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OAK RIDGE NATIONAL LABORATORY

OPERATED BY

CARBIDE AND CARBON CHEMICALS COMPANY

A DIVISION OF UNION CARBIDE AND CARBON CORPORATION

(143

POST OFFICE BOX P
OAK RIDGE, TENNESSEE

   
ORNL 1716

Th document ons ts of 3] pages

Copy’d( of 265 copres Se es A

Contract No W 7405-eng 26

ANP DIVISION

TURBULENT HEAT TRANSFER FROM A MOLTEN FLUORIDE SALT
MIXTURE TO SODIUM POTASSIUM ALLOY IN A

DOUBLE TUBE HEAT EXCHANGER

D F Salmon

DATE ISSUED

NOV 3 1954

OAK RIDGE NATIONAL LABORATORY
Operated by
CARBIDE AND CARBON CHEMICALS COMPANY
A Division of Union Carbide and Carbon Carporation
Post Office Box P
Oak Ridge Tennessee

  

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m 3 445b D349L57 4

 
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CONTENTS

Introduction

Description of Equipment

Test Procedure

Method of Calculation

Correlation of Data

Test Results

Discussion of Results

Conclusions

Nomenclature

Appendix 1 Equation for Intermediate Axial Stream Temperature with Logarithmic Distribution
Appendix 2 Derivation of Equations for Wilson Line Analysis

Appendix 3 Physical Properties of the Fluoride Salt NaF ZrF , UF, (50 46 4 mole %)
and of Sodium Potassium Eutectic Alloy

Appendix 4 Sample Calculation of Data Point 4

 

o A A

10
12
13
16
18

19
22
 

TURBULENT HEAT TRANSFER FROM A MOLTEN FLUORIDE SALT MIXTURE TO
SODIUM POTASSIUM ALLOY IN A DOUBLE TUBE HEAT EXCHANGER

D F Salmon

INTRODUCTION

Circulating fuel reactor systems for high per
formance high temperature power plants place
exacting requirements on the fluids which must
serve as heat transfer media It 1s necessary that
the fluids have good heat transfer properties be
stable chemically at an elevated temperature have
a reasonably low melting point be compatible
with container materials and require only a min
mum in pumping power Aside from the chemical
problem involved in finding materials with which
the proper amount of nuclear fuel may be com
bined there are the research and the experimenta
tion required to determine whether the above

mentioned specifications are met

Mixtures of fluoride salts were found to show
promise for the circulating fuel application This
report 1s concerned with an experiment to measure
the heat transfer characteristics of the fluoride

salt mixture NaF ZrF , UF , (50 46 4 mole %)

The primary purpose of the experiment was to
make a correlation of film heat transfer coeffi
cients and a secondary purpose was to determine
the effect on heat transfer of deposits resulting
from corrosion or mass transfer of container ma
terials

 

DESCRIPTION OF EQUIPMENT

A schematic diagram of the various components of
the test apparatus 1s shown in Fig 1

The only pump available for the fluoride salt
circuit was a type 316 starnless steel sump pump
capable of delivering 10 gpm at 40 ft of head and
3600 rpm  This pump was designed for high
temperature application and for liquids which could
not be sealed against directly at the shaft in the
ordinary manner It had a water cooled rotary face
seal for maintaining an inert gas blanket on the
fluid being pumped An automatic level control
system was provided for maintaining the liquid
level in the pump within prescribed limits

The heat transfer coefficients were measured in
a double tube heat exchanger The fluoride salt
was cooled in the center tube by a countercurrent
flow in the annulus of sodium potassium alloy
(hereafter referred to as NaK) The center tube of
the heat exchanger made of nickel was 0 269 in
in inside diameter with a length to diameter ratio
of 40 The outer tube was 3‘4 in  schedule 40
type 316 stainless steel pipe which was rigidly
connected to the center tube at one end and
bellows joined at the other end to allow for dif
ferential expansion

Heating of the fluoride salt was accomplished in
a length of 1 in schedule 40 Inconel pipe by
electrical tube furnace elements assembled on the
pipe and covered with preformed insulation The
NaK stream was cooled by natural convection of
air in a section of finned pipe which was ducted
and provided with a damper for control

The NaK was circulated by a conventiondl
electromagnetic pump The fluoride salt and the
NoK flaw rates were measured by water calibrated
venturi tubes the calibrations were corrected to
reflect the discharge coefficients and the dif
ferences 1n densities of the respective fluids An
electromagnetic flowmeter was also available for

determining the NaK fiow rate

Inlet and outlet temperatures of the fluoride salt
and the NaK were measured by fixed Inconel
sheathed Chromel Alumel probes on the center
lines of the piping An adjustable probe that was
provided in the annulus of the heat exchanger
could be brought in touch-contact with the outer
surface of the center tube wall for temperature
measurement  These probes were calibrated to
]/2°F against a National Bureau of Standards

 

[~ |
 

certified platinum—platinum-rhodium thermocouple
in a calibrating furnace. Thermocouple readings
were taken on a Leeds and Northrup K-2 potenti-

SURGE TANK
— FLUORIDE SYSTEM

——=—LIQUID METAL SYSTEM

HEAT EXCHANGER-,

—e— CENTRIFUGAL PUMP

HEATER SECTION

     

 

FLOWMETER

 

VENTURI

 

 

Figt 1

VENTLURI
FLOWMETER

ometer, and an ice-bath cold junction was used.
Figures 2, 3, and 4 are photographs of the test
equipment,

UMCLASSIFIED
DWG 18344

ELECTROMAGNETIC FLOWMETER

LEC

COOLER

   

FEFH iHH} F T
— = — A H-

 

|

|

1

1

|

—
ELECTROMAGNETIC g

PUMP

Schematic Diagram of Bifluid Loop.

