ORNL-2198.txt

 

 

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“ AEC RESEARCH AND DEVELOPMENT REPORT ... 02 &

Features of Aircraft Reactors

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ANALYTICAL AND EXPERIMENTAL STUD IES
 OF THE TEMPERATURE STRUCTURE

 
    
 

WITHIN THE ART CORE

H. F. Poppendiek
N. D. Greene

L. D. Palmer

G. L. Muller

G. M. Winn

  
 
   
   
   
  
 
 
 
  
  
   

 

 

OAK RIDGE NATIONAL LABORATORY
OPERATED BY

UNION CARBIDE NUCLEAR COMPANY

A Division of Union Carbide and Carbon Corporation

POST OFFICE BOX X - OAK RIDGE, TENNESSEE

 

   

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Bty o Wk TP s A A h e e

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ORNL-2198 bz
C-84 - Reactors-Special

Features of Alrcraft Reactors

 

 

 

This document consists of 106.pages.
Copy & of 272 copies. Seriles A.

 

 

Contract No. W-T4O5-eng-26

Reactor Experimental Engineering Division

ANALYTICAL AND EXPERIMENTAL STUDIES OF THE TEMPERATURE STRUCTURE
WITHIN THE ART CORE
H. F. Poppendiek
N. D. Greene
L. D. Palmer

G. L. Maller
G. M. Winn

DATE ISSUED

JAN 31 1957

 

  

 

OAK RIDGE NATIONAL LABORATORY

 

Operated by
UNION CARBIDE NUCLEAR COMPANY
» A Division of Union Carbide and Carbon Corporation
Post Office Box X
Oak Ridge, Tennessee R AT
. RN Vr%?f&{v 2
t&:;}fi'xr ‘?y m MARTIN MARIETTA ENERGY SYSTEMS LIBRARIES

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-1~ ORNL-21 "y
c-84 - Reactors-%
Features of Aircraft Reactors

  
   
   

INTERNAL DISTRIBUTION

 

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Document ‘Reference Section

 

142, AP Plant Representative, Baltimore .
143, AF Plant Representative, Bufbank e
144, AF Plapt- Rep?esentatlve, Nhriéfite_fih:u
145-147, AF Planfirneprésent@t;xg;’sfifi’%;yhnica
148-149, AF P1§E$NREfi?eSentgfiaafi;“figéwg% g
150. AF Plant-®RepPds Sentadim 1dge
151. Air Mefewse€¥“Riéa
152. Air Research and Development Command (RDGN)
153. Alr Technical Intelligence Center
154. Allison Division ,
155-157. AN ect Office, Fort Worth '
158 .8 ¥ que Operations Offig !
1598 Fdbdh 4l National laboratoryd # %a@ g
160§ & {;;srces Special Wespodd $4b¥dt, ‘Sandia
161§ b Jpreed ‘Spe¢ial Neapofs b #eft, Washington
1628 Bsikil Becretary of thefAfr¥Fgrffe, R&D
163-168¢ ¥ m Energy Commission, SNasHl ik-#on
1698 H1ge Memorial Institufeg £ § §
170-17 M Plant (WAPD) NN
175 j of Aeronautics # £
17 | of Aeronautics (CPAF¥ |
c1THE of Aeronautics, (RneB) HEpresentative
17§ ‘ _. Operations Offifed g 28
 17§.2CHiNoflo Patent Group @ E S Z 2
178 .SCHilfor Naval Researclf f # 4 £
179 - R r-General DynamiffsgCirfofation
179 Ehgiker Research and ey

 

<, W -] o
180-183. Genedhl Electric Compfnf'fl
184, Hartford Area 0ff1ce~J‘j
185. Headquarters, Air Force Speciel Wespons

Hoa TR

 

Feif gPm¥nt Laboratories

 
 
 
 

Center

 

 
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Lo Operations Office
Blls Atomic Power Laboratory
189 & , £

187i

f Beientific Laboratory

gd¥isory Committee for Aeronautics, Cleveland
jayisory Committee for Aeronautics, Washington
ks D& velopment and Material Center

Sbns Office L h
fwiation, Inc.ciAsrophy31cs Division)
¥iviation, Inc. (Canoga Park )’ |
bhfigent Corporationjof America |

blef of Naval oy%rations (OP-3610

201-220. Pratt $hil ¥ Bt 5y Aircraft Divfigian ( X Projegt) (1 copy ea. to
G’o Eo - =F o ! 7. g
R. A.

  
   

’?C E. Holtsinger,

. Farmer, H. £
AP Schmickrath,

f; W. Kelley, A}}‘:

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. §§ .zs
. 2 ",
.
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?R, N. Wallace, a

   

 
 
  

221. | g

222, ?f Aviation Medicine fivjf%-

223. i4 Electric Products, Igfg % i

22k, *bject Rand 4 B % S F

225, i{y of California Radigt$on B # Livermore .
206-245, r Development Center W WCESE ea. to C. D. Gasser

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d) ‘ , o x
246, Technica& Research Group, New York P g

27, Division of Research and Development, AEC, O
248-272, Technical Information Service Extension, Oak Ridge

 

 
 

TABLE OF CONTENTS

Page

SMARY '.‘.....l..lfl.......’..‘...l.......................I.........

NOMENCLATURE 4. coeveesroneanssocososcoaceocoasoencenssesocososnesss
INTRODUCTION .. cieiencoreancacsessrsasoeocensenensosensosoncnocsosss
MATHEMATICAL HEAT TRANSFER ANALYSES +.veeveocconorcscaccccocnoeoseoss
Uncooled Core Wall Temperature Structure ....,.}.....;...........
A Cooling Analysis for Variable-Gap Channel (Idealized ART) .....
Radial Fuel Temperature Structure with Wall Cdoling cesesscenannse
Transient Temperature Analyses ...............é.;....;...........
EXPERIMENTAL SYSTEM Pe ettt eeaiteettenesntasesatseerecnrotnaeas

Technique .......l....'.‘.i.........l.............";....l........... 30

BERERR ow -

Electrode GEOMEtrY veveeeeeeeeeeroreonnssoosssaseccoccooscaneseos 31
Flow Clrcult v rtereeteeeeeeesoeonoeaososcosoneeoosnnonsenenes 33
Half-Scale Core Model Tececesirettestetestesesoscesoassasnsensnss 33
Power Circuit and Instrumentation ......ceeiveeeeseeneccooeeeeens 42
EXPERTMENTAL PROCEDURE .. .uiveuseercencocecaconoenoosnnnncconeoneses Lg
Calibration ....covecuriiiiiieiieieeinerersronaccsosaonnannsansenss U9
Operational TechniqUe .iueeeeeeeeeeeesocecosecocesoooeososennsss.s 50
MEAN AND TRANSIENT TEMPERATURE RESULTS vvveveocecsccnsocsocecacoeens 53
SWIrl-Flow Case; TWO PUlDS tveeeeerereroroocascocenoesoosenonsses 53
Vaned-F1low Cas€; TWO PllIDS «eueeueesrosooeonosoonescsennennnennn, 59
Swirl-Flow and Vaned-Flow Cases; One PUmD ..eeeeeeesnn.. ceesssesses 1
GENERAL COMPARISON OF HYDRODYNAMIC AND THERMAL FIELDS .............. T3
CONCLUSIONS . 4ovcooesncsoneocncesacnsssneooereossosesssscosconnooses TT
ART Core ....cc0ve ®erecesseessressrenscrsssastsresasccsrrosccnnce [T
RefiectoreModerated Reactor Cores in General ...cceeeescoorcecees 79
New Core Configurations .vecieieeeeeereoeeseonsosssesoseocencnnesa 80
ACKNOWLEDGEMENTS « e vveuausennsnornennensosensesssnsonaonennenneas 81

  
-yil-

Page

   

P & =
wlectrolysis Research ..eeceees.. Ceceseseseevsesescsscstasacscracnas 02
Physical Properties of Electrolyte ...e.ceececescsosesssssscssseans 85
Materials of Construction and Flow System Components .ceceeecesees 92
Calibrations weeeeeecerccesossosocosoccssscssssoscsssnssnsssnsoses I
REFERENCES .eccovecccsssosoncssssasscessscsossscssssssnsscsssssansssesces I9

i

 

 

 

 
 

SUMMARY

This report is concerned with a series of studies which describe the
temperature structure within the core of the ART for several different
entrance flow conditions. Both analytical and experimental techniques of
analysis are used in the investigation. Mean and transient temperature
fields are predicted on the basis of the mathematical behaviour of ideal-
ized cores; these results are compared with experimental temperature meas-
ufements obtained in a half-scale model of the ART core, within which the
volume heat sources are generated electrically. |

The heat transfer studies presented here reveal the following facts
about the ART core:

1) Unless the core shell walls are cooled, maximum wall temperatures
ranging from 1750°F to 1850°F (depending upon the type of entrance
flow) will exist near the core exit. About three per cent of the
heat generated within the core must be extracted to accomplish
the cooling task.

2) Unless the sodium coolant flows through the cooling annuli in a
uniform fashion, hot and cold spots will exist in the core shells.

3) Peak fuel temperatures at the core exit, under wall cooling con-
ditions, are from 100 to 170°F higher than the mixed-mean fuel
temperature (depending upon the type of entrance flow).

4) The temperature structure within the core is significantly asym-
metric with respect to peripheral position when one pump is not

in operation.

