .

. - .-

.. .

Table €3-1 (Continued)

Run

Tin

(OF)

(lb/hr)

Tout

NO. (OF)

q/A

Balancea

h r@tu/ o f t *OF)

NPr

Heat

(Btu/hr*ft' x io+)

154 155 156 157 158

1496.1 1466.3 1475.0 1479-7 1466.3

1523 3 1484.7 1488.2 1502.7 1483.8

27.2 18.4 13.2 23.0 17.5

3057 0 3205.2 3262.2 3505 8 1282.2

2.80 1.99 1.45 2.72 0.76

1.04 1.02 0.99 1.07 0.89

5740 5551 5229 6627 2236

23,719 23,214 23,861 26,192 9,284

5.1

159 160 161 162 163

1466.7 1471.3 1472.4 1463.7 1470.0

1492.6 1492.2 1494.4 1522.0 1527 5

25.9 20.9 22.0

1401.6 1512.0 1615.2 1254.6 1425.6

1.22 1.06 1.20 2.46 2.76

0.99 0.93 0.99 1.04 1.05

2708 2741 3033 2675 3071

10,171 11,107 11,853

5-5 5.5 5.5 5 -2 5 92

1480.0 1486.9 1501.6 1513 9 1064.6

1535.8 1539.2 1546.2 1561.7 1080.1

55.8

2.85 3-71 4.21

3334 4385

11 770 16,497 22,512 28,499 4,524

5 01 5 01

0.9

1.07 1.02 1.06 1.02 0-97

72.5

44.6 47.8

1513.8 2135.4 2803.2 3471.0 1797 0

1066.3 1069.8 1049.0 1061.6 1062.o

1082.2 1084.0 1081.2 1076.2 1078.5

15.9 14.2 32.2 14.6

16.5

2346.0 2722.8 202.2 1597.8 1318.2

1.26 1.31 0.22 0.79 0.74

1.01 1.05 0.9 0.9 0.94

2340 2905 320 1445 1041

5 ,938 6,939 493 3,986

1064.6 1235e2 1247.0 1255.8 1273.2

1080.3 1262.7 1270.6 1296.0 1294.4

15.7 27.5 23.7 40.2 21.2

1460.4 1106.4 2333 4 3001.8 3219.6

0.77 1.03 1.86 4.07 2.30

0.99 1.01 1.04 1.04 1.09

1337 1591 3560

58.3 57.5 52.3

15.5

5.60

5852

6892 1737

4645

4752

9,464 10,884

5.5 5.5 5.4 5.5

-b NSt

71 557

124.8 120.7 113.7 144.1

67.668 63.927

48.6

81.181 27.265

58.9 59.6

32.943

66.0 58.2

36.980 32.754 37 571

66.7 95.3

5 00 127.2 4.9 149.8 15.9 37.7

33 394

41.151 54.119 72.942

86.348 14.620

50.9 63.2 7.0 31.4 22.6

19.818 24.811 2.671 12.161

3,322

15.7 15.6 16.3 16.0 15.9

3,690

15 -7

29.0

4,731 10,200 13,693 14,944

9.3

11.274 16.075

9-1

34.6 77.4

8.7 8.6

101.0 103.3

-!= 0

8.713

36.39 47.638 49.533

. .

.. ... .

.. . . . . ...

....

. ~ .... ..

.. . .

..I.

_____ . _ _ ,._I__.I. "

....-...----I.

Table B-1 (Continued)

Tin ( OF)

Tout

200 201' 202' 203' 204'

1279.6 1237.8 1250.7 1252.2 1258.4

1303.7 1263.8 1272.6 1276.2 1282.4

205' 206' 207C 208c

1229.9 1231.7 1243.6 1247;2

210 211 212 213 214 215 216

Run

No.