 

Fig. 2.

Instrument and

Power Panel.

 

 

 
= HEAT EXCHANGER

T

FLUDRIDE SALT
HEATING SECTION NS

VENTLURI FLOWMETER

SUMP TANK AND FLRNACE

8 UNCLASSIFIED |
PHOTO & 5881

MoK FLOWMETER
ELECTROMAGNETIC

¥

-

L i ’rd-"-r:fl-hlh—.-:_l.__— |

e - ¢ | Nek COOLER
BYPASS FILTER CIRCUIT | B H

 

Fig. 4. NaK Loop.

 

 
TEST PROCEDURE

The melting point of the fluoride salt was approxi
mately 960°F ! and consequently 1t was neces
sary at all times to maintain the walls of the
fluoride salt system above this value In fact the
walls were kept at from 50 to 100°F above the
melting point as a precaution against freezing
For all runs the electrical power to the fluoride

 

]Physrcal Property Charts for Some Reactor Fuels
Coolants and Miscellanecus Material (3rd Edition)
ORNL CF 53 3-261 (March 20 1953)

salt heaters was controlled to maintain a constant
inlet temperature to the heat exchanger  The
fluoride salt pump speed was set to give a desired
flow rate and this flow was maintained for a
series of different NaK flow rates The damper to
the NaK cooling section was adjusted in each
case to hasten attainment of steady state condi
tions before data were recorded Data were taken
during each run at each NaK flow rate a total of
80 data points was taken

 

METHOD OF CAL CULATION

A heat balance on the fluoride salt and NaK
streams in the heat exchanger was made initally
to serve as a check on the validity of the data and
to provide the basis for calculation of the heat
flux g/A_  The value of g used for determining
the heat flux was an average of that obtained by
applying the first two of Eqs 1 to the fluoride salt
and NaK streams

(1)

wF C‘F AtF

Sy
It

wN CN AL‘N
U, Ao AILM

where the subscripts F and N refer to the fluoride
salt and the NaK respectively The insulation
heat loss from the heat exchanger was neglected
since 1t was in actuality less than 1% The over
all heat transfer coefficient was calculated from

the third of Eqs 1
q/Ao

 

(2) u, = ~

LM

The adjustable probe located 16 diameters down
stream from the fluoride inlet provided the outer
surface temperature of the center tube from the
outer surface temperature the inside surface tem
perature was determined by using the conduction
equation

 

| %
n

q, D)
3 t - oy
3 wF wN 2flkwL

A loganthmic axial distribution of temperature

was assumed for calculating the stream tempera
ture opposite the measured wall temperature Der
ivations of the equations for obtaining these
temperatures are presented in Appendix 1  The
following equations were then used to arrive at a
film heat transfer coefficient

9a
(4) by =
Altpg 4y = twr]
and
7 v
) by =

Altun = thio 4y

An individual heat transfer coefficient may be
distingui shed from the film coefficients given above
in that 1t 1s obtained by separation of the over all
coefficient defined in Eq 2 Some such separation
process s always required when the difficult
problem of measuring surface temperature is not
attempted  In this case the valuable graphical
analysis of the over all heat transfer coefficient
attributed to Wilson by McAdams? is useful The
analysis 1s based on the premise that a plot of
]/Uo vs 1/0% 8 will produce a straight line if one
of the fluid velocities s held constant and the
other 1s varied over a specific range of values
Wilson s method was applied to the data of this
experiment as shown in Fig 5 where 1/U_ 1s
plotted against 1/v,,° 8 The run with the greatest
number of values for NaK velocity was used to

 

2y H McAdams Heat Transmission 2d ed
McGraw Hill New York 1942

p 273

 
establish the slope of the lines The lines were
extrapolated to 1/v,,9 8 = 0 which was equivalent
to letting the NaK velocity approach infinity in
which case the NaK film resistance /b, ap-
proached zero

 

By assuming the value of »_ to be constant
along each of the Wilson lines an individual co
efficient for NaK was separated form the over all
coefficient by using the following equation (derived
in Appendix 2)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

An individual heat transfer coefficient for the ]
fluoride salt was then separated from the extrapo (7) by =
lated over all coefficient at ]/UN0 8 by using the _]___ 122 — 0 0000788
equation (derived in Appendix 2) U, F
122
(6) by =
— 0 0000788
C SSFE
0 G 23303
9
o
8 e
/
/0/
/0‘(0
//
7
/
6 . ///a
< // /
-|$ /t A//
5 / ]
/ - A DATA POINTS 3 4 5
/‘ /.—A‘ A DATA POINTS 24 25 26 27 28
4 A ® DATA POINTS 2 6 7 8
// O DATA POINTS 9 {0 11 12 13
//
e
3
%o 01 0z 03 04 05 06 07 os 09 010
-
Fig 5 Wilson Line Plot
CORRELATION OF DATA

Dimensional analysis of the physical properties
together with the hydrodynamic and geometric
factors affecting heat transfer between a turbulently
flowing fluild and a bounding surface such as a
tube gives a product function of the Nusselt

Reynolds and Prandt| moduli  The function s
usually written as
(8) Nu = CRe™Pr?