 
 

_— "2 L

5) The core shell interface afid fuel temperatures are transient in *
nature (frequency spectrum ranges from about L/2 to 4 cycles per
second).
It is stiggested that a greater research effort is required to determine
how seriously these temperature structures influence material strength and
corrosion. Some of the general principles upon which circulating-fuel re-
actors should be designed from the standpoint of heat transfer and fluid

flow are discussed. Several reactor cores other than the ART are reviewed,

 

 

 
eddy

 

 

-3- ‘Ffigfififli

NOMENCLATURE

Letters

cross sectional heat transfer area, ftz

thermal diffusivity, £t2/hr

fuel thermal diffusivity, £t°/hr

Inconel thermal diffusivity, ft?/hr

distance between coolant channel walls in Figure 3, ft
distance between fuel channel walls in Figure 3, ft
heat capacity, Btu/l1b °F

coolant heat capacity, th/lb oF

fuel heat capacity, Btu/1b °F

Inconel heat capacity, Btu/lb °F

frequency, cycles/sec

coolant heat transfer conductance or coefficient, Btu/hr ft2 °F

fuel heat transfer conductance or coefficient, Btu/hr £t° OF

reciprocal of the thermal diffusion length, £t 1

thermal conductivity, Btu/hr £t° (CF/et)

sum of turbulent and molecular conductivity, Btu/br £t° (CF/pt)
fuel thermal or eddy conductivity, Btu/hr £1° (°r/ft)

Inconel thermal conductivity, Btu/hr £t2 (°r/£t)

channel wall thermal conductivity, Btu/hr £t° (°F/ft)

total axial length of channel or core, ft

coolant mass flow rate, lh/hr

fuel mass flow rate, lb/hr

 
q

qcooling

qfuel
4

r

tey

t, (¥)

tinterface

m

g

t
mo

e ‘I‘Efifil'7

total electrical power generated in the electrolyte in core, >
Megawatts

heat transfer rate, Btu/hr -
channel or core cooling heat transfer rate, Btu/hr

heat generation rate within volume of fuel, Btu/hr

cooling heat transfer rate at interface 1 in Figure 3, Btu/hr

distance from channel center, ft

distance from channel center to where the reference temperature
td is stipulated, ft

one-half distance between channel walls, ft
breadth of channel walls in Figure 3, ft

temperature, °F

a uniform step function temperature distribution, Op

mixed-mean-coolant temperature, oF

mixed-mean coolang temperature at entrance of channel, °F -
fluid temperature at channel center,-oF

°F

a reference temperature at radius Ty

mixed-mean fuel temperature, p

mixed-mean fuel temperature at entrance of channel, °F
initial temperature distribution, °F |

fuel-Inconel interface temperature, p

mixed-mean fluid temperature, °F

mixed-mean electrolyte temperature at entrance of core model, 0F

mixed-mean electrolyte temperature at exit of core model, °F *

uncooled channel or core wall temperature, F

fuel-wall interface temperature in Figure 3, °F

 

 
 

 

coolant-wall interface temperature in Figure 3, F

total temperature fluctuation, °F

axial fluid velocity distribution, ft/hr

mean fluid velocity, ft/hr

mean vectorial fluid velocity, ft/hr

radial volume-heat-source distribution, Btu/hr ft3

3

mean volume-heat-source, Btu/hr ft
mean volume-heat-source of coolant, th/hr ft3
volume-heat-source of fuel at channel center, Btu/hr ft3
mean volume-heat-source of fuel, Btu/hr ft3

radial volume-heat-source distribution in fuel, Btu/hr ft3

radial volume-heat-source distribution in Inconel wall, Btu/hr ft3
mean volume-heat-source of channel wall, th/hr ft3

axial distance from core entrance, ft

¥y coordinate which is normal to the x coordinate, ft

thickness of Inconel wall, ft

weight density, lb/ft3

fuel weight density, lh/ft3

Inconel weight density, lb/ft3

channel wall thickness, ft

eddy diffusivity, £t>/hr

a mean eddy diffusivity of a high velocity fuel eddy, £t2/hr

time, hr

kinematic viscosity, fta/hr

coclant kinematic viscosity, ft?/hr

fuel kinematic viscosity, ft?/hr

current density, am.ps/in2

 

 
Terms

 

 

 

 

 

 

 

 

 

Wiid

h 4r
Nu, = fk , Fuel Nusselt Modulus for channels
f
yc_ v
Pr = 2 Prandtl Modulus
Y,C .V
Pr, = —ELL | Fuel Prandtl Modulus
hig
u hro
Re = v , Reynolds Modulus‘for channel
ficab
Re = v’ Coolant Reynolds Modulus for channel
c
ushro
ReS = v , Vectorial Reynolds Modulus for channel or core
fisfhro
(Res)f = =5 , Vectorial fuel Reynolds Modulus for channel or core
f
T = (tf - tc)
Ty (tfi' tci)
N =5 lc “m 1c
£ pf ¢ pc
2
o _ Wfbfs ] chcs ] Wwas
Dp cpf o, cpc B, cpc

U Overall heat transfer conductance or coefficlent, th/hr 't

 

Normalized vectorial velocity profile

Ko i

2 oF

 

 
 

 

 

 

 

 

 

 

-7- Viod)

r
p =
0
W Wb
il
W c
AtVHS - The wall temperature rise above the mixed-mean fluidotemperature
¢ that exists for the coolant with no wall heat flux, F
AmVHS The wall temperature rise above the mixed-mean flgid temperature
f that exists for the fuel with no waell heat flux, F
//AthS Dimensionless wall-fluid temperature difference
—}2 for a parallel plates system with a uniform
\ ko uniform W(r) volume heat source and no wall heat transfer
AmVHS£ Dimensionless wall-fuel temperature difference
—> for a parallel plates system with a uniform
w.r volume heat source and no wall heat transfer
f o
uniform W (reference 2)
kf f
A‘tVHSf Dimensionless wall-fuel temperature difference
— for a parallel plates system with a nonuniform
Wfro volume heat source and no wall heat transfer
nonuniform W (see section on Mathematical Heat Transfer
k f
f Anslyses)
to -t Dimensionless wall-fluid centerline temperature
7 r2 difference for a parallel plates system with no
f o wall heat transfer
n arallel plates
T

 

t -t
m
Wors
parallel plates

 

ke

 

Dimensionless fluid temperature above the mixed-
mean for a parallel plates system

 
— 8- vi%d
INTRODUCTION

During the period 1953-1954, the ANP Project made the decision to de-
sign and construct a 60-Megawatt circulating-fuel reactor of the reflector-
moderated type which was named the ART (reference 1). The circulating fuel
flows into a thick annular core whose flow cross-sectional area increases
by a factor of four from the inlet to the equator, and then decreases by a
factor of four from the equator to the core exit. A preliminary heat trans-
fer analysis of the proposed core configuration was conducted at that time.
It was shown that the ART core would have certain unique thermal character-
istics which would perhaps be undesirable. These characteristics were
identified as follows:

1. Large Radial Temperature Differences Within the Fuel

Mathematical temperature solutions for a simplified flow system
revealed that significant radial fuel temperature differences
would exist in the reactor core primarily because the volume heat
sources within the fuel were high and the mean thickness of the
fuel annulus was great (reference 2). The core shell wall tempera-
tures were so high that a wall cooling system capable of extract-
ing several per cent of the heat being generated within the core
was required.

2. Asymmetric Temperature Core Shell Structure

From elementary fluid flow considerations, it became apparent that
flow asymmetries could exist under certain circumstances in the

fuel passing through the core or within the sodium flowing in the .

'k;_::i wall-cooling annuli that had been proposed (reference 3). Under

 
s -9~ Nl

such circumstances, asymmetrical core shell temperature dis-
tributions would be established, giving rise to hot spots.

3. Transient Temperature Field

On the basis of fluid flow phenomena, it was believed that the
four-to-one area expansion ratio in the northern hemisphere of
the core would, in general, create unstable flow within the ART
fuel annulus. The combination of a nonuniform radial tempera -
ture profile and an unstable velocity field would, of course,
generate a transient temperature field that could initiate
cyclic thermal stresses in core shell and heat exchanger tube
walls.

One of the first steps taken in evaluating the abeve problems vas to
study the fluid flow in simple systems that in a sense approximated the
actual ART fuel annulus. Nikuradse's classical experimental study of fluid
flow in diverging and converging channels (reference 4) was used to describe
the flow features in the northern and southern hemisphere of the ART core
for the straight-through flow condition (reference 5). On the basis of
Niku;adse's work, flow asymmetries and transients were predicted to be pre-
sent in the core for this case. The investigation of fluid flow between
curved channels by Wattendorf (reference 6) yielded fundamental information
on velocity and eddy diffusivity distributions which was used to estimate
the asymmetric hydrodynamic structure in the ART core for the case of super-
posed rotational flow (reference 7).

In 1954 the phosphorescent particle technique was first used to study

the flow features in a quarter-scale model of an early version of the ART

 

 
core. For stralght-through flow, large reverse-flow layers were found to
exist on the outer core wall (reference 8); these were typical of the flow
separations found by Nikuradse in large-angle diverging channels. When a
significant rotational component was superposed on the axial flow, a reverse-
flow layer next to the inner wall in thé northern hemisphere was observed
(reference 9), These flow visualization studies as well as a quantitative
investigation of the velocity structure in the core (reference 10) also
demonstrated that the flow was generally transient in nature because of
hydrodynamic instability. These data substantiated the earlier belief that
flow transients would exist in the ART core and supported the prediction
that corresponding temperature transients would also be present. Detailed
information on this hydrodynamic research, chiefly with quarter-scale models,
is to be summarized in ORNL-2199.

Mathematical analyses of the temperature structuré in an idealized ART
core with sodium wall cooling were carried out (references 11 and 12). De-
terminations of cooling requirements and sodium flow rates were made. From
these analyses maximum fuel-Inconel and sodium-Inconel interface temperatures
at the core exit were calculated. The presence and magnitude of the high
temperature peak within the fuel a short distance from the core walls was
also described. Inconel-fuel interface temperature fluctuations in the ART
core shell and heat exchanger tubes were considered. Estimates of interface
temperature fluctuations under conditions of momentary flow stagnations and
high-velocity flow instabilities were made.

In order to determine information about the asymmetries in the mean

temperature structure within the ART core and wall and fluid temperature

“-“3 .‘i“ —
LN
£

 

 
- 1. W

fluctuations, it was decided to obtain experimentally the core wall and
fluld temperature structures. Several types of entrance flow conditions
wvere studied in a hqlf-scale core model for the uncooled-wall case. The
volume heat source was generated electrically within an electrolyte which
circulated through the core model. The experimental mean and transient
temperature fields determined in this system were generalized and compared
with predicted temperature fields (references 13 and 14).

After the detailed analytical and experimental descriptions of the
mean and transient ART core temperature structures presented here, the in-
fluence of the temperature field on structural integrity will be considered.
Certain fundamental research on corrosion and material strength is suggested

in view of these heat transfer studies.