Heat

9/A

NPr

(Btu/hr*fta

24.1 26.0 21.9 24.0 24.0

3392.4 1351.2 1717.8 2050.2 2299.2

2.76 1.18 I. .27 1.66 1.86

1.07 1.07 1.01 1.16 0.99

5050 2406 2762 4029 3625

16,088.0 7,660.9 9,200.0 10,435.5

8.94 8.89 8-79

1255.0 1255.4 1268.1 1270.6

25.0 23.7 24.5 23.4

1395.0 1704.0 2036.4 2338.8

1.18 1.36 1.68 1.84

1.01 1.10 0.97 1.12

2119 3004 3122

5,910.9 7,238.9

9.41

46-1

9-39

8,947.4

4337

10,359.7

65.3 67.9 94.2

1132.4 1168.4 1203.4 1138.1

1156.1 1215.4 1226.7 1168.7

70.1 150.8

1.69

1.01 1.01 1.03 1 .Ob

2416 3049 2823

6,512

30.6

2110 2105 2102 2654

3477

8,566

1149.6 1256.1 1276.2 1310.6

51.7 8.0 18.0 30.1

2807 2887 2914 2791

4.92

1.01 0.97 1.03 1.05

3573 4335 4490

8,297 12,374 12,957 13,454

13.3 9.2

217

1097.9 1248.1 1258.3 1280.6

218 219 220

1288.1 1293.8 1118.5

1341.7 1383.2 1155 7

53.6 89.4

2753 1593 1140

5 -03

1.03 1.03 1.02

4915 2999 1082

(OF)

59.9

136.1

3.38 1.69 2.76 0.79 1-77 2.85 5.04 1.51

a Heat balance = (sensible heat gained by f l u i d %ist = C

aIsu (WP r

(p/ps).-0*l4

Test s e c t i o n oriented v e r t i c a l l y .

(BtUl h r - f t *OF)

(lb/hr)

(OF)

Balance

4616

5,892.4

7,696 8,230

8.4 9.14

9-08 9-00 12.5 10.8 10.2 12 ;2

109.8 52.3 60.0

87.6 78.8

52.5

66.3 61.4

75 -6 77.7

-b

*st 53.017 24.7 28.6 41.9

37.7 21.5 30.7 32.1

44.9 22.15 28.96 27 89 32-07

31 -27

8.8

97.6

44.98 46.89

8.2

100.3

49.10

14,035 8,620

7.7 7.3

3,554

12.8

106.9 65.2 23.5

52 56 32.12 9.60

heat l o s s ) / ( e l e c t r i c a l heat generation).

94.2

mble B-2. Experimental Data for Heat-Transfer Studies Using the Salt Hitec (KNO, -NaN08-NaNG ; 44-49-7mole $) Run No.

(OF)

(lb/hr)

537.6 540.8 567.5

677.3 591.3 621.0

139.7 50.5 53.4

157.2 1375.2 2071.8

0.85 2.69 4.30

96 97 98 gg

574.8 601.4 698.4 618.5

624.3 650.7 658.5 672.5

49.5 49.3

4.21 3.04

54.0

2195.4 1589.4 1097.4 630.6

101 102 103

608.8 633.1 618.8 582.2

702.4 657.2 634.8 669.1

93.6 24.1 16.1 86.9

592.8 640.2 1551.6 1603.8

104

Tin

Tout

(OF)

50.1

d A (Btu/b:bta x 10 1

2.13 1.32 2.15

0.60 0.97 5.41

aHeat balance = (sensible heat gained by fluid

Heat Balancea

% 11.3 10.2

0.99 1.05 0.9

283 5 24%. 4 3516.6

2,314 15,450 25,640

1.08

4450.9 3045.6 2473.8 1386.4

27,578 21,716 15,349 9,165

1332.4 1656.8 4151.9 3096.6

9,065 9,142 20,848 22,357

1.00 1.06 1.03 1.10

0.99 1.05 0.99

heat loss)/(electrical heat generation).

9.3

10.1

9.3 9.1 8.7

17.0 150.0 211.0

267.1 182.7 148.4 83.2

ijst 7.34 64.3 93.1 119.7 84.2 69.3 39.2

8-3 79-9 37.6 8.9 99.4 47.7 9.4 249.1 117.6 84.1 9.1 185.8

APPENDIX C COMPUTE3 PROGRAM

ISN C078 ISN 0679 ISN 0080

GO TO 420

D l 11 11 576.+ 11110.-1576. )/l36.0O-33.001*l D l Il-33.03)l I F lDlIl.GE.1635.. LNO.D(Il.LE.16l9.l D l I l = 0 1 II+Oo.4

408

7944 7988 79080 79801 79cc

19cc1

ISN 0090 ISN 0 0 9 1 -II.S--M

0092

ISN OC93 ISN .O.C94 ISN 0 0 9 5 ISN 0096 ISN 0 0 9 1

IJN. acoa194 0 0 9 9 ISN 0100 ISN 0101 ISN 0102 ISN 0103

U R QlOf

ISN 010s ISN 0106 ISN 0107

2 3 FiIRHATilH DO 2 5 1=1 - _. - J=D! PRIN 24 FORM 25 C ON1'I Dl4ll-DUl 4 014 2 I =DU( -. FTC=OUJ+I C TC =DU I 4 2 UYAVG=AVG C4LL TKEA PRINT 51 5 1 F'3RMAT lH1 r4Xr9HSUBSCPI PT 16X16HU CATL*9Xr6HC CAT4 1 -Q0.38.-ll~.N . PRINT 52.i.W-II i.ctri FCRYA 111 X r I 3 9 OX rF e.2rOX 9 FO.2 I 52 58 C ON11 hUE C COhSTANTS FOLLCW. THE THERMAL K ' S #RE TEPP CCPENDENT

___

R1=.180/2.