The relationships of these parameters for ordinary
fluids such as water gases or oils as differ
entiated from liquid metals have been empirically
determined from the data of many experimental
investigations
the exponent » 1s 0 8 However for the constant
C and the exponent p there 1s variation in the
evidence the values depend on whether the fluid
1s being heated or cooled on the magnitude of the
fluild viscosity and on whether the evaluation 1s
based on the bulk temperature of the stream or on
an average of this temperature and the surface
temperature

McAdams recommends® for fluids of high wvis
cosity that 1s presumably higher than twice
that of water the Colburn equation

The generally accepted value for

1
1
(9) Nu = 0023 Refo BPrf 3

or that of Sieder and Tate

1 014 )
(10) Nu=0027{— Re0 8p; 3
Fuw

For these equations the Reynolds modulus
should be in excess of 10000 The viscosity
correction term (pL/yw)o 14 compensates for the
variation 1n the temperature difference between the
bulk temperature of the stream and that of the wall
In the transition range of Reynolds modult from
approximately 2 100 to 10 000 called by McAdams

the dip region 4 there ts a dependency on the
fength to diameter (L/D) ratio of the heat exchange
surface the amount being afunction of the Reynolds
modulus Eckert® states that the equation of
Hausen

 

3ibid p 168
YUbid p 167

= R G Eckert Introduction to the Transfer of Heat
and Mass p 115 McGrow Hill New York 1950

u 014 2é
(1) Nu =0116 (— (Re ® - 125)

P
4| (oy?
Pr 1+ [—
L

will satisfactorily reproduce values in the Reynolds
modulus range from 2300 to 6000 Equation 11 1s
also useful for the entrance region of tubes where
the velocity profile has not developed fully al
though the Reynolds modulus based on mean
stream velocity 1s sufficiently high for full develop
ment

The theoretical approach to turbulent heat trans
fer in a tube has advanced to the stage where
experimental values can be predicted with very
good agreement von Karman s postulation of three
zones tn the flow field namely the laminar sub
ayer the buffer layer and the turbulent core was
largely responsible for the advance Although the
theoretical approach was not used in this work
reference will be made to an extension of von
Karman s theory by Boelter Martinelli and Jonassen
(as described by Eckert®) and by Martinell1 7 The
extension concerns the temperature rotio (t -
t)/(tw - tc) which was determined by them and
plotted as a function of Reynolds and Prandtl
modult  The result gives the amount of deviation
expected when center line temperature rather than
bulk temperature 1s used to evaluate physical
properties in correlating experimental heat transfer
data

The correlations discussed above for ordinary
fluids do not hold for liquid metals which have low
viscosity and high thermal conductivity and thus
very low Prandtl moduli  Thermal conductivity 1s
important even in the turbulent core of the stream
where for ordinary fluids 1t 1s assumed in the
equations that all the heat is transferred by mixing
action  For heat transfer to liquid metals 1n a
tube Martinelli® derived an equation which was
later greatly simplified by Lyon ? but there is as

 

Sibid p 125

7R C Martinelh Heat Transfer to Molten Metals
Trans Am Soc Mech Engrs 69 955 (1947)

81bid p 947 959

R N Lyon Forced Convection Heat Transfer Theory
and Experiments with Ligquid Metals ORNL 361 (Aug
19 1949)
ye%% abundance of data to substantiate therr
wor

There 1s no widely accepted procedure for calcu
lating heat transfer to turbulently flowing fluids
in annult  whether they are ordinary fluids or
liquid metals The usual practice 1s to apply the
tube equations with an equivalent diameter sub
stituted and to add a correction term consisting
of the ratio of annulus diameters to some power
One equation for liquid metals 1n annult corrob
orated in particular with NaK by Werner King
and Tidball (described in the work of Claiborne 19)

 

IOH C Ci iborne A Review of the Literature on Heat
Transfer 1n Annuli and Noncircular Ducts for Ordinary
Fluids and L quid Metals ORNL CF 52 8 166

1s the following

(12) Nu,, =1[49 + 00175(Re x Pr)° 8]

The bracketed quantity 1s equal to 07 of Lyon s
expression’ for Nusselt s modulus in a tube and
the diameter ratio correction 1s recommended by
Monrad and Pelton who experimented with ordtnary
fluids tn annular spaces The work of Monrad and
Pelton 1s described by Claiborne'® and also by
McAdams !

 

”W H McAdams Heat Transmission 2d ed
McG aw HIl New York 1942

p 201

 

TEST RESULTS

A total of 80 data points was taken during the
test but only 19 of the points were used in the
analysis for this report The remaining data were
not used because of fouling that occurred on the
fluoride salt side of the heat exchanger as a result
of mass transfer of iron from the stainless steel
pump parts When the heat exchanger was sectioned
a layer was found which built up gradually from the
hot end to a thickness of approximately 0 030 in
at the cold end Spectrographic analysis showed
the layer to be pure iron

The basis for selecting the data points that were
analyzed 1s indicated in Fig 6 where the fluoride
salt system pressure drop Is plotted as a function
of volume flow rate The points are compared with
a theoretically calculated curve of pressure drop
vs volume flow rate The chosen points fall on
the curve representing an unfouled condition while
the rejected points lie considerably above this
curve The sequence of the measurements can be
traced Instances can be seen where pressure drop
increased sharply without increase in flow and 1n
other cases where pressure drop remained constant
while flow increased

The data points used in the analysis and the
pertinent calculated quantities are tabulated In
Table 1 Physical properties of the fluoride salt
and the NaK are plotted as functions of temperature

in Appendix 3 A sample calculation of data point
4 1s presented in Appendix 4

The fluoride salt flow rate was varied from 1 to 5
gpm and the system pressure drops for these flows
were respectively 5to 55 pst The NaK flow rate
was varied from 17 to 9 25 gpm the NaK system
pressure drop was not measured Reynolds numbers
for the ranges of flow rates given were 4 400 to
21 000 for the fluoride salt and 21 000 to 100 000
for the NaK

Limits of the over all heat transfer coefficient
based on the outside area of the center tube were
1140 and 2550 Btu/hr ft2 F Fluoride salt film
coefficients from 2000 to 8200 Btu/hr 12 F were
calculated