 

 

 
— -12- oA

MATHEMATICAL HEAT TRANSFER ANALYSES

1. Uncooled Core Wall Temperature Structure

It was determined from the ART hot critical experiment that, on the
average, the volume heat source at the core wall was two times as large
as at the centerline. Thus, a new radial temperature solution account-
ing for the source variation in a parallel plates system was derived.
An earlier analysis (reference 2) only accounted for a uniform radial
source distribution. The boundary value problem is defined by the

following equations:

u(r) g& = 3 [a + €(u, r)] g% + Wy

7cp
a9 (. - - (1)
Th (r = ro) =0
t (r = rd) = t,

From the activity data obtained in the hot critical experiment by

A. D. Callihan et &l, it was determined that the averaged, ;adial power
density distribution could be represented satisfactorily by a hyperbolic
cosine function (see Figure 1). This power density function together

with the generalized turbulent velocity profile was substituted into the
above differential equation. The solution of this boundary value problem
for established flow was obtained (reference,izj, and it was found that

the resulting uncooled-wall temperature abovg the mixed-mean fluid tempera-
ture was more than twice as great as the corresponding temperature differ-
ence in a uniform volume-heat-source system. The two temperature profiles
in dimensionless form afe shown plotted in Figure 2 for Re = 100,000 and -

¥Pr%=’§ which are representative of ART conditions.

 

 
 

-13- ORNL=~-LR-DWG, 17989

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

LOCAL ACTIVITY/ CENTERLINE ACTIVITY AND W/ WE

 

 

 

 

 

 

 

 

2-6 I I
o
2.4
2.2
o

2.0
{8 °

i
‘.6 — - -

w_¢_ = cosh r k,p —\ OA
{.49 4
L~ o
A
2 P o
A
/o
10 pmo—"t"2T" o
08 RELATIVE ACTIVITY DATA
(CALLIHAN ET. AL.)
0.6 A 10in. LEVEL
O EQUATOR
04
0.2
o I
0 0.2 0.4 0.6 0.8 {.0
¢ p WALL

Fig. 1. Activity Data for ART Core and a Simplified Radial

Volume - Heat

- Source Distribution

 
-14- ORNL-LR-D!/G. 17990

 

3.0

 

 

A

2.2 \
2.0x 1079 \

C R

 

 

 

 

 

 

 

 

 

 

 

_t-te 16 w_. cosh roKop
wmroz wc
K {4 \ )
{.2 N

10 xio"‘\ \ -
AN
L\

N

N

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.2 N
0 1
1.0 0.8 0.6 0.4 0.2 0
WALL i ¢ ’
"o

Fig. 2. Dimensioniess Radial Temperature Distributions in
Parallel Plates Systems with No Wall Heat Transfer (Re=100,000
and Pr: 4)

 

 
- ¥ :
. '
-

2.

-15-

  

A Cooling Analysis for a Variable-Gap Channel (Idealized ART)

A variable-gap channel representing the spiraling annular passage

through which the fuel flows in the ART with the swirl-flow entrance

was studied. The variable-gap channel was divided into a series of

channels with parallel walls, having different wall spacings. The

heat transfer analyses of these individual channels were performed as

described previously in ORNL-1933. The idealized system shown in

Figure 3 for each channel is defined as follows:

a)
b)
c)
d)
e)

£)

Thermal and hydrodynamic patterns are established (long channels).
Steady state exists.

Volume heat sources exist in the fuel, wall, and coolant.

Physical properties are invariant with temperature.

The fuel channel is being cooled nonuniformly along its length by
the coolant.

The walls of the fuel channel are thin.

The three equations describing heat flow from the fuel to the coolant

can be expressed as,

dg, = h.dA (AtVHS + tp - tl)
f
iz‘wa k_
Gy + g dh =g () - b))
dg, + W 5 dA = h dA (1:2 -t - AL, )

c

From equations (2), (3), and (4) one can obtain,

dql

= Usdx (1;f -t + AtVHsf - AtV.Hsc - Atw)

(2)

(3)
(%)

(5)

 

 
ORNL-LR-DWG. 17991

_]6..

 

 

 

 

COOLANT X
3
1
FUEL
p A
1
COOLANT
—— 8 —
Ky
%
t
t2
Q

 

 

* Fig® 3. An Element of the Varioble-Gap Channel (Idealized ART)

 
The two additional equations arising when making a heat rate balance on

the two fluld streams in a length dx are,

Wb dA m_c
_ M Ml
a9 =3 2 ©)
dg, + W b dA = m.ccpcdtc - W b dA (7

From equations (6) and (7) one can obtain,

 

 

 

dT = - Ndg, + M"dx (8)
where,
T = tf - tc
N =2 lc T om i |
I pf c pc
2
v Wobs _ Wébcs _ W bs ‘fi%

mfcpf mccpc mccpc

Upon substituting equation (5) into (8) and reducing, one obtains the

 

 

 

 

 

solutions,
| M", -NUsx M"
T + AtVHsf- AtVHSC- at, = (T + AtVHSf- AtVHSc- oty - wo) e + TS (9)w
1 M" ~-NUsx M"
4 = § (To+ AtVHSf AtVHSc ot Img) (L -e ) + ¥ X (10)
q, + W 8sx + W b sx
1 W ccC
te " By < m (11)
c pe
Wfbfsx 94
b =Y “me T om,ec (12)
£Opf “e Cpr
2
U ‘
£, = - B (T + Atmsf' AtVHSc-Atw) + AtVHSf+ t, (13)

|
N 18- v oL

& w
t, =t - U‘E-(T + AtVHSf- A“vnsc Axw) - on | (14)

The fuel, wall, and sodium temperatures within the ART core as well

as the sodium cooling requirements and flow rates were determined with

the mathematical relations developed above for the following specific

conditions that define the ART core with the swirl-flow entrance.

Reactor fuel: Fluoride composition No. 30 with properties evaluated
at 1425°F

Coolant: Sodium with properties evalusted at 1125°F

Wall material: Inconel

Fuel power densities: Radial profiles obtained from "ART hot

critical” experiment (see Figure 1)
Inconel wall power density: A mean value of 5& watts/cc
Beryllium power density in vicinity of sodium annuli: A mean value of
16.5 watts/cc
Equivalent power density in sodium™: A mean value of 52,8 watfs/cc
Mixed-mean fuel temperature rise:; About 350°F, depending upon the

total reactor power and wall-cooling losses

 

Gamma and neutron heat generated in the beryllium reflectors is carried
away by sodium flowing through cooling holes and annuli. The heat gene-
rated in the thin layers of beryllium (next to the annuli) flows into
the sodium and hence raises its bulk temperature. In the anslysis, this
heat flow was simply treated as an equivalent volume-heatesource term in
the sodium itself. Although this technique correctly accounts for all
the sodium heat transfer, the beryllium-sodium interface temperature is
not explicitly determined. However, a separate calculation of the
beryllium-sodium interface temperature shows that it lies only about

4°F above the bulk sodium temperature.

gt -."i;

 

 
 

m, = 2.25 x 10° 1b/hr
(Res)f = 372,000 (footnote 2)
Prf = 2.3
fi} = 60 MW per reactor core volume (3.23 ft3)
Nuf = 1920
m, = 0.102 x 10° 1b/hr
Rec = 125,000
From the fuel Reynolds and Prandtl numbers given above, the following

uncooled-wall temperatures above the mixed-mean fuel temperatures were

 

 

 

 

determined:
Stymg_ .
> = 4,5 x 10 7 (reference 2)
Wf r, '
uniform W
k f
f
“ves, . s
— = (2.26) (4.5 x 10™7) = 10.2 x 10
W, r
fk 2/ nonuniform W (footnote 3)
£ £

 

2. A mean vector Reynolds number for the fuel was uSéd in the analysis be-
cause the maximum variation of the local vector Reynolds number was only
+ 12 per cent.

3. The analysis of the radisl temperature structure in the ART fuel under
actual nonuniform radial power density conditions described above in-
dicated that the dimensionless radial temperature difference for the
nonuniform power density case was 2.26 times greater than the corres-
ponding temperature difference for a uniform radial power density systenm.
An entrance length analysis which is discussed in a later section of this
report showed that the thermal and hydrodynemic flow layers are established
by the time the fuel arrives at the exit of the idealized core. However,
the whole northern hemisphere lies in the entrance region. The fact that
both the local Nusselt number and A‘vns functions vary in compensating

.H‘%fifirfashions in this entrance region validates the analysis there.

 
o Rt

The calculated temperature distributions in the fuel, wall, and
sodium coolant streams are shown plotted in Figure 4. The sodium flow
rates and cooling requirements in the variable-gap channel system per-
tained to a passage having identical vall areas from which heat was
transferred to the coolant streams. In the getual ART annulus systenm,
the inner asnd outer wall areas are not ideatieal; thus, the results of
the variable-gap channel snalysis were apportioned to account for the
fact that the ART outer wall area was larger thaa the lnner wall area.
The flow rates and cooling requirements so obtained follow:

flow rate in inner sedium annulus: O0.071 x 196 1b/hr

6 1b/hr

flow rate in outer sodium ennulus: 0,133 x 10
total cooling power capacity of sodium stream in Ipnmer annulus: 0,89 MW

total cooling power capacity of sodium stream im outer amaulus: 1.65 MW

total cooling power capaclty of both sedium streams: 2.54 MW

 

 
TEMPERATURE (°F)

1600
/
//“"‘__—_
i e
1400 / :
- =
//
1200 // —]
1, ///
//
B
—
10000 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

AXIAL DISTANCE (X/L)

Fig.4. Temperature Structure Within Idealized ART Core.

 

-lz_
3. Radial PFuel Temperature Structure with Wall Cooling

In order to illustrate the nonuniformity of the radial fuel tempera-
ture profile at the exit of the reactor core, the following analysis is
presented. The radial fuel temperature profile for the uncooled wall

case, under the representative ART conditions of Re = 100,000 and Pr = 4,

 

i1s graphed in Figure 5. 1In order to maintain the Inconel-fuel interface
temperature at the core outlet at approximately SOOF below the mixed-mean
fuel temperature, about 3 per cent of the heat generated in the core must%
be removed by the wall coolant. The radial fuel temperature profile for
this case was obtained by the superposition process described in reference 11
and is graphed in Figure 5 for purposes of comparison. Note that the peak
fuel temperature above the mixed—mean fuel temperature in the wall-cooled
case was still 62 per cent of the corresponding peak temperature difference .
for the uncooled wall case.