R4 K1 K1

.. ..

ISN 0112

ISN 0113 ISN 011.4

ISN 0115 ISN 0116 ISN 0117 ISN 0118 ISN 0119

I sN_-0 !?!O _. ISN 0 ! I 194 0 ! 2 ISN 0 13 ISN 0 .I !4 L 9 - 0 13... . . ISN 0 11!6 ISN 0 12 .2! 7

ISN

ISN 0 12 ISN a

1SK.Q ISY 0

1 9a 1SN 0

aoE

81a 818 100

101 110 120 132 133

134 135 136 137 139

140 141 1SO 160 110 180 190

ISN O l l l

79CCZ 79cc3 7900 80 804 b0a1 808 80c 80d

20t 210 220 2 30

n= L.

SP DA ole-0.5 TSNO-OFC G N S T A N ~ S xLIll=.750

..-

XLlI)=XLlwl+DX 60 CONTI hUE T4D=lO (271 +Dl281 112. 141 = I D ( 2 9 ) + D l 3 0 1 I 12. T 8 8 I = ( O l 3 1 l + D l 3 2 l ) 12. 1860~~0~331~0134~l12~ IFlTAO.GT.TAIlG0 TC 61 T I =TAX G J TO 62 6 1 74=TAO

236 240 2 50 255 260 270 280 285 2 90 390 305 310 315 320 325 330

335 340

SN G 13 6

5h 613’b

ILSN 0 13 9

1‘SN 0 14 0 1 SN 9 14 1 1 SN 0 14 2 1ISN- _O 14 -3 i SN 0I4 4 IISN 0 14 5 IiSN 0 14*6 1ISN 0 14 1 IISN 0 I 4* 8 119! -014 i1SN 0 i3 1 11 9 4 0 151 1ISN 0 1,512 IISN 0 1,513 1ISN 0 151 4

...

.- -

iiut=iae

63 TO 70 5 8 TIN-TFB lDUT=TA 7 0 CONTINM . I F ITA-T.B81 .73 r?l.r71 7 1 ’ 6 0 12 I = l * 2 4 WZ5-I TO11 l=ClMl 72 CONTINCE G(1 TO 80 73-00 15 J = l p 2 4

!sn 0152.

ISN 0 1 5 6 ISN 0 1 5 7 ISN 0158

6 2 IFlTBBO.GT.TB8Il 6(! T J 6 3 TB b it~e1 G 1 TO 64 6 3 199=Tf180 6 4 C3NTINM I F IT4-188l66r68r68 6 6 lIN=T4

475 480 490 500

. .

TO~II=C(Il 75 CONTINCE 8C CONTINLE C CARE YUST bE TLKEN klTH REGARD TO SIGN CCLVENTION FOR FOLL’WIING 0 AN0 0 1 QWM=400. /03.6*0 ~41)*200.*3.412/0149~

ISN 0159

345 350 355 3 60 365 390 400 410 420 53c 440 450 460 470

510 520 530 540 550 560 510 5 75 576

577

oid5

ISN

OtL=K4*.315*17.

ISN 0169

ISM 0170 1% 0 1 7 1 1.sn-o17r-. ISN 0113 1% 0174 ISN 0175 -

ISN 0118

ISN 0119 ISM 0180 ISN 0 1 8 1 ISN 0182

s = % O T * SPH1*ITOUT-1 I N I OODP= OF /12. * 3 . 1 4 * ~ 1 * L l * i 4 4 . OBAL=I9F-OlCLLI /OW* - - _ x i ~ . ~ e - -. . . . . X l = X l - e250 X2=F TC +C TC-1 X2 =X 2- 2 50 110 PRINT 111 111 F JRMAT I l H l r 0 9 X r l H X r l l Xr3HXIDr 10x11HH r l l X r ZHTBr 1 l X rZHTIrllXr2HTO r l 2 X v2HNtJr 1 1 X r 2rR €9 12X r2HPR I - -.- 8