Heat fluxes at the outer surface of the center
tube from 196 000 to 484 000 Btu/hr 12 were
obtained

Minimum and maximum fluid velocities in the heat
exchanger were 8 to 30 fps for the fluoride salt and
1to 65 fps for the NaK Fluoride salt temperature
at the heat exchanger inlet was varied from 1200 to
1400°F and the corresponding outlet NaK temper
ature was varied from 1050 to 1250°F The range
of the axial temperature differences through the
heat exchanger was 10 to 42°F for the fluoride and
37 to 300°F for the NaK  The logarithmic mean
temperature difference varied from 172 to 305°F
60

50

40

30

AP (psi1}

20

4

DWG 23304

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

FLOW RATE (gpm)

Fig 6 Fluoride Salt System Pressure Drop vs Flow Rate for Each Run

68.] _ 64
g8-65
63/< ie;?
66
57 5
a N
51\ /5 3\ \n /
52\\‘9 0/ /56 O /
53 ——9 ~ 8-55 | g~g o ,
Ne2
58 59 60 ’
74 /
46 47 /74 75 / 4
49> 0&473
50 \70/
487169 72 7
Yy
40/®,45
4t 42 43~ " -44
7
UNFOULED
37 38 /
39 34 35 .
36:&/ /
77 ,
_ g ~76
79
78/ /
30 4
29 3132 —
/ >~ THEORETICAL
33 /
27 /
20 24 I\ 25 26
22 —F\ 23 28
e
19 21 2. '
/ 7
14 67 8— A
18\ /7
1516 170} ’
g
///
sS4
/,.)(9 10 11 12 13 13q
0 20 30 40 50

60
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TABLE 1 MEASURED AND CALCULATED RESULTS OF HEAT TRANSFER EXPERIMENTS
MEASURED OR DATA POINTS
CALCULATED
QUANTITY (1 2) 3) {4) (5} © 7} (8 {9 (10) a1} (12) (13) [ (13 (24) (25) (26) n (28)
, 12205 (13433 | 13230 (13237 |13215 (13171 (13288 [ 13308 [ 13157 | 13328 |1333.4 (13337 [1333.4 [ 13342 [ 14291 | 14193 {14230 [14208 [ 14053
N1 11545 (11402 | 11819 [ 11798 [ 11645 [1102.4 [ 11183 | 1126 0 | tos7 4 [ 10582 | 10571 | 10532 10546 10552 | 1267.4 | 12327 | 12284 | 12229 | 12007
N 11519 (11851 | 11950 [1201.4 | 12035 (11150 [ 19429 {11519 | 1083.4 [ 10539 | 10536 | 10498 |[10535 | 10561 | 12533 {12187 | 12176 [12141 | 1214 5
At 101 268 148 146 156 |272 298 28.3 a7y |43 a5 423 Mne 424 25.3 269 270 284 276
Ary 000 |829 1087 |19 |s48 |571 482 385 814 598 499 430 37.4 370 1508 | 966 71.4 542 466
we 4580 | 4060 {8110 | 8450 |8450 |3810 |3810 | 3310 2300 2300 (2300 {2300 (2300 | 2300 {4050 |4325 4325 |4290 | 4340
wy 2250  |1170 | nso 1160 {1700 2235 | 2560 | 3060 1320 | 1940 | 2405 | 2780 }2120 | 3120 | 635 1196 1700 [ 2360 | 2950
e 14320 |33700 | 37200 | 38240 | 40850 (32150 | 35200 | 33 420 | 27 000 | 29,400 |29 600 | 30150 | 29900 | 30200 | 31780 | 36040 |36200 (37750 |37 100
N 16720 | 24000 | 31800 {32190 {35750 {31640 (30600 (29200 | 26600 | 29050 |29760 | 29620 |28950 1 28620 23750 | 28620 | 30040 |31 700 | 34 100
153520 | 28850 | 34500 |35220 (38300 {31895 | 32900 | 31310 | 26800 | 29225 [29680 |290885 | 29425 | 29 400 {27765 | 32,330 33120 |34 725 |35 600
A 1724|2302 1841 (1886 |18946 (2300 (2206 [2099 (2794 |2840 (2802 2809 |276.4 |2769 21R6 |2199 2161 12103 2144
U 1138 {1582 (2362 | 2357 [2553 | 1750 1882 1882 1212|1300 1338 | 1342 1342 1340 1600 1858|1931 2080 | 2096
Fi0 4) 12183 | 13334 (13180 (13188 {13159 | 13067 | 13170 | 13196 [ 13011 [ 13167 13168 [13168 [13178 [ 13165 [ 14203 | 14103 [14128 {14099 |1394 6
N(D 4 10902 (11115 | 11456 | 11423 11343 {10804 | 10992 [ 11108 | 10262 | 10348 |10372 | 10326 |10406 | 10398 12154 |1200.4 {11971 [12020 |1i826
WF 11682 1155 (12312 | 12366 [12437 | 11485 | 11775 | 11848 | 11116 | 10847 [10848 {10812 {10845 | 10870 |1282.4 | 12527 [1252.4 {12506 | 12519
b 4780 (3785 |&150 {4620 8190 |3110 | 3840 | 3590 2182 | 1950 1977 | 1961 1950 1980 |[3108 |[3185 (3182 |3360 | 3855
by 3230 (4950 |8830 [7520 [7160 !vi700 | 9500 | 9610 5910 119320 122840 | 21970 (28800 | 22800 |9240 |22,280 [20400 |36200 |14 100
bew1 ) 5740 [ 5740 [5740 [3055 | 3055 | 3055 2025 |2025 [2025 2025 [2025 |2025 [3672 (3472 [3e72 3672 3672
TR 770 | 7500 (10100 (10880 (19230 (19230 | 7040 [11570 {15400 | 16120 |16720 | 15880 |4700 | 8580 | 9430 14 600 15/400
N g 812 625 1030 {117 1380 |525 615 601 372 326 N 328 326 332 478 486 486 516 601
N 803 123 2195 (1845 (1780 |2910 [2360 2364 |1480 |483 571 548 79 570 2283 (5515 |505 8950 |3495
Newr ) 9 55 9 55 955 [518 516 518 339 339 339 339 339 339 5 64 564 5 64 564 5 64
N ywi 1914 {1873 (251 261 478 47 4 760 |288 384 402 402 3965 (1163 |212 2335 {381 38,15
R o 9040 110260 |19 970 | 20800 {20620 | 9100 | 9300 | 938O 5450 | 5640 | 5640 | 5640 |5640 | 5640 12200 {12800 |12880 |12700 |12 470
R g 8610 (9080 (18170 {19080 |19 180 | 7880 {8000 | 8090 4435 [ 4400 (4400 | 4390 | 4400 | 4400 10680 (10820 ;10980 [10750 |10 780
Ry 72700 138750 |39100 (38420 |56,300 |72100 | 82400 | 101300 |41 600 61800 | 75900 |87 700 | 98400 | 98 400 | 21580 | 40600 |57700 |80 100 | 100 200
Pr 675 513 535 535 543 |5355 5 43 535 564 [536 536 536 536 536 393 407 402 408 426
L 7 09 579 587 58 585 ]657 63 620 69 686 686 689 4 86 4 86 4.50 480 472 481 4.93
Py 000811 /000596 | 0 00596 | 0 005% [0 0059 | 0 00611 | 0 00611 [ 0 00596 | 00063 | 0 00629 | 0 00629 | 0 00629 | 0 00629 | 0 00629 | 0 00579 | 0 00579 |0 00579 |0 00579 | 0 OS8O
Nmb idi i whi hd k h f h Fi v &
R me rome d | 1 fd pi 13
DISCUSSION OF RESULTS