An enalysis of the degree of decay of the fuel temperature peak, for

the wall-cooled case, in the short passage between the core exit and heat

exchanger entrance will be discussed in a following section of this report.

 
 

-23- ORNL-LR-DWG.

 

 

3.0 l
- Re = 10°
| Pr= 4
W= Wq:_ cosh roky p
quoling
—_— = 3. { PERCENT
] uneI
2.0

 

_——NO WALL COOLING

 

 

 

 

 

 

 

 

 

 

 

t -1 i
— 10
. Wil N
k
WALL
COOLING
0
-1.0
- 1.0 0.8 0.6 0.49 0.2 0

 

P

Fig. 5. Radial Fuel Temperature Distributions in a Parallel
Plates System with and without Wall Cooling

 
 

Ve
- -
4. Transient Temperature Analyses
The hydrodynamic studlies conducted with the quarter scale ART core
models revealed that, under unstable flow conditions, a series of different -
types of flow phenomena existed in the vicinity of the core-walls; high
velocity layers, stagnant layers, and reverse flow or separation iayers
could be identified at different moments during the complicated turbulent
history. Two specific transient processes will be considered; namely, the
cases of a momentary flow stagnation and a high velocity eddy for an Inconel-
fluoride system will be analyzed.
-a., Momentary Flow Stagnation
Postulate that, at time equal to zero, the fuel contiguous to the
Inconel wall remains perfectly stagnant for a short period of time
(perhaps several tenths of a second). The problem is to determine the .
transient temperature structure in the Inconel wall, in the adjacent
fuel, and at the 1nterface between the two. The equations which definel

this @oundary value problem follow:

 

2. W (y)
gg = aI §;§-+ ;%E‘;? 0<y< yi (Incoqel wall)
P
: 2, Ww.(y)
At dt f
6 "8 T3 ¢ ,Y>YI (Fuel)

£ dy 7fcpf

t(e = 0, y) = ti(Y)

(15)

“k g% (8, y = 0) =h, [t(e,y = 0) - tc]

 

 
- -25- e

An analytical solution of this set of equations would be 1aboriousu
and was actually not required for this specific study; thus, a solu-
tion was obtained very quickly by the graphical technique. A 0.2
second flow stagnation in the fuel with a volume heat source of 2 kw/cc
created a 208°F temperature rise within the fuel at a sufficient dis-
tance from the wall where heat conduction was no longer important.
However, the Inconel-fuel interface only increased by 48°F during the
seme time interval because of the transient conduction of heat into the
Inconel. Thus, in the case of flow stagnation in an Inconel-fuel sys-
tem, the wall-fuel interface fluctuation is only about one-quarter of
the value occurring in the fuel at some distance from the wall.
b. High-Velocity Eddy

Consider the case of a momentary high-velocity eddy which flows
past the core shell wall in the vicinity of the equator where the in-
fluence of the divergent flow exists. The problem is to estimate the
transient temperature structure in the Inconel and fuel for such a
case. The mean boundary layer thicknesses and turbulent conductivities
for the swirl-flow case were obtained from the fundamental velocity
data for simple ducts and converging and diverging channels. Some of

the results are shown in Table ;fi

 

A mathematical solution to a slightly simplified boundary value problem
was derived, however, which could be used to closely approximate the
transient temperature behaviour of this system.

 
- -

 

 

TABLEH‘

Region Thermal or Eddy Conductivity’, Btu/hr £t (°F/ft)
Inconel Shell 13
Laminar Sublayer 1.5
(0 < y<0.001)
Buffer Layer 12.8 (a mean value)
(0.001" < y < 0.0058")
Turbulent Core

y = 0.0058" 56

y = 0,182" (1/10 of mean radius) 1550

¥y = 0.912" (1/2 of mean radius) 4270

 

5. The eddy conductivity of a fluid is the sum of the molecular and tur-

€
bulent terms, keddy = k(1 + v Pr).

'Ejfi&gi

 
 

R -

On the basls of the hydrodynamic research conducted in quarter-
scale models of the ART, i1t is believed that the sudden high-velocity
fluctuations observed near the core boundaries were due to momentary
high-velocity eddies which greatly increase radiasl momentum and heat
transfer during thelr existence. The following boundary value pro-
blem represents an idealized description of the transient temperature

structure during this event.

xu _ Pt
3 "~ 8 32

y

y<o
t(Y:O) =0
lim t(y,e) =0
y —> -
(16)

3 _ o
8 T °r 3

y
£(y,0) = t_ y =0

lim t(y,8) = t,
y——>= =
Tt is assumed that the high-velocity eddy suddenly presents the
Inconel and thin laminar sublayer and buffer layer with a new slab of
fuel having a new higher or lower uniform temperature above the initial
datum, ta' This new slab also has a higher eddy conductivity represent-
ative of a region a short distance from the wall where the eddy originated.

The source terms in both the Inconel and fuel have been neglected here.

 
- -28- W : . -.4

 

A layer of Inconel having the same combined thermal resistance and
capacitance as the thin laminar sublayer and buffer layers was added
to the Inconel wall.

The solution to this houndary value problem is proéaic and can
be found readily in the literature (reference 15). The ratio of the
actual Inconel-fuel interface temperature6 to the uniform fuel step

function temperature, t g) Was evaluated for several dif-

interfza.ce‘/t
ferent eddy sizes. A typical one, which was defined by an eddy coming
from 0.18 inch from the wall (a mean kf equal to sixty times the value

for Inconel) was t = 0.79 in 0.2 second.

interface/ta
The high velocity eddy analysis presented above is based on a con-
servative system. From photomicrographs of the surface of Inconel ex-
posed to fuel, it was observed that the surface roughnéss was of the
same size as the thickness of the calculated laminar sublayer. Many
hydrodynamicists believe that if this is the case, then there would be
no laminar sublayer. Further, the layer thickness used in the above
analysis was calculated for the average flow condition; actually, it
would be tfiinner because of the momentary higher local velocities. The
thermal resistance and capacitance of the laminar sublayer as well as
the buffer layer were so small that the calculated ratio, tinterface/ta’

given above would only increase 12 per cent if these two layers were

neglected. It is also pointed out that in the analysis it was postulated

 

 

The actual Inconel-fuel interface was located at y = - 0.009 inch; the .
9 mil layer represented the equivalent fuel laminar sublayer and buffer
layer described above.

 
- -29- LR

that a slab of fuel was suddenly exposed to the boundary layers and
the Inconel; however, the high-velocity eddy would continually supply
new fuel, thus further raising the temperature ratio calculated above.
Finally, calculations have been made which show that the thermal con-
ductivity of a layer of Inconel, penetrated uniformly with subsurface
corrosion volds, can suffer a significant reduction. For example,
the reduction in conductivity of a uniformily pitted layer having a
void volume of 30 per cent would be 38 per cent.

The above calculations indicate that high velocity eddies of the
type pictured here can transfer heat so effectively that Inconel-fuel-
interface temperature fluctuations are not drastically reduced below

the temperature fluctuations in the fuel,

 
[ -30- sl
EXPERIMENTAL SYSTEM

l. Technique

In order to determine a more detailed description of the mean and
transient temperature structure within the ART core, it was decided to
perform a heat transfer experiment in a half-scale model of the core.
The most effective way of generating heat within the volume of an aque-

T

ous solution' flowing through the model was found to be the "resistance
heating" technique, fising alternating currefit. This method was :found to
possess the following advantages:

a) High specific powers are attainable.

b) Fluid and surface temperature measurements can readily be made.

c¢) Proper electrode spacing and voltage regfilation yield control

of the power density distribution.

d) Power densities can be accurately determined from voltage and

current measurements.

In order to obtain sufficiently large temperature differences within
the electrolyte flowing through the core, intense volume heat sources had
to be generated. It was observed, hdwever, if the alternating current
densities at the electrodes of the system were in excess of a certain

value, then undesirable hydrogen and oxygen liberation would occur at the

electrode surfaces. Hence, it was necéssary to so adjust the electrical

 

7. Other methods of generating volume heat sources were studied, but were
not found to be readily applicable; they were induction, dielectric,
ultrasonic, and radiant heating. |

V . :;-‘:" St —
}n F Ay
e fi .

 

 

 
 

— -

resistivity of the electrolyte, by varying the specific gravity, so that a

meximum current density just below the critical value for gas generation
was obtained. It was also found that platinum electrodes made it possible
to obtain higher current densities. Further details on electrolysis re-
search can be found in Appendix 1.
2. Electrode Geometry

It was found essentially impossible to create an electric flux field
within the electrolyte flowing through the core which would generate g
volume heat source that would peak sharply at the core wall as previously
shown in Figure 1. It was possible, however, to create.an electric flux
field which was nearly uniform throughout the whole core. It is possible
to transform the experimental temperature profiles obtained in the uniform
power density case to those corresponding to the nonuniform power density
case (ART) with the aid of the mathematical temperature solutions carried
out previously for these two systems,

The electrode arrangement used in the experiment is shown in Figure 6.
It can be shown that if the axial potential gradient is a uniform value
throughout a conducting system (linear voltage drop), & uniform volume
heat source will be generated. The electrode arrangement in Figure 6
Yielded a potential field that had an axial potential gradient that was
within + 6 per cent of being uniform (excluding the extreme ends of the
potential field); this means that the volume heat source was within + 12

per cent of being uniform. The potential difference of each electrode set

was adjusted such that the potential drop between adjacent electrodes re-

-

mained constant.