18-o n & . ISW 0 1 1 7

I O . /12. 01 IO 143l-OI25l I /OXL+lD(44i -01 26 I l / b x B l

112

0184 0185 0186 018s 0189 0190 0191

660 7 10 720 730 140 810 823 821 a30 840 841 e45

a so

851 852 862 863

IS?+ 0183 ISN I!% ISN 1% ISN ISN 194

578 580

585 590 610 640 650

064

XOO-X/ 12.*RlI TB 11 ) = T I N t QoCP*3 ~ 1 4 * 2 ~ * R l * X / ~ O C T / S P H 1 / 1 4 4 ~ H I I I *OtOP/ I T I I I 1-1 e t I I I C4LL PPCP(AEh0rPRNCrIvu rRHOrTB( I I r R l r CCkOr SPHlt MOOT I

865 870 e 80 890 895

ISM 0 1 9 2ISN 0 1 9 3 ISN 0 1 9 4

. 114

115

ISN 0195 ISN 0196 I S N 0191

I.SY-0 198I ISN 0199I I s N ornoI

450

I S N 0201 ISN 0202 ISN 0203I

451

1sN-Bzb4 I S Y 0205 1% ape1

452

NUN011 l = H l I )*2.*Pl /12./CCNO PRINT 114rX r X O O * H I I l * T I 1 I I 9 1 1 I 1I ;TO1 I l r NUN01 1 lrREYO*PPNO FORMAT (1HO19F13.4) CONTINLE HA VGOA VG I H rFTC r CTC 9 x 1 X2 1 PRINT 450rHAVG F 3 R M A T I l H 3 ? ~ A V GH BTU/HRSOFTOEGF 0 rClO.2) M4VGdVGf T ~ ~ F T C ~ C T C I9x21 X~ PRINT 4 5 1 9 LAVG FORMkTl1HO~'AVG INhER MALL TEMP DLGF 0 'rF10.3) B A V G ~ A V G I T B ~ F T~CTCIXI C rX2) PRlNT 452nPAVG FORMAl11.HO~8.AVC RULK TEPP OEGF = 'rF10.31 04VGoA VG I TO*FTC *CTC*Xl 9x2 1 PRINT 4 5 3 * C A S FORMATllHO~*AVG OUTER MALL TEMP DLGF 0 *rF10.31 NUAVGoAVCI kLNOrFTt tCTC 9 x 1 r X 2 j PR 1 NT 4 5 4 hUAVG

1SN 0 2 0 7 ISN 0208I 1SN OM91

453

897 900 910 920 930 935 940 950 955 960 970 975 900 5 9c 995

low

1005

1010 1015 1017

ioin 1019

1020a 102OB

102993 l020B2

1020c 10200

1020E 1020F

10z0t

1020J .

I S N 0228 ISN. 0 2 2 9

ISN 0230 ISN 0 2 3 1 ISN 0232 ISN 0233 I S N 0234 I S N 0235 1% 0 2 3 6 ISN 0237 I S N 0240

1020J3 102OJ4 102055 1020Ll 102012 1020L3

P R 1 N l 97.G

. PRINT 99rRHO 9 9 FqRMAT 11HOv'BULK PRINT l001PU 100 FORMAT IlHC*.BULK

SALT OENSITV L f V F T 3 SALT VISCOSITV LBlHPFT

- _----.-..!w_N~--~@1 *corn, -

. *rT35rFlb.Zl

101 FORMAT IlHOv'BULK SALT CCNO BTU/HRFTDEt%F PRINT 4 7 2 e T I N 4 7 2 F O R M A T l l H O ~ * I N L E TTEPP OEGF 'r135rF10.31 PRINT 473rTOUT 473 FORMATllH0~'OUfLET TEMP DEGF 0 '.T35.F10~31

1060 'rT35rF10.3l

1065

1080 1090

.._.

T35*F10.5)

1110 1120 1130 1140

A 1 50

1160

4 1 4 F 3 R M A T l l H O ~ * T O U l T I N DEGF 0 'rT35tF10.3) PRINT 471 . C D M . 411 FURYllTflHOr*MASS FLOk PATE LE/HR 0 'rT35*F10.3) PRINT 477.EENO I S N _ O ~ . _ _ _ - . . 4 ? 7 . F 3 ~ ~ lfIHC**RULK lT REVNCLCS NO& 0 *T35*F10.21 ISN 0 2 4 5 PRINT 4 7 6 PRNO ISN O H 6 478 F'JRYAT (lHC*'BULK PRANCTL hO. 0 * r T 3 5 r F 1 0 . 3 l PRINT 410rCDDP I S N 0247