The fluoride salt results are compared with Eq 9
in Fig 7 and with Eqs 10 and 11 1n Fig 8 A
least squares analysis of the data in Fig 7 de
termines a line to within 4% of Eq 9 while the
averaging line compared with Eqs 10 and 11 s
approximately 20% low |t appears then thatevalu
ating the physical constants at an average of the
bulk temperature and the wall temperature produces
a better comparison of the results for the fluoride
salt with correlating equations for ordinary fluids

The scatter of the fluoride salt data 1s no doubt
a reflection of the erratic nature of the heat bal
Although the axial temperature differences
measured were small and would result in large
percentage errors for a small discrepancy in ab-
solute value they would tend to be consistent
The electromagnetic flowmeter readings for the
NaK would likewise be consistent even if tn error
The fluoride salt flow rate on the other hand al
though measured with an accurately calibrated

ances

venturi was quite likely the cause of the scatter
ing The pressure measuring technique on this
venturi involved closely controlling liquid levels
in the transmitters by means of floats and auto
matically operated solenoid gas valves

The length to diameter ratio of the center tube
warrants some consideration here For short tubes
where the velocity profile and boundary layer have
not developed fully the heat transfer coefficients
will be greater than those for established flow
Investigations cited by Brown and Marco'? indicate
the himiting (L/D) ratio for this condition to be 40
Hoffman'3 shows entrance length that 1s number
of tube diameters where the film coefficient 1s 1 1
times the established value plotted as a function

 

20 | Brown and 5 M Mareo Introduction to Heat
Transfer 2d ed p 110 MecG aw Hill New York 1951

By w Hoffman Turbulent Forced Convection Heat
Transfer in Circular Tubes Contarming Molten Sodium

Hydroxide ORNL 1370 (Oct 3 1952)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

o
DWG 23305
2X10
O RESULTS FROM USE OF MEASURED WALL TEMPERATURE
A RESULTS FROM USE OF WILSON LINE ANALYSIS
EQUATION (9)
10% /
o
i
7
P o
“ //z‘
a 5
z //
i
Vet
Q/fl/g
4// Q
e &
///
/ [
; y4i
//@
10
10° 2 5 104 2 5 103
R g

Fig 7 Comparnison of Fluoride Salt Results with the Colburn Equation

10
w 2 08

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2X10
© RESULTS FROM USE OF MEASURED WALL TEMPERATURE
A RESULTS FROM USE OF WILSON LINE ANALYSIS
10°
V.
EQUATION (11) /~———EQUATION (10)
v |
WITH = 40 i
o A //
O
o / ;:/
1, / L
BN
= s
2 / /
: A
o
- /s 2
A |7 2
7 o©
7//
// A
D/
2 A,
VI
10 3 4
10 2 5 10 2 5 10°

Fig 8 Comparison of Fluoride Salt Results with the Sieder and Tate Equation and with the Hausen

Equation

of Reynolds modulus times Prandtl modulus for
molten sodium hydroxide Since the fluoride salt
has a comparable Prandtl modulus the plot should
be applicable and for the range of data of this
expertment entrance lengths up to 50 are ind:
cated Therefore 1t would be expected that the
fluoride salt results would be slightly high and 1t
1s possible that such a condition 1s masked by
the fouling that occurred