 

 
Aes v s .
%.‘éa{!;’
! v g

ENTRANCE

 

 

 

UNCLASSIFIED
PHOTO 26304

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

EXIT

 

 

 

 

Fig. 6. Electrode Arrangement, Voltages, and Potential Field for Half-Scale Core.

sy

—ze-
— -

A dilute solution of sulfuric acid (1% by weight) was used for the t
circulating electrolyte. Some of the physical properties of this solution
are presented in Appendix 2,

3. Flow Circuit

A perspective drawing of the ART volume-heat-source system is shown
In Figure 7. The components consist of an electrolyte reservoir, two
centrifugal pumps, flow-control valves, and orifice meter, the half-scale
core model, and a water-cooled heat exchanger. The entire flow system
was enclosed by plywood and Plexiglas walls in order to protect the opera-
tors from sulfuric acid in the event of a system leak. The electrolyte
was pumped from the reservoir to the test section (where heat was generated
within its volume) to the heat exchanger (where it was cooled) and finally
back to the reservoir. Information on materials of construction and flow
system components, excluding the core model which will be described next,
can be found in Appendix 3.

4. Half-Scale Core Model

Figure 8 shows a cross-sectional view of the core model including
entrance and exit sections. A transparent Plexiglas pipe was located at
the core entrance so that the presence of entrained gas in the electrolyte
could be observed. A mixing chamber used to obtain a mixed-mean fluid
temperature was also located in this pipe. The two flow control valves
located above the pump volutes were used to simulate single and dual ART
pump operation. A view of the pump volutes and the core entrance region
1s shown in Figure 9. The flow either spiraled through the core unguided

(swirl-flow entrance) or was guided by a set of turning vanes (vaned-flow
 

"

Pl PFAND LIGHT

 

ENCLOSURE

HALF SCALE CORE MODEL —

PIPE AND LIGHT

 

 

 

 

 

 

SETwEE
ORNL-LR-DWG. 17994

ORIFICE

HEAT EXCHANGER

ol |_———RESERVOIR

 

- < PLEXIGLAS FRONT WALL

 

 

 

 

-rg_

PUMPS

 

MANOMETER

Fig 7. ART Volume-Heat-Source Experimental System
ORNL-LR-DWG 1CB19A

t FLOW IN

  
    
  
  
     
    
    

ENTRANCE TC MIXING CHAMBER

THERMOCOUPLE THERMOCCUPLE

   
  

PERFCRATED PLATES

BOLTARON VALVE

 

HONEYCOMB
STRAIGHTENER

PUMP AND HEADER
MOCKUP

ALTERNATE ENTRANCE SYSTEM

THERMOCOUPLES LOCATED ON
ISLAND AND SHELL WALLS

ELECTROCES (24)

{SLAND

SHELL

PERSPECTIVE VIEW CF
MIXING CHAMBER BAFFLES (TYPICAL)

EXIT MOCKUP

THERMOCOUPLE

 

————

FLOW OUT

 

THERMOCOUPLEJ

EXIT MIXING CHAMBER

Fig. 8. Cross-Section of Half-Scale ART Core Model Including Entrance and Exit Section.

-gs...

 

 
 

UNCLASSIFIED
PHOTO 26251

 

‘ ELEG D 41 12

| R AT oy
. W T EE T e |

Fig. ?. Top View of Pump Volutes and Core Entrance.
— -

entrance). The turning vanes in the core entrance are shown in Figure 10.

#Wall temperatures within the core model were determined by forty No. 36

»

W

gauge copper-constantan thermocouples, located about 0.030 inch below the

i,

%

Plastic surface, and twenty-four No. 30 gauge platinum-platinum + 10% rhodiumi’i

thermocouples which were honed flush with the wall surfaces. In all cases,
the junctions fiere of the butt type, and the couples were positioned in a
plane parallel to the wall-fluid interface. Figure 11 shows a view looking
down into the core from the entrance. This photograph was made after the
first two sets of runs were completed. The simulated bellows on the island
is observed in the center, and around it are seen the dark Platinum elec-
trode rings in the outer wall of the core. Several copper-constantan ther-
mocouples may be séen through their transparent Araldite resin coverings.
The copper-constantan thermocouples were spaced st five axial stations;
four were loecated 90o apart at each station on the inner and outer walls.
The platinum-platinum + 10% rhodium thermocouples were spaced at four axial
stations; three were located 120° apart at each station on the inner and
outer walls. Table 2 gives the couple positions.

Platinum tubes, 1/16 inch in dismeter, with platinum + 10% rhodium wires
inside joined at the tips were fashioned into thermocouple probes whose Junc-
tions were positioned in the flow stream L/8 inch below the exit plane (see
Figure 12). The probe tips were rotated hSO from the vertical so that they
faced in the general direction of the rotating flow from the exit of the
core.

An exit section similar to the ART exit can be seen in Figure 8; a

mixing chamber to measure the exit mixed-mean fluid temperature iz also

 

 
Do
ly

ol

—

Fig. 10, Pump Volutes and Core Entrance Region with Top Removed,
Mounted on Core Test Section with Guide Vanes in Entrance.

| PHOTO A

 

 

-gE-

i g‘

 
 

 

Fig..11. View of Inside of Core Through Entrance.
B e e i e e e e e e = M b o e e -l

 
Distance from Core
Midplane (inches)

TABLE 2

Copper-Constantan
Thermocouples

 

 

'f. 500
6.000
3.375
1.500
0.000
-1.500
-3.375
-6.000

-7.500

X

Platinum~-Platinum + 10%
Rhodium Thermocouples

 

 

 
-41- _ }

ORNL-LR-DWG, 17995

    
    

   

 

/
DIRECTION OF
ROTATING FLOW
| /
THERMOCOUPLE
PROBE (TYPICAL)
23/64"
k A
)
-/ k\___‘_/_.___ 'L:
/

 

 

 

 

 

 

43/64" /////////
PLANE OF CORE EXIT
/ ts8"

4 +
\\\\\:\\ { \¥¥¥§§<~45° N Q§:* \QF\\ N

 

 

 

Z

   
 

FLOW

iy

 

 

 

 

 

. SECTION A-A

mii Section Through Core Exit Plane Showing Thermocouple Probe
Lo ons.

 

 
~Lo-

 

shown. A transparent pipe through which the solution could be inspected
for gas generation followed the mixing chamber.

A photograph showing the assembled core model with power leads and -
thermocouple leads in place can be seen in Figure 13.
5. Power Circuit and Instrumentation

Figure 14 shows a schematic diagram of the electrical power system.
A saturable reactor shown in the diagram was only used to control the
voltages of the end electrodes at certain times. The voltages of the
intermediate electrodes (3 through 22) were controlled in pairs by vari-
able autotransformers. The power level was controlled by varying the
strength of the acid solution up to one per cent by weight, thus changing
its resistivity. The maximum total power dissipated in the test section
was about 125 KW. -

Figure 15 shows a photograph of the control and instrument panels.
The power control Variacs are on the panels at the right with their volt-
meters and ammeters. An accurate voltmeter (less than one per cent error)
with a selector switch so that any electrode potential could be measured
was installed later and used throughout the experiments. Accurate ammeters
(less than one per cent error) were used to measure the currents drawn by
the electrodes. The total electrical power dissipated within the core model
was obtained by summing the individual wattages consumed by the individual
electrode pairs.

Mean temperature measurements were obtained with the copper-constaޣan
thermocouples. The voltages of these couples were recorded on four twelve-

point recording potentiometers which are shown at the far left in Figure 15;

 
-43-

} ! -l i
J -l e ‘--

UNCLASSIFIED
PHOTO 25940

 

 

 

Fig. 13. Overall View of Core Model.

 
-44-

TD-E-4589 Rev. E
UNCLASSIFIED

gl E;l

TEST SECTION

N

3=

 

oY

 

 

 

 

 

 

 

=000

 

 

 

 

 

 

 

 

 

 

 

 

 

 

@ 230/15
-5
W PT-
%
e
e

AT4

T3
h ~YE
SchLE 0500 W 4 — FET
o=-3a0 # Ses s - 08GO
O-55
- ",

 

 

 

 

 

 

 

 

 

 

 

 

  

 

 

 

 

 

 

 

 

 

 

48920

 

 

oy J00A, LINE

 

Fig. 14. Schematic Diagram of Electrical Power System.

 

 
_— -
portable precision potentiometers were used most of the time to obtain these
voltages, however. The platinum-platinum + 10% rhodium thermocouples, which
were normally used to obtain transient data, were also used to determine
méan voitages to verify the copper-constantan measurements,

Two methods of measuring temperature fluctuations were used. One con-
sisted of connecting a sensitive mirror galvanometer, made by the Hathaway
Instrument Company, to the platinum-platinum + 10% rhodium thermocouples
(see Figure 16). Galvanometer deflections were then calibrated in terms
of couplé voltages or temperatures. Motion pictures were made of the gal-
vanometer deflections. The second method of measuring transient tempera-
tures involved using a Brush recorder with a special isolated preamplifiers.
A photograph of this system is shown in Figure 17.

To protect the test section and the people working with the experiment,
several automatic safety controls were included in the electrical system.
The power circuit to the core model was instantaneously opened by control
equipment when the following events occurred:

a) reduction of electrolyte flow rate below a preset value

‘b) - reduction of cooling water flow rate below a preset value

c) opening of door to room containing the volume-heat-source

experiment.
An alarm system immediately made known the occurrence of any of the above

events.

 

8. This amplifier had an input circuit which was isolated from the remainder
of the circuit. This permitted the detection of small varying D.C. volt-
ages in the presence of high A.C. potentials. The amplifier circuit was
modified so that the range of flat frequency response was increased.

 

 
PHOTO 25938

e

UNCLASSIFIED

 
 

iy

.S

A

 

Fig. 15. Control and Instrument Panels.

 

 
-47- ORNL-LR-DWG. 17997

Pt -Pt+ 10% Rh
TRANSIENT THERMOCOUPLE

/\

-_— —_—t —t = — = = e — —TEST SECTION

 

       

LENS SYSTEM

 

L o|-——-2F LIGHT SOURCE

 

HATHAWAY
GALVANOMETER
SUSPENSION

-+Vq—

Fig. 16. The Hothawaoy Galvanometer System

 
UNCLASSIFIED
PHOTO 26252

!‘: ".l‘J‘ '.“-l -
&a}s;. #5"1

_B :y_

 

Fig. 17. Components of Electronic Transient Temperature Recording System.

 
1.