-I S-M. 0241 - - .-

ISM 0242 ISN 0 2 4 3

1050 1055

i i ro A180 1185

1190 1200 1210 1220 1230

470 FgRMAT(lHO**NET HEAT F L U I PTU/HRSOFT = * 11331E12.51 P R l Y T 4f6*CBAL 476 FORMAT (lHO**HEAT BAL4hCE **135*F13.3J DEFH=MOOT*SPHl*( TOUT-TIN J / (2.*3.14*RI *L/ 144.W WAVG-BAY(;l I P4 I NT 475 t CEFH 4 1 5 FC)RMAT(lHl t * H BY DEF BlU/HPSQFlDEGF **T35rF10.2J I S H P ~ 4 - ~. . - - NNO*D€FHf2.*R1/12. /CCNC ISN 0255 P R I Y T 4751 tNNO 4 7 5 1 FORMAT (lHO**NUSSELT NC. * rT35rFlO.21 ISN 0256 C FROM MERE ON THE YNO USE0 ltILL BE THE INTEGRATED VALUE NYO=NUAVG ISN 0257 ISN 0258 01 **3*EETA*32 .2*RHO**2* (WAVG-BAVGI/( YU/36CO. l**Z GRNO= PRIYT -9Bl-rGRIO 19B ~ S ' - F ~ R M A T ~ ~ H O ~ * G R A Sho. H O F= a r ~ 3 5 r ~ 1 0 . 4 ~ ISN 0260 GLN0*3.14/4. *RENO*PRhO+Z .*R1/ (X2-Xl I ISN 0 2 6 1 PRINT 4752 rGLNO ISN 0262 4752 FORMAT flHO*'tRAETL NO.(C-81 *rT35*F10.41 ISN 0263 BTRHa.O722*lGRNO*PRhO+Z . * R l / ( X Z - X 1) J **O.75 ISH 0264

ISN 0248 ISN ISN ISN ISN ISN

0279 0250 0251 0252 0253

on9

E ?! -o_-B3--ISN 0266

IsH-0267

ISN 0268

- -

ISN O h 4 ISN On5

09F =NNO/PR hO**O.4 OBHICOND/( Z.*R1/12. PRINT

4111 . e m

J +C .023*( RENO1+0.8 J*( PRNO**O.4)

ISN 0279 ISN 0290 ISN 0 2 8 1

I F (TA-188) 2001210r210 200 D ~ ~ = ~ O ~ ~ D ~ * I . l _ S * ~813~139-. (~ZNO. 33GO TO 220 .210 DLH~COND/Dl*l~75*~GLhO + BTRCl*r0.33 220 CONlINUE STH=SM*(ML*W.l4l COLH=O.O23*(Dl *GJ*+O .9/Ol*CCNO*rd.667*SPHl**O.33

____ ISN 0267

1mLonsISN 0277

ISM

one.

I94 02eO

ISN 0291 ISN 0 2 9 2 1% 9293 ISN 0294 i3N ISN 0296

Oh5

ISN 0291

ISN 0298 ISN 0299ISN 0300 ISN 0 3 0 1 ISN 0302

COLH~_CLH*~U**O~.33/MU**O.8 FGRNO=FGPNC/W**2 I F (TA-TBBI 230&!40*240

GO TO 250 240 CL MH2 L W / YU**G 33 t 1 + 0 e 0 15* (FG PNC I **Om 3 3 I -250 CONTINUE CF .CF/YU**C.?3 CRENO=RENO PRINT 4911 tCOLH 4 8 1 1 FIRM41 (lHC**COLBURh T t R B H BTtI/HRSPFlDEGF * iT35rF10.2J C4LL PROP( REM)*PRNC* IrU rRHOtWAVGtR1 t CCNOt SPHlrMDOT J S T l M = S l T H / (MW*0.141

1235 1240 1245 1250 1260 1270 1290 1291 1292

1292a 12928 1293 1294 1295 1296 1297 1298 1299 1300 1301 1310 1320 1330 1340 1350 1355 1351 1358 1360 136011 . 13608 1360c 13600 136DE 1361 1361A 1361400 1361AO 1361A1 13618 136181 1361C 13610 1136101 136102 136103 136104 136105 1361D6 i 33 6 1I ~ 87 1 1361E 13b1f 1362 13628 1362C 1363 1364