Another point to be discussed 1s that in all the
correlating equations a bulk temperature was used
for evaluating the results while center line or
axis temperatures were measured in the equipment
The work of Boelter et al 7 when applied to
salts indicates the ratio (z, -~ t)/(tw - tc) for
the fluoride salt results to be 0 92 and the ratio
for the NaK to be approximately 0 58 For the

fluoride salt data therefore the discrepancy in
volved In using an axis temperature rather than
a bulk temperature 1s small and certainly within
the accuracy of the experiment but a large amount
of uncertainty arises for the NaK data This
uncertainty 1s borne out In the comparison of the
NaK results with Eq 12 in Fig 9  The relation
ship between axis and bulk temperature however
has hmited meaning for the NaK stream since 1t
was flowing in an annular space

Failure of the measured NaK heat transfer co
efficients to coincide with the theoretical equa
tions does not necessarily reflect on the accuracy
of the fluoride salt measurements but it indicates
the difficulty involved and the greater precision
required in making liquid metal heat transfer corre
lations

11
NCLASSIFIED
DWG 23307

EQUATICN (12)
Ly
FOR 5" 25

O RESULTS FROM USE OF MEASURED WALL TEMPERATURE
A RESULTS FROM USE OF WILSON LINE ANALYSIS

 

Fig 9 Comparison of the NaK Results with the Werner King and Tidbaill Equation

 

CONCLUSIONS

The fluoride salt can be considered to be an
ordinary fluid with respect to heat transfer and the
equations in the literature can be used to design
heat exchange equipment or to predict its per
formance A similar conclusion was made by
other workers at ORNL for the nonuranium bearing
fluoride salt mixture NaF KF LiF (115420465
mole %) '* This would not include cases where
the fluid had self generating heat sources

Use of iron bearing alloys such as type 316

 

144 W Hoffman Preliminary Results on Flinak Heat
Transfer ORNL CF 53 8 106 (Aug 18 1953)

12

stainless steel together with material not con
taining tron 1n high temperature fluoride salt circu
lating systems will result in mass transfer of the
iron to cold surfaces if there 1s turbulent flow and
if there extst large temperature differences Fric
tional resistance to flow will be greatly increased
and heat transfer performance of equipment will
be likewise impaired

The Wilson Line approach can be used to de
termine heat transfer coefficients of fluoride salts
at elevated temperatures 1n a double tube heat
exchanger where sodium potassium alloy 1s used
as the cooling or heating fluid
NOMENCLATURE

Constant

Outer area of heat exchanger center tube ft2

Inner area of heat exchanger center tube ft2
Transverse flow area of heat exchanger annuius ft2
Constant

Specific heat of the fluoride salt Btu/lb °F
Specific heat of the NaK Btu/Ib F

Constant

Product of specific heat and mass flow rate for the fluoride salt

Btu/hr °F
Product of specific heat and mass flow rate for the NaK Btu/hr °F
Tube or pipe diameter in general ft
Inner diameter of center tube ft
Outer diameter of center tube inner diameter of annulus ft

QOuter diameter of annulus ft

Equivalent diameter of the annulus or hydraulic diameter (D] ~ DO)

ft
Film heat transfer coefficient for the fluoride salt Btu/hr ft2 F
Film heat transfer coefficient for the NaK Btu/hr ft? °F
Thermal conductivity of center tube wall material Btu/hr ft °F
Thermal conductivity of the fluoride salt Btu/hr ft °F
Thermal conductivity of the NaK Btu/hr ft °F
Length of heat exchanger center tube ft
Differential length of center tube ft
Constant equtvalent to (U nD ), Btu/hr ft F
Constant
Constant
Rate of heat transfer from the fluoride salt stream Btu/hr
Rate of heat transfer to the NaK Btu/hr

Average rate of heat transfer between the fluoride salt and NaK
streams Btu/hr

Differential rate of heat transfer Btu/hr
Bulk temperature of stream °F

Bulk temperature of fluoride °F

Bulk temperature of NaK F

Axis or center line temperature of stream °F
Temperature of tube wall surface °F

Inlet fluoride axis temperature to heat exchanger F

13
14

F2
N1

N2

L

F(0 4)
EN(o 4)

At F
At
At

At

A‘LM

Qutlet fluoride axis temperature from heat exchanger °F

QOutlet NaK axis temperature from heat exchanger °F

Inlet NaK axis temperature to heat exchanger °F

Fluoride axis temperature at 0 4L °F

NaK axis temperature at 0 4. °F

Center tube surface temperature on fluoride salt side at 0 4L °F

Center tube surface temperature on NaK side ot 0 4. °F

'Fo 4) + th} oF
2

Fictive fluoride salt film temperature at 0 4L [
Differential fluoride salt bulk temperature °F
Differential NaK bulk temperature F

Over all heat transfer coefficient based on outer area of heat ex
changer center tube Btu/hr ft2 °F

Over all heat transfer coefficient at zero ordinate of Wilson plot

Btu/hr ft2 F
Mean flow velocity ft/hr
Mean NaK velocity in annulus fps
Mass flow rate of fluoride salt Ib/hr
Mass flow rate of NaK |b/hr

Temperature difference of fluoride salt and NaK at any cross section
of heat exchanger °F

Temperature drop of fluoride salt through the exchanger °F
Temperature rise of NaK through the exchanger °F

Temperature difference of fluoride salt and NaK at hot end of ex
changer °F

Temperature difference of fluoride salt and NaK at cold end of ex
changer °F

Logarithmic mean of At and At, F

Constant (EI]— + Cl-> hr °F/Btu
F N

Constant 3 1416

Mass density evaluated at bulk temperature Ib/ft3

Mass density of fluoride salt evaluated at axis temperature 1b/ft3

Mass density of NaK evaluated at axis temperature |b/ft3

Absolute viscosity evaluated at bulk temperature Ib/hr ft

Absolute viscosity of fluoride salt evaluated at axis temperature

Ib/hr ft
Absolute viscosity of NaK evaluated at axis temperature Ib/hr ft

Absolute viscosity of fluoride salt evaluated at film temperature

Ib/hr ft
Nu

Nu

Nu

Nu

an

Re

Re

Re

Ff

Re

Pr

 