EXPERTMENTAL PROCEDURE

Calibration
a. Brush Recorder and Hathaway Systems
When all the transient thermocouples within the core model were
held at some lknown, uniform environment temperature, a zero reading
was obtained on the Brush recorder. The environment temperature was
then raised to some new uniform temperature level and the deflection
of the Brush recorder again noted. The calibration constant was there-
by derived directly in degrees centigrade per recorder scale division.
An alternate method of calibrating the Brush recorder was used to verify
the previous method. A direct current signal was applied to the Brush
amplifier and then changed by a known increment. This increment was
then convgrted to a temperature change, and the Brush recorder scale
deflection was noted. The calibration constant so obtained was found
to be within > per cent of the one determined by the previous method;
The Hathaway system was calibrated in the following manner. The
output of the platinum-platinum + 10% rhodium thermocouple was ifipreséed
directly upon the galvanometer suspension. The light arm deflection was
noted for a given thermocouple environment temperature. The temperature
1e§e1 was then raised a known numberrof degrees, and the deflection of
the light arm recorded.
b. Thermocouple Response
An experimental and analytical study of the response of the tran-

sient thermocouples under periodic and step function conditions was

 

 
— -50- b

conducted. It was found that the thermocouple response itself was far

 

greater than those associated with the Brush recorder and Hathawasy gal-
vanometer suspension systems.
c. Frequency Response of Recorder and Galvanometer
Calibration of the frequency response of the Brush recorder was
accomplished by impressing a known signal of variable frequency on
the system input. The amplitude of the output on the Brush oscil-
lograph was measured, and the results appear in Appendix 4 in terms
of percentage of D-C response versus frequency in cycles/sec. A
similar calibration of the frequency response of the Hathaway mirror
galvanometer was made. The results are also presented in Appendix k.
Both of these Brush recorder and Hathaway response curves show that
the 60 cycle per second response is very small compared to the low
frequency spectrum.
d. Orifice Meter
The orifice meter was calibrated by measuring the weight flow

rates and manometer deflections over the range of operating conditions.
The calibration for a two-inch orifice is presented in Appendix 4; a
graph of the mean Reynolds number as a function of manocmeter deflection
can also be found there.

2. Operational Technique
Four sets of volume-heat-source experiments were conducted during this

investigation. Two sets of measurements were made with a swirl-flow en-

trance; in one case, both simulated pump inlets were open, and in the other

_—
i
 

_— -

case, one inlet was closed. Two additional sets of measurements were
obtained with vanes located at the core entrance; the one and two pump
flow simulation was again examined.

All heat transfer and fluid flow data were recorded only after the
following steps were completed in the indicated sequence:

a) The system was filled with the electrolyte.

b) The electrolyte was circulated through the system by means of

the two pumps.

c) The datum temperature of the electrolyte was maintained by an
automatically controlled cooling water flow rate in the heat
exchanger.

d) A predetermined voltage distribution for the electrode system

. was established before the power was applied.

e) Power was turned on.

f) A final check was made on the desired electrode voltage dis-
tribution as shown in Figure 6.

g) Thermal equilibrium was established in the flow system. The
external core model environment temperasture was matched to the
mean fiall temperature within the core in order to establish the
uncooled-wall condition.

During the subsequent period of data recording, 1t was observed that
the mean temperature and electric flux fields were extremely stable. For
example,_the variation in the mean temperature structure was less than
one-quarter of one per cent. Further, only negligibly small gaseous elec-

f products existed in the exit flow as detected by the Tyndall light

i
-

 

L,

 

 

 
 

— 52

scattering effect. A minute amount of leakage current was conducted

through the external flow circuit from the core (less than 0.001 amps).

 

 

 
o -5

MEAN AND TRANSIENT TEMFERATURE RESULTS

1. Swirl-Flow Case; Two Pumps

 

Fifteen complete power runs were made for the core model using the
swirl-flow entrance. Both flow valves were open, thus simulating the ART
flow with both pumps in operation. The ranges of parameters investigated
follow:

66,000 < Re < 256,000
L <Pr<s
5<t -tmi<10°F
0.08 < P, < 0.12 Megawatts

The heat balances obtained for the system were within + 5 per cent of being
perfect. Typical meang, uncooled wall and mixed-mean fluid temperature
profiles obtained in these experiments with a uniform volume heat source
are presented in Figure 18 in a-.generalized form. The asymmetries in the
outer and inner core wall temperatures can be explained on tpe basis of
hydrodynamic asymmetries. For example, the high inner core wall tempera-
ture in the northern hemisphere existed because of a separation region which
completely encompassed the inner wall (island wall) in that region.

The hydrodynamic structure in the northern hemisphere of both the swirl-
flow and vaned-flow entrance cases is extremely complex. The sheaf stress

and turbulence distributions are unknown in that region. Therefore, it was

 

9. The word "mean" in this case denotes an average with respect to time at
a particular location as well as an average with respect to peripheral
position.

 
ORNL-LR-DWG, 17998

 

 

 

 

 

 

 

 

 

 

0.8 IDEALIZED ART (THEORETICAL) 7~ B

t - tmi ,7 /
tmo tmi /
0.7 7
INNER WALL + /<// N_MIXED MEAN FLUID

0.6 4

o L —] / \—OUTER WALL
0.4 ///
// Re = 256,000

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

03 // Pr=4.8
0.2 //
0.1 //"‘
0 k]
| 0.2 0

0 0. . .3 0.4 0.5 0.6 0.7 0.8 0.9 )
AXIAL DISTANCE, X/L

Fig. 18. Mean, Uncooled Inner ond OQuter Core Wall Temperature Measurements for the Half-Scale ART
with a Uniform Volume Heat Source (Swirl Entrance)

_vg_
o -55- o

felt that predictions of the detailed, uncooled-wall temperature structure
in the entrance region would probably be too simplified and hence were not
madelo. A calculation of the entrance 1eng££ in a simple parallel plates
system was made along the lines of Latzko's analysis (reference 16). It

was found that the entrance length for the swirl-flow case was about 36
dismete¥s. This meant that the flow was established in most of the southern
hemisphere because the physical, vectorial channel length in this case was
also 36 diameters. Consequently, the solution for established temperature
structure ifh a éarallel plates system (reference 2) was used to predict the
Jocal uncooled wall-fluid temperature difference in the southern hemisphere.

It can be shown that,

t -t r At
m

 

o o VHS
————— = = Re Pr{ — (17)
tm.o ?mi ML Wri

- uniform W(r)

This relation was evaluated with the aid of the solution in reference 2 for
the swirl-flow case and is seen graphed in Figfire 18; the predicted tempera-
ture profile lies between the experimental temperature profiles for the
inner and outer walls. .

Variations in the experimental uncooled core wall temperatures with
respect to peripheral position were observed in the system. For example,

the uncooled wall-fluid temperature difference, on the inner wall in the

 

10. Nevertheless, a series of laminar and turbulent flow heat transfer
analyses pertaining to entrance regions in simple flow systems were
derived, Cases where both thermal and hydrodynamic patterns are being
developed were considered. A paper on these analyses is to be prepared
in the future.

L T .
R R W
- "" - (‘_
e

 
-56- © o
oty i
L{.‘J_iifi

;quatorial region, varied by plus or minus 30 per cent from the mean wall-
fluid temperature difference at that plane. The corresponding variations
in wall-fluid temperature difference for the cooled-wall core would prob-
ably be much less because the peripheral variation in the heat transfer
coefficient no doubt would be a compensating factor.

The experimental temperature profiles obtained for the uniform power
density case were transformed to those corresponding to the radial, non-
uniform power density case (Figure 1) with the aid of the mathematical
temperature analyses presented earlier in this report. The axial mixed-
mean temperature diétributions for both the ART axial pofier distribution
(reference 21) and the uniform axial power distribution are compared in
Figure 19. The maximum difference is seen to be less than one per cent
of the total mixed-mean temperature rise. The results can be seen in
Figure 19 together with a corresponding analytical solution. Note that
wall temperatures as high as 1750°F would occur if the wall were not
cooled.

Typical transient wall and fluid temperature data are shown in Fig-
ure 20 in terms of the total temperature fluctuation divided by the axial
temperature rise of the fluid going through the core. The frequencies of

- the temperature fluctuations for this half-scale model varied from about
one-half cycle per second to four cycles per second., The frequency range
of temperature fluctuations in the full-scale ART system, operéting with
flfioride fuel, should be similar to that in the half-scale model experi-
ment with the acid solution. A simple average of the maximum wall and

f¥uid temperature fluctuations with respect to peripheral position was

% -

 
t _'mi

t mo~ tmi

ORNL-LR-DQ&. 17999

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.5
1.4 //
INNER WALL /
{.3 I \ /
1.2 IDEALIZED ART (THEORETICAL) \K /
[, — ————— d— — — w—
1.1 __..__-—--'/ p g / \
-
1.0 - = / \/“P
0.9 —
0.8
/ MIXED MEAN FLUID
0.7 ) | h
/ 3
06 - / OUTER WALL
r |
05 // . I
/ Ot, CALCULATED FROM
0.4 HOT CRITICAL EXPERIMENT
S ACTIVITY DATA
0.3 —
Re = 256,000
0.2 Pr=4.8 -
0.4 G
0(

0 01 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 .0
' AXIAL DISTANCE, X /L

Fig. 19. Mean, Uncooled Inner aond Outer Core Wall Temperature Profiles for

the Half - Scale ART with a Nonuniform Volume Heot Source(SwirI-'Flow
Entrance P S P %

 
 

 

 

 

 

 

 

t— | SQC —P

 

 

 

N
\WAVAY

 

\/©

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fig. 20. Typical
for Swirl—Flow Case.