ISN O P 3 ISN ISN ISN ISN ISN

OM4 0305

0306 0307 0308

492 FJRMAT(lHOr-!S-T TUROULEkT H @fU/HRSCFTOEGF 'rT35rF10.2) P q t N T 4 8 2 1 rHTRW 4 C 2 1 FORMAT (IMOr'HAUSCh TR H ATU/MRSOFTDEGF 'rT35rF10.2 # PRINT 483rSlM 493 FORMAT (IHOr'S-1 LAMlNIR H BTU/HRSQFTCEGF *rT35rF10.2) PRINT 484.DLH

1369A 1369 i369e I 136902 1369C1 1369C2 1369C3 1369C4 1869C5 1369C6

1370a

isW oii6

P R I N l 485 r STF 485 F3RMAT IlHOr'S-T FICTOR 'rT35rF10.3) ~. -.--- .- .. -. .. PRINT 4 8 6 r E T L 496 FJRMATtlHUr'EFF TUDE LENGTH I N * rT35rF10.3# VRAT+I VRAT/MU)**O.14 PRINT 4 e i r m ~ 487 FORMAT ( l H O r * V I S R I T I O TO 0.14 'rT3SrF10.4)

ISN 0 3 2 0

€_Twa5Ll

JSY..-03zL

_ _ _ I _

ISN 0 3 2 2 1SN 0 3 2 3 ISN 0 3 2 4 ISN 0325 ISIS 0 3 2 6

.--.QFMES~E*YMT-

032-2

ISN 0 3 2 8

.__

05%

13708

1370c

I -

PRINT 4e8.CFACT 488 FORMAT (1HOr'MART FACTCR c A LOOK A T A SMCOM CURVE TWRU ISN 0330 CALL V L S f l C r F T C r C T C r Z I I S N 0331 GO TO 6 -ASLQX+OBz __ ..-€YO __ .AEONS FOR EXTERNAL- REFEREKES

isN

1365 1366

13bbA 1361 1368

_____ __

rT35rF19.3) DATA POINIS

PAY BE EDUCATIONAL

1372 1373 1374 1375

1376 1377 1378 1379 1380 1390

1391 1400 1401

Y c

COMPILER CPTIONS NAPEL M A I N ~ C P T ~ O 2 ~ C I Y E C N f ~ 6 ) , S O U R t f , E B C O f t , Y O L I S T ~ O E C K ~ L O A*ONOEO ~ ~ A IPT NO1 0 NOXREF C THIS FUNCTICN CCCYITS 3 R 0 CROFR CRTHOGCY4L S I N S BY AVERAGING VALUES A 1.o C BEGINYINC k I T H NO. Y A T X I AN0 ENOINO U I T H I CCNSECUTIVE VALUES AT X Z A 11 ISN 0002 FUNCTICN AbG(**Y*I t X l * X Z l A82!O I S N 0003 O I W N S I O N Y(50l 9X(?iOIrb(4lrP('50r4I * S P 2 ( 5 0 * 4 1 A 3io I S N 0004 REAL NPILS A 3i5 ISN n005 A(lI=O A 4PO I S N 0006 AL(ZI=O A Yio 1% OC07 A(3I=O A IO At4110 A '0 I S N 0008 1SN 0009 P ( 1111=I. A 1'2 I S N 0010 P( 1r 2 I =I. A 7'3 ISN .Qoll--. - - .P( 1 p . 3 ) 11.1 A 74 ISN 0012 P 1* 41 -1 A 75 ISN 0013 NP-1-1 A 90 DO 490 L m 2 . l I S N 0014 A 95 ISN OCIS X t L I =L-1 A 97

A210

I S N 0030

550 C9NTINUE PRINT 6 C O 600 F'JRMAT ( l H l * l 0 H O R I C I N A L *13HLEAST S C I I A R t S t l O H PGEVI 09 730 J s l r I L $%A 1 U*.P( J p l I + I t 2 I *Y (J t 2 I +A( 3 1 F-( J * 3 I + A ( 4 I *e( J 4 1 POE V I (LS-Y t J + W l I 1*100./Y( J+M-II PRINT 650*Y(J+C-L I*LS*PCkV FOR MA 7 (Ft3.2 t 5 X ~ F 8 . 2r 5 X F8 e 2 I 650 700 CJNTINLE x 3=x2- x I