 

 

PrD v
HF

PrD Vg

 

Kry
D v

pNeN

 

 

 

Absolute viscosity evaluated at tube surface temperature |b/hr ft

Nusselt modulus (tube)

Nusselt modulus for fluoride salt

Nusselt modulus for NaK

Nusselt modulus for an annular passage

Reynolds modulus

Reynolds modulus for fluoride salt

Reynolds modulus for fluoride salt with viscosity evaluated at tpy

Reynolds modulus for NaK

Prandtl modulus

Prandtl modulus for fluoride salt

Prandtl modulus for fluoride salt with viscosity evaluated at try

Prandtl modulus for NaK

15

 
16

APPENDIX 1

EQUATION FOR INTERMEDIATE AXIAL STREAM TEMPERATURE WITH
LOGARITHMIC DISTRIBUTION

To evaluate the temperature difference across the film at the point in the heat ex
changer where the center wall temperature was measured it was necessary to determine

the stream temperature at this position
® @

., _L
! A,

Aty

 

l—— D‘_{
ok

K

>

~

 

 

— . |
Aty _‘“_"N_ /-N// — ¢
} art
gl —e |‘m— N

By assuming a constant over all heat transfer coefficient with steady state operation and
neglecting heat losses the basic equation for this configuration is

 

 

 

 

 

 

(N dq = -wFCthF = -,uNcthN = UoerodLAt

For the fluoride stream
U aD dLA:
O 0o

2 dt ., = -~
(2) F v er

To integrate Eq 2 At must be written as a function of L This is done in the usual
derivation of the logarithmic mean temperature difference found in the literature there-

fore

(3) At = Arje”PML

The constants have been grouped and simplified as follows

= C and WNEN = CN

 

“F°F T “F
] ]
B = — — —
CF CN
M = UaaD
o
Substituting Eq 3 in Eq 2 gives
MAt,
@ dp = - oML g
F

 
Integrating and considering the boundary condition when L. = 0 and tp =tg, Eq 4
becomes
At _
(5) tp = tgy - E(l ~ o FML)
In like manner for the NaK stream
At, )
(6) ty = I —fi(l ~ o7 AL

Equations 5 and 6 can be written for the position where the wall temperatures were
measured at 0 4L and also changed to involve only the measured temperature quantities
By noting that

] - N
BC. = 1 - Mn and BC, = M
At tn
n
and by using Eq 5
04
0 e S
N 5
T,
and by using Eq 6
At fitf
' A At \® 4
(8) N &) = TN —-——K;[l -<Zt—2-> }
N 1
A

17
18

APPENDIX 2

DERIVATION OF EQUATIONS FOR WILSON LINE ANALYSIS

In a liquid to liquid heat exchanger where neither fluid changes phase if one of the
fluid velocities 1s held constant and the other 1s varied over a range of settings 1n turbu
lent flow the film coefficient of the fluid at constant velocity can be determined by a
graphical method called the Wilson Line or Wilson plot

When the mean temperature of the constant velocity flusd does not vary appreciably the
film coefficient will be essentially constant The film coefficient of the other fluid
where there are not large changes of physical properties with temperature 1s a function
solely of the velocity

The graphical method was used 1n this experiment to obtain coefficients of the fluoride
salt and thus separate the over all heat transfer coefficient to obtain a NaK film coeff
cient |f the series resistance concept 1s used the over all coefficient 1s related to the
film coefficients as follows

1 o ? 1
Uo bFD 1 2"aw bN

(1)

 

Equation 1 neglects the resistance of any foreign deposits on the heat exchanger walls
but such deposits would enter the equation 1n a term similar to that for the wall res:s
tance that 1s the middle term in the right side of the expression

The equation relating the NaK coefficient (Eq 12 in the text) reduces to

(2) by = a + bUNOB

ForD_ =0329mn D =02691n andk =34 8 Btu/hr ft °F Eq 1 above becomes

1222
= - + 00000788 +

0
F a+buN

(3)

 

1
Uo 8

Sincethe NaK velocity 1s the only significant variable a plot of l/Uo vs 1/a + buNo 8)
should produce a straight line For such a plot the constants a and b must be known
They could be taken from Eq 12 of the text instead 1/U_ was plotted against 'I/vN0 8,
as 1s usually done with ordinary fluids The data of the experiment proved to be fairly
well correlated by straight lines

Inspection of Eq 3 above shows that when the term involving ”No 8 approaches zero
or when the Wilson Line 1s extrapolated to the zero ordinate 1t 1s posstble to write for
all the intercepts

1222

(4) + 00000788

 

]
Uoo F

From Eq 4 it 1s possible to solve for the fluoride salt film coefficient that s

1222
(5) by =

1
— ~ 00000788
)

oo
Since, the fluoride salt film coefficient 1s essentially constant along any of the lines 1t
is possible to separate the NaK film coefficient from any of the over all coefficients
Substitution in Eq 1 above gives

1 1
b = =
(6) N ] 1222 1
— — —— - 00000788 —
Uo bF Uo U

 

]

oo

 

APPENDIX 3

PHYSICAL PROPERTIES OF THE FLUORIDE SALT NaoF ZrF, UF, (50-46-4 mole %)
AND OF SODIUM POTASSIUM EUTECTIC ALLOY

The physical properties of the fluoride salt were taken from the third edition charts of
the ANP Physical Properties Group' and are represented as a function of temperature in
Fig 10 The charts are revised pertodically as new data become available The NaK
properties given 1n Fig 11 were taken from the second edition of the Liquid Metals