_Y
CORE-EQUATOR
fe— | 5©C —>
f\. / — 1
N VN
MID-STREAM
BEYOND EXIT
| | |
0 1.0 2.0 3.0
TIME (sec)

= 0.18

ORNL-LR-DWG. 18000

Re
W

 

w

256,000

(UNIFORM)

Transient Surface and Fluid Temperatures

_89_
- -59-

obtained. Typical measurements uncorrected for frequency response are

shown plotted as a function of axial distance in Figure 21 for the uniform

 

pover density case. These fluctuations would, of course, be larger
the nonuniform power density case. Note that the outer wall temperaté?g
fluctuations are greater than those measured at the inner well; this dif-
ference appears to reflect the Rayleigh stability criterion. A detailed
frequency response correction is laborious because of the difficulty in
determining instantaneous frequencies for the complex fluctuation spectrum.
However, on the basis of a mean fluctuation Prequency of about two cycles
per second, one would expect to increase the magnitude of the fluctuations
given in Figure 21 by a factor of about 1.5,
2. Vaned-Flow Case; Two Pumps

Six complete power runs were made for the core model using the vaned-
flow entrance. Agein, both valves were opened to simulate normal ART
operating conditions. The ranges of parameters investigated follow:

60,000 < ReS < 180,000
L<Pr<s
5<t -t <10°F
0.08 < P, < 0.12 Megawatts

Heat balances were again within + 5 per cent of being perfect. Typical
mean, uncooled-wall and mixed-mean fluid temperature profiles for a uni-
form volume heat source are presented in Figure 22. Note that the high
inner wall temperatures in the northern hemisphere obtained in the pre-

vious swirl-flow case are no longer present because the vane system almost

 
ORNL-LR-DWG. 18001

 

 

 

 

 

Res = 256,000
W =W (UNIFORM)

 

 

0.8

 

0.7

 

0.6

 

0.5

 

3
3
-09-

0.4

—_ _ OUTER WALL
0.3 T——

 

 

0.2 ——— INNER WALL

 

 

 

D
MIDSTREAM-’@
0. PROBES

0o 2 4 6 8 10 12 {4 16 18
AXIAL DISTANCE FROM INLET (inches)

 

 

 

 

 

 

 

 

 

 

 

Fig. 21. Peripherally Averaged Moximum Temperature Fluctuations for Swirl- Flow Cor@";

 
ORN Lm. 18002

 

 

 

 

 

 

 

 

 

1.4
,.J‘-{‘- e ————
f_r_‘,&?: 1.3 /
g ) //
IDEALIZED ART (THEORETICAL)-—>/
11 n T ——
OUTER CORE WALL — —t
/| e

 

N | /)/
0.9 INNER CORE WALL — e _—

08 / -
t =t /// /
tl'l'n:."'vni 0.7 L

/ / /<—MIXED MEAN FLUID

06 /

0.5 //

0.4 / / /

0.3 Reg = 131,000

Pr = 4.0

0.2 / /
0.1 //

ok |

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 E

AXIAL DISTANCE, X/ L e

 

 

 

 

_19_

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fig. 22. Mean, Uncooled Inner and Outer Core Wall Temperature Measurements for the Holf-Scaleg
ART with a Uniform Volume Heat Source (Vaned Flow Entrance)

 
m— -

completely eliminated the flow separation in that region. However, the

uncooled-wall temperatures in all other regions were higher for the vaned-

y
LN

flow case than those for the swirl-flow case because the latter case was

L%

“

characterized by a significantly higher vector Reynolds number,

A calculation revealed that the entrance length in a simple parallel
Plates system corresponding to the vaned-flow case was about 29 diameters.
Since the ph&sical vectorial channel length was only 16 diameters for this
case, the thermal boundary layers were about 67 per cent of the fully estab-
lished values at the idealized core exit. However, the analytical, uncooled-
wall temperature profile for the southern hemisphere shown in Figure 22 was
carried out for established temperature conditions.

Peripheral variations in the experimental uncooled-wall temperatures
were again observed. Hofiever, they were generally larger than those found
in the swirl-flow case. For example, the uncooled wall-fluid temperature
difference, on the inner wall in the equatorial region, varied by + 90 per
cent from the mean temperature difference at that plane,

The experimental temperature profiles obtained for the uniform pover
density case were transformed to those corresponding to the nonuniform
power density case as was done previouslyf The results can be observed in
Figure 23 together with the analytical prediction. Note that wall tempera-~
tures as high as 18500F would result if the walls were not cooled.

Typical trangient wall and fluid temperature data for the vaned-flow
case are presented in Figure 24. The frequency spectrum of the temperature .
fluctuation for this case was, in general, similar to the one found for the

swirl-flow case. However, at certain flow conditions in the northern

.
s

 
 

_63_
ORNL-LR-DWG. 18003

 

 

 

 

 

 

 

.8
1.5 _________’( A
NEAUZED ART

(THEORETICAL)
OUTER CORE WALL \

1.2 e T~

f/ ‘\
/|
/ INNER CORE WALL

t = tmi
— 09 / / —

tmo— tmi 7/ / /7
/ flxsn MEAN FLUID

/S

 

T~
o

 

 

 

 

 

 

03 / Reg = 431,000

Ve e as
e

0 0.1 0.2 0.3 0.4 05 0.6 0.7 0.8 0.9 1.0
AXIAL DISTANCE, X /L
Fig. 23. Mean, Uncooled Inner and Quter Core Wall Temperature Prafiles for

the Hoalf-Scale ART with a Nonuniform Volume Heat Source (Vaned-Flow Entrance)

 

 

 

 

 

 

 

 

 

 

 

 

 

 
-64-
ORNL-LR-DWG. 18004

 

 

 

 

 

 

 

 

 

 

 

 

|
I ~<—1{ S@ec » l
A\ 1
At
} \l — - 0.25
—— 7 - — = — tmo~— tmi
INNER WALL - EQUATOR
Re, = 131,000
W = W (UNIFORM)
VANED ENTRANCE
- { S@C
/ N 1. - T[— Atg -
—_— = 0.18
trno' tmi
\J X

 

OUTER WALL - EQUATOR

 

- { seC -
A\ \ A/ | et

MID-STREAM
BEYOND EXIT

L]

0 1.0 2.0 3.0
TIME, sec.

 

 

 

 

 

 

 

 

 

 

Fig. 24. Typical Transient Surface and Fluid Temperature
for the Vaned-Flow Case .

 

 
— 55-
hemisphere, some large amplitude, low-frequency fluctuations were note in
the vaned-flow case, Maximum wall and fluid temperature fluctuations,ggi
averaged with respect to peripheral position, are shown in Figure 25 aéj;
function of axial position; frequency response corrections were not maégi

The outer wall temperature fluctuations in the northern hemisphere were
significantly lower for the vaned-flow condition than in the previous case.

However, wall and fluid temperature fluctuations in the southern hemisphere

were somewhat larger for the vaned-flow case. These increases in fluctu-

ation magnitudes appear to correspond to similar increases in the mean radial
temperature differences for the vaned-flow case. ‘
The four heavy platinum thermocouple probes located just beyond the

core exit were used to obtein local fluid temperature fluctuations as well

as a mean radial fluid temperature distribution in that region. The tran-
sient temperature distribution within a platinum probe was calculated for

the case of a sudden step function increase in the temperature of the elec-
trolyte flowing past the probe. A similar calculation was made for the
probe on the basis that it was made of Inconel rather than platinum;l. It
was shown that shortly after the step function had been applied to the two
systems (about 0.03 seconds), the fluid-metal interface temperatures of both

probes increased almost by the same amount. The centerline temperature of

 

1l. A comparison of these two cases allows one to describe the probable
transient temperature behavior in the Inconel heat exchanger walls
under high frequency cycling. Note that the radial wall thickness
of the Inconel tubes (25 mils) and the platinum probes (35 mils) were
nearly equal.

 

 
 

L
i .:_’fr"-q

4} Voo
ey

e ORNL-LR-DWG. 18005
1.0

 

 

0.9

 

 

0.8
Re, = 131,000

0.7 W = W (UNIFORM)

 

 

 

0.6

Atg

 

0.5

 

tmo~ tmi

 

04
_—1 INNER WALL

0.3 —— X
0.2
MID-STREAM
— PROBES

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0o 2 49 6 8 10 {2 14 {6 {8
AXIAL DISTANCE FROM INLET (inches)

Fig. 25. Peripherally Averaged Transient Temperature Fluctuations for the Vaned-Flow Cofi

.

 

-99-
o -

the platinum probe (where the thermocouple was located) had increased by
an amount that was 88 per cent of the temperature rise at the probe-fluid
interface. However, in the case of the Inconel probe, the centerline tem-
perature increased by an amount that was only 61 per cent of the temperature
rise at the probe-fluid interface; for this case, the centerline temperature
had only increased by 18 per cent above the original initial temperature
level as compared to a 52'per cent increase for the platinum probe. Further,
more than one and one-half times as much heat was transferred to the platinum
probe. These simple calculationslindicated that the temperature fluctuations
measured in the center of the platinum probe would be at least as large as
those which would exist at the surface of an Inconel tube located at that
position under such rapid transient conditions.

A graph of the mean radial fluid temperature distribution just beyond
the core outlet in terms of the mixed-mean fluid temperature at core in-
let and outlet can be seen in Figure 26. The uncooled core wall tempera-
ture profile is not symmetrical about the channel centerlinelz; its shape
is quite similar to the theoretical one shown previously in Figure 2. It
is noted in Figure 26 that, upon the comparison of the measured fluid tem-
perature distribution with the mixed-mean fluid temperature at exit, more
area between the two curves lies above the mixed-mean temperature than
lies below it. This is as expected, because the mixed-mean fluid tempera-
ture is averaged with respect to velocity as well as temperature. Hydro-

dynamic studies have shown that more fluid flows axially through the inner

 

l2. The reason for thié temperature asymmetry will be more fully discussed
in a following section of this report.
ORNL-LR-DWG. 18006

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

)
/
FLUID TEMPERATURE7 //
y,
2 Z_MIXED-MEAN FLUID TEMPERATURE OUT
1
O~
o
1
0.2
0.1 7
4 /—MIXED-MEAN FLUID TEMPERATURE IN (ZERO)
0 4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1. O
INNER WALL OUTER

NORMALIZED DISTANCE BETWEEN |INNER AND OUTER WALLS
Fig. 26. A Comparison of the Rodial Fluid Temperature Profile with Inlet and Qutlet Mixed—Mean Temperaturj

 

(Vaned-Flow Case)
 

L -69-

portion of the channel at exit than flows in the outer portion. It is
also pointed out that the radial fluid temperature profile plotted in
Figure 26 is based on only four thermocouple determinations; it would
have been desirable to have had more data to establish a mean profile.