I S N 0031

1513 0032 ISr C 0 3 3

I W DQ3-%

I S N 0035 I S N 0036 ISN OC37 ISN 0038 I S N 0039 t SN .0040

/2.1 I 4 A ( 4 I * ( X 3 - 6 .*X3**2/kP+30 ./hP/ /2. 1-20 ./PP/(NP-I I / ( NP-2.1

8 b

8 I S N OC41 ISN 0 0 4 t

ISN 0043

AVG=AI NT/X3

. RE TURN €10

NP-I.I*(X3**3/3 .-X3**2 *(X3**4/4.-X3**3+X3*X3lI

1220 A230 A240 A250 A270 4200 A290 a3c0

A305 A310 A320 A330 A340 A350 A351 A352 A353 A354 A390 A440 A450

COMPILER - .- -._--

194 o m 2 I S N 0003 I S N @OO$ ISN 0035

?opt.-. .- -

ISN O C 0 7 ISN 0008

I S M OW9 ISN O C l O 1m 0011

!FoCl_z_. I S M 0013 I S N 0014 194 0 0 1 5 ISN E016 ISM 0017

O f T I OMS NAY€= M A I N r C P l ~ 0 2 r L I M E C N T ~ rSOURCEtEBCUICrYOL1 60 ST rOECKrLOADrYAPrNOFOI T r N O I OrNOXREF F i J N Z ' t l O K W f C R h I N E S ?t#iRRAL K FOR IhCR-8 K 10 FUNCTICN T l t T E M P F l K-. 20 TEMPCI tTEWPF-32.1*5. /9. K30 IF ~IEMPC-440~lLOrlOrZO K40 10 TK=O.ltO+ ( .155-.128) /ZOO .+tTEwPC-?09 1 K 50 GO TO 80 K60 2 0 I F -tE-kPC=JOO. 1 3 0 r 3 0 1 4 0 K70 3 C TK =O 160+ t e l 74s. 160 1 16 C. ( TE CPC -440 1 k00 63 TO 00 K 90 $0 IF (lEWPC-68C.15Or5Or6C uiao 5 0 TK=0.174+( . 1 9 3 - ~ 1 7 4 1 / 1 0 0 ~ * t T E ~ P C - 5 0 ~ . ~ u110 K120 _. GO _t_o 65 I F t l E M P C - 7 4 0 . 1 7 0 r 7 O r 7 5 U130 IC TK=U.ZOB+~ . ~ ~ O - . ~ O B I / ~ C . * ( T E C P C ~ ~ O . ) K140 GO TO 80 K150 1 5 TK=0.230+( .248-.2308 /160.*tTFMPC-140.) K160 B C TK=TK*57.82 a1r0 R E TURN . U300 €YO ((301

T-THTS

eo.

CCJMP I LC R OP T I ON 5 NA YE MA I hr IYP 1102 * L I NCCNT 1 6 0 *SOUR CEr t BCOI Cr YOL I ST IOECK r L O A 0 r MAPI YO€ 01Tr NC'I C r NOXREF 1: T H I S SUaPlJlrYfkE TAMES 1h AFRLV Y YHCSC 1 S l VILUE IS 4 1 M h I T H I TOTAL A19 C CONS~CUTIVE VALUES 4NO REPLACES T H I S A R R I V U I T k AN NTH ORCER F I T A l l S!J8ROUTINE V L S t V i M i I r Y l ISM OM2 A20 I S M OC03 A 30 01 W € NS I ON V I50 I r X I 5 0 I r A I 4 I IP I 50 9 4 I r S P2 I 501 4 I REAL lyP.LS I S M 9034 A35 b40 I S N 0005- .. . . A50 I S N 0006 A 60 194 OW7 A0110 A 70 I r n 0038 414I=O ISN t o o 9 A 72 P I 1r l I = l . A73 ISN 0010 P.ll.21 =I. A 74 ISN 0011 P t 1r 31 =l A 75 I S M 0012 P I 1e41 4. A 90 ISN 0013 NP.1-1 A95 ISN 0 0 1 4 0'1 4 9 0 L I Z 9 1 A 97 ISN 0015 XILl=L-l A100 ISM OOl6 P I L . l l = 1. a110 I 52- .ow- . . - P!& t 2 l =l -2. * X I L l / hP A120 ISN 0018 P I L 931 -1 m - 6 . * X I L l /hP+5 *X iL I I X I L l - 1 I /NP/l NP-1 I P I L r 4 k -1.-12.*XlLl /NP*3O.*X I L I * ( X I L l - 1 . I /NP/lNP-1. I A 1 30 I S N 0019 -2O.*X 111 *IX I 11-1. I *I X I L 1-2 I /NP/ I NP-1 I /INP-2 I A 131 a A135 ISN 0 0 2 0 490 CONTIIIM A140 ISN 00.21 SP2 II r 1I =NP*l. A150 . SP21 - - -..-1921 = I h P + l I* I hP+2 . I / I 3 e*NPl 1sw-oa_zz- - A I 60 1SN 0 0 2 3 SPZI 1131* I NP*l. l * l N P + 2 . I *(NP+? I/ I 5.+lrP) /I NP-1 I A170 ISM 0 0 2 4 SPZI 1 - 4 1 *I hP*1. I *I hP+2 - 1 *INP*3. I*( NP*4. I / I 7.*NPl I1 NP-1 I /lNP-2. I 1200 194 002s 0'1-550 J-1 r 4 A210 1% 0026 0 0 soa a = i 9 t A220 K r J l 1SN 0 0 2 7 A ( J l = A I Jl + V t K * M - l l * P A230 ISC! -bP. C ONTI.hUE A240 A I 5 1 *A IJ l / J P Z l I IJI. I S M OC29 A250 ISN 0 0 3 0 550 CONTINUE A270 ISN OC31 PRINT 600 A280 13HLEAST SCUARES r 10H POEV I ISN 0032 630 FIRMAT 11HlrlOHORIG1h4L A290 S IN 0033 09 700 J = l r I A294 IS! _. I F lN.LT.31 A l 4 l * O A295 ISb 0 0 3 6 IFlN.LT.2l A131+0 A296 1F IN. 11.1 I A 12) I'J ISN OC38 L S s L I11 *P( J r 1 1+112 I * P I 512 1441 3 l * F l J r 3 ) + A I ) * P I Jr 4 I A300 I S M 0040 P Ok V I I L 2-V I J+ Y1) I *100. / V L . I + M-1 I A305 I S N 0041 A31C ISM o w A320 lur.9*3 65 0 FORMAT IF8.2r5XrF8.2r5XrF@.Zl A330 ISN nC44 V I J+M-l I =LS A350 I S M OC45 XC C'JNTINUE A370 ISN 0046 RE 1URN A371 Isrl O C 4 7 E YO