Handbook 1%

 

5 N Lyon (ed ) Liquid Metals Handbook NAVEXOS P 733 (Rev ) (June 1952)

19

 
20

VISCOSITY (Ib/h £

DENSITY {1b/ft%)

e 4
DWG 23308

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

50
mp=960 F
AN Cp=031£003(Btu/lb °F)
40
(1022 F-1562 F)
HEAT OF FUSION=50 cal/cm3
[ VISCOSITY

30

20 \\‘\

10

0 / 20

0\\ k CONDUCTIVITY /
e
10
210 0
———] p DENSITY
o
200 \
190
{80
900 1000 1100 1200 1300 1400 1500 1600

TEMPERATURE ( F)

Fig 10 Physical Properties of the Fluoride Salt vs Temperature

F)

THERMAL CONDUCTIVITY {Btu/hr ft
HEAT CAPACITY (Btu/1b-°F)

DENSITY (1b/ft3)

UNCLASSIFIED
DWG 23309

 

14
13
12
0 270 11
{0
09
08
07
0 260 06
05
04
0 250
170
55 0 165
54 0
53 0 160
52 O
51 0 15 5
500
49 0 150
48 0
47 0 14 5
460
450 140
200 300 400 500 600 700 800 900 1000 1400 1200

TEMPERATURE (°F)

Fig 11 Physical Properties of NaK (56 wt% Na-44 wt% K) vs Temperature

VISCOSITY (lb/hr ft)

THERMAL CONDUCTIVITY Btu/hr—it2( F/ft)

21
APPENDIX 4

SAMPLE CALCULATION OF DATA POINT 4

Experimental Data

tpy = 1323 7°F
tpy = 1309 1°F
tyy = 1179 8°F
ty, = 1067 9°F
wp = 8450 Ib/hr
wy = 1160 Ib/hr
t,n = 1201 4°F

Heat Balance

9p = wpCpltpy = tp))
(8450)(0 31)(14 6) = 38 240 Btu/hr

In = wnenltny = tno)
= (1160)(0 248)(111 9) = 32 190 Btu/hr

(Heat loss less than 1% and therefore neglected)

gp —ay 6050

— = 16%
95 38 240

 

g = 35220 Btu/hr

Over all Heat Transfer Coefficient
qav
U = ——
o
AoAtLM

(tpy —tn1) = {tpy —tn2) 1439 - 241 2

 

Aty = - 188 6°F
LM
In—— 2412
F2 N2
35 220

U =——— - 2357 Btu/hr ft2 °F
° =0 0792(188 6) W

Wall Temperatures

1201 4 (measured)

 

 

whN
D,
Tgy In
th = th +
27k L
w
0 329
35220 In
02
=12014 + ————— = 1236 6°F

27(34 8)(0 922)

22
Stream Temperatures

At, (At2 )04
t =tpy ———m—|1 = {—
F(0 4) Fl AtN At

1
1 -
AtF

 

1323 7 1439 [1 - 1229] = 1318 8°F
(1-766) -

AtN
At,—

‘AtF Aty \® 4
EN(o 4) = INy ‘——At"—l “\ %
N

1
1

 

 

AtF

1179 8 — (4 947 66) = 1142 3°F

Film Coefficients

 

 

 

 

 

b qav
F =
Az[‘F(o 4) " t, ]l
35 220 ,
= —————+—— = 6620 Btu/hr ft< °F
0 0647(82 2)
b qav
N ———————
Alt, N~ tN(o 4))
35 220
—— = 7520 Btu/hr ft2 °F
00792059 1) v
Wilson Line
1 ,
— = —— = 0 000425 hr ft< °F/Btu
U, 2357
wy 1160(144)
vy = = =2 15 ft/sec
PnAL, (48 2)(0 448)(3600)
Lol osa
v 08 184
From Fig 5 at = 0 for this line 1s 0 000292
o0 UNO 8
1222
g = ——————————= 5740 Btu/hr ft? °F
— 0 0000788

0o

23
1
- = 7500 Btu/hr f12 °F

bN
11222
— 00000788

U
o

 

 

F

Dimensionless Moduli

At tp, = 1278°F

cp = 031 Btu/lb °F
Ry = 252 Ib/hr ft
kp =134 Btu/hr ft °F

beD, 662000 269)

 

 

Nu, = e N7
CF TR T T134(12)
4w 4(8450)(12)
Re ., = _ - 19 080
fl'p‘.Fsz (25 2)(0 269)
CEiE; 0 31(25 2) ’

 

/
3
Prp, = T =583 (Prp)° = 1801

1

- 4
Nup(Prp) ° =62

At ¢ = 1319°F

F(0 4)
cg = 031 Btu/lb °F
pp =23 1 Ib/hr ft

kp = 134 Btu/hr # °F

At t,p = 1237°F

27 5 tb/hr ft

=
It

wF

b D

FP: 6620(0 269

Nu, = 8600289
ko 134(12)

 

- 4w 4(8450)(12) 20 800
°F TupD. | (23 1)(0269)

 

“FEF 031023 1)
Pro = =

- 535
F
kr 134

 

24

 
]
(F’rF)é =175

 

 

At 1y ¢ = 1142°F
cy = 0248 Btu/Ib °F
py = 477 Ib/it?
py = 04 Ib/he ft
ky = 16 65 Btu/hr ft °F
bnDe  7520(0 495)
Nuy = = ~ 1845
ky 16 65(12)
PNP YN 47 7(0 495)(2 15)(3600)
ReN = = = 38 420
EN (12)(0 4)
CNEN  0248(0 4

ky 16 65

Rey x Pry =229

25