oozs

c o r __

ul W

APPETJDIX D ,

CHEMICAL ANALYSES AND PHYSICAL PROPERTIES OF THE SALT

l i II

Analyses of t h e Fluoride Salt Mixture Table D . l . (LiF-BeFz-ThFc-UF4; 67.5-20.0-12.0-0.5 mole 4 ) Before, During, and After HeatTransfer Determinations

Impurity

Weight Before

7.14

2-57 42.1 1.87 45.4

20 PPm

Cr Fe

e 5 PPm 78 PPm

C10 ppm

Th U

Duringa

After

7-27 2-53 41.3 1.84 46.4

6.64 2.46

43.5 1.72 45.4

0.66

a Analysis made j u s t p r i o r t o removal of the f i r s t t e s t section.

Table D.2. Thermophysical Woperty Data f o r Molten Salt Mixture LIF-BeF,-ThF4 -uE, (67.5-20-12-0.5 Mole $1

Uncertainty ~~~~

p (lb/ft-hr) =

0.187 exp [8000/T(oR)]a

k (BtU/hr*ft-OF) =

Ref.

~~~

0.69b

p (lb/ft3) = 230.89

- 22.54

13 X

lom3t

C (Btu/lb* OF) = 0. 32ka P Liquidus temperature e 895"Fa

12 12 12

aEstimated values f o r the salt mixture LiF-BeFz-ThF4-UF4 (68-2011.7-0.3 mole 4).

bMeasured value f o r the subject salt mixture.

59 ORNL-TM-4079 INT-L

1. L. B. Alexander 2. J. L. Anderson 3. S. E. Beall 4. M. Bender 5. E. S. B e t t i s 6. E. G. Bohlmann 7. C J. Borkowski 8. C. E. Boyd 9. R . B. Briggs 10. R. H. Chapman 11. S. J. Claiborne, Jr. 12-21. J. W. Cooke 22. W. B. C o t t r e l l 23-27. B. Cox (K-25) 28. F. L. Culler 29. J. H. DeVan 30 J. R . DiStefano 31 S. J. D i t t o 32 A . S. Dworkin 33 W. P. Eatherly 34 D. M. Eissenberg 35 J. R . Engel 36 D. E. Ferguson 37 L. M. F e r r i s 38 A. P. Fraas 39. J. H. Frye 40. C. H. Gabbard 41. R. B. Gallaher 42. W. R. Gambill 43 R. H. Guymon

44.

45 46-55. 56 57 58 59. 60. 61. 62.

P. N. Haubenreich

R. H. W. P. R. J. 0. A. T.

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