It was of interest to determine what the peak fuel temperatures would
be in the ART core exit. These temperatures were estimated for both the
swirl-flow and vaned-flow cases as follows:

a) The experimental radial temperature profiles for uniform volume-

" heat-source conditions were transformed to profiles corresponding
to an averaged nonunifofm volume-heat-source distribution (see
Figure 1).

b) The results of the wall cooling analysis described in the section
on Mathematical Heat Transfer Analyses were ther used to determine
the peak fuel temperatures.

Local fuel temperatures so estimated ranged from 100°F to 170°F higher than
mixed-mean fluid temperatures for the swirlfflow and vaned-flow cases, re-
spectively.

' The complicated question of how much decay takes place in the fuel
temperature peak (for the wall-cooled case as described in Figure 5) as
the fuel flows through the short exit passage to the heat exchanger en-
trance wfis investigated. This passage was divided into two regions. The
First half of the passage was treated as a simple curved-wall channel sys-

tem, and the second half was considered to be & simple straight channel.

The decay of the turbulent thermal boundary layer in the curved channel

t

 

 
system on the convex side (where the high temperature peak exists) was

 

oy S :
el
AR Y

carried out by the usual Von Karman technique with the exception that, in

this case, hydrodynamic data (velocity profiles and wall shear stresses) *
characteristic of curved channel systems were used. The results for the

first half of the passage showed that, on the convex side, the boundary

layer would take about 80 diameters to become established (because of the

great decrease in eddy diffusivity on that side of the chfinnel). As the

physical length of that portion of the passage was only 9 diameters, a

pegligible decay of the peak would occur in that region. Thermal boundary

layer decay in the second half of the passage was calculated on the basis

of the work of Latzko (reference 16) for straight ducts. The results in-

dicatéa that it would take about 33 diameters for the thermal boundary

layers to become established; the physical length of that portion of the -
passage was oni& 9 diameters. On the basis of the functional relation-

ship between boundary layer thickness with axial distance in the passage,

this means that at the heat exchanger entrance there would be approximately

a 36 per cent decay of the original fuel temperature peak. On the basis

of these simplified decay analyses and the previous experimental and an-

alytical studies of the fuel temperature structure within the core itself,

it was estima.tedl3 that peak fuel temperatures at the heat exchanger en-

trance will be about 90°F in excess of the mean fluid temperature for the

 

13. Peak fuel temperatures were calculated at the core exit in the manner
outlined in the previous paragraph. However, the actual volume-heat-
source distribution near the outer wall was used rather than the aver- .
aged profile shown in Figure 1. \

s -

AT

 

 
[ “Tl-

swirl-flow case and about 150°F in excess of the mean fluid temperature
for the vaned-flow case.
3. ©Swirl-Flow and Vaned~-Flow Cases; One Pump

buring both the swirl-flow and vaned-flow experiments, a series of
runs were made for the simulated case of one-pump operation. In general,
it was found that relatively large peripheral and axial asymmetries ex-
isted in the uncooled-wall temperature distributions. The wall and fluid
temperature fluctuations were also larger than had been found for the cor-
responding two-pump experiments. Typical uncooled-wall temperature data
are shown in Figure 27 for the swirl-flow case. The peripheral locations
of individual temperature measurements are not indicated in the figure.
Note that now, some points lie below the mixed-mean fluid temperature and

other points lie far above.

 

 
 

' TR S

t-tmi

tmo—

tmi

1.3

{.2

0.8

0.7

0.6

05

04

0.3

0.2

0.1

n

ORNL- LR-Dag . 18007

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Operation

o 0
0
A
,/
T / A
A
0
A~ 4 / 1
~
N
: .
A ~—MIXED~-MEAN FLUID
A
A /
0 CORE WALL
o A ISLAND WALL
. /
/)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 T’:
X :
L
Experimental Uncooled-Wall Temperature Measurements for Swirl-Flow Case with One Pump
 

. 13-

GENERAL COMPARISON OF HYDRODYNAMIC AND THERMAL FIELDS

It is obvious from analytical considerations that there is a direct
relationship between the hydrodynamic and thermal fields for a given flow
system. The forced con‘i@i@fii‘heat transfer equations contain heat flow
functions that are uniquely defined in terms of the fluid velocity com-
ponents.

Several specific examples of how the steady velocity field influences
the steady temperature field have already been mentioned in the past section;
it may be of interest, at this point, to examine in more detail one such
case. In Figure 18, it was observed that the uncooled outer core wall tem-
perature at the core exit was significantly greater than the one at the
inner wall. This feature can be explained by studying the vectorial veloc-
ity distributions in the southern hemisphere shown in Figure 28. Note that
these velocity profiles, which were determined from experimental axigl and
tangential velocity measurements (reference 17), are asymmetric in shape.
Consider the channel flow to be divided into a narrow inner layer and a
wide outer layer, which possesses a somewhat lower velocify. From the pre-
viously developed analyticael temperature solutions for a simple parallel
plates system, it would be expected that the outer uncooled core wall tem-
perature would be greater than the corresponding inner temperature.

A comparison of the transient velocity and temperature fields was also
made. A study of the fluctuating velocity structure in the vicinity of the

core walls was carried out with motion pictures (reférence 18) of dye fila-

ments in a full-scale plastic model of the core. Frequencies of the fluid

 

 
 

-74-

ORNL-LR-DWG. 18008

 

1.0

   

~
N

AT EXIT
alfl | NN
| \20L/D UPSTREAM \
FROM EXIT \

0.4

 

 

 

 

 

Us max

 

 

0.2

 

 

 

 

 

 

 

0

0 0.2 0.4 0.6 0.8 1.0
INNER OUTER
WALL WALL

NORMALIZED DISTANCE FROM INNER WALL

Fig.28. Vectorial Velocity Profiles in Reactor
Core Exit (Swirl- Flow Case)

 

 
— 75-

velocity fluctuations as well as their angular displacements in the
vicinity of the walls were determined by counting the total number of
cycles a fluctuating dye filament underwent in a given unit of time as

well as by observing angular displacements. Figure 29 shows a plot of

 

the angular dye filament dis;_)l&moafl.tmentleL as a function of time, together
with wall temperature fluctuation measurements obtained in the half-
scale volume-heat-source system; both sets of measurements were determined
for the outer wall in the equatorial region. The velocity data presented
in Figure 29 suggests a mean frequency of perhaps one cycle per second,
whereas, the wall temperatures appear to be varying with a frequency of
about two cycles per second. This agreement is satisfactory because the
fluctuation frequency in the half-scale model should be double that of
the full-scale water model at the same Reynolds number. No attempt was
made to compare the magnitude of the dye filament deflections with the
temperature amplitudes chiefly because the exact locations of the dye

filaments from the core wall were variable and unknown.

 

14. Note, since the temperature frequency spectrum was limited to l/é to
4 cycles per second, only the fundamental mode of the velocity data
should be compared to the temperature date.

 
ANGLE FROM HORIZONTAL
PLANE (DEGREES)

STATION#5- OUTER SHELL WALL

1" ABOVE MIDPLANE OF FULL-SIZE CORE
AVG. HELICAL Re

= 290,000

ORNL-LR-DWG. 18009

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

40
20
- FUNDAMENTAL MODE
] 77 UK Y Lasrny, 2O
&V' - ‘\:\\A \ A AVERAGE
-20 \/ L:I:'/"A Y ] L
-40
-60
TRANSIENT TEMPERATURE MINUS MEAN TEMPERATURE OF CORE WALL
Pt- Pt + 10% Rh THERMOCOUPLE AT STATION 4
{.500" ABOVE MIDPLANE OF HALF-SCALE CORE
AVG. HELICAL Re = 256,000
0.2 | | .
~
T

0.1 / QDAMENTAL Mooer\ /.\

0 AN \ _/ \

N / — N

-0.1 ~—— <
-0.2

0

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

ELAPSED TIME (sec.)

 

Fig. 29. Comparison of Transient Velocity and Temperature Data in the Swirl -Flow

Case
I -T7- bty

CONCLUSIONS
l. ART Core

The following statements about the thermal structure within the ART
core can be made on the basis of the results obtainéd from the heat trans-
fef and fluid flow research presented here:

a) Unless the core shell walls are cooled, maximum wall temperatures
ranging from 17500F to 18500F (depending upon the type of entrance
flow) will exist near the core exit. About 3 per cent of the heat
generated within the core must be extracted to accomplish the
cooling task.

b) Unless the sodium coolant flows through the cooling annuli in a

15, hot and cold spots will exist which will in-

uniform fashion
fluence local shafie, strength, and corrosion of the core shells.
c) Iocal fuel temperatures at the core exit, under wall cooling con-
ditions, are from 100°F to 170°F higher than the mixed-mean fuel
temperature (depending upon the type of entrance flow). Decay
calculations indicate that peak fuel temperatures will not be at-
tenuated markedly as the fuel flows through the short exit passage
to the heat exchanger entrance. These nonuniform fuel temperature

distributions must be taken into account in estimating heat ex-

changer wall temperatures.

 

15. A study of the nonuniformity of the sodium flow through the cooling
annuli for two types of eccentric flow conditions was conducted and
the results reported in reference 19.

= —

 
 

— -7

d) The temperature structure within the core becomes significantly
asymmetric with respect to peripheral position when one pump is
not in operation.

e) The core shell interface and fuel temperatures are transient in
nature (frequency spectrum ranges from about L/2 to 4 cycles per
second). Cyclic stress calculations, on the basis of these tem-
perature fluctuations, indicate that stresses as large as + 13,000
psi will exist in the surface layers of the Inconel core shells
if the metal is elastic. The influence of these temperature fluc-
tuations on corrosion and material strength is unknown at present.

It has been demonstrated that some hot spots as well as some high fre-

Quency thermal cycling will exist in the ART system. This suggests that a
greater research effort is required to determine how seriously these temper-
ature structures influence material strength and corrosion. Some thermal

cycling research has already been initiated by the Heat Transfer and Physical

Properties Section.

 

 
 

— 15

2. Reflector-Moderated Reactor Cores in General

During the past several years, the heat transfer and fluid flow re-
search on high-temperature reflector-moderated reactors has brought to
light certain fundamental problems which prevent the attaimnment of opti-
mum thermodynamic efficiencies. These problems are:

a) High fuel temperatures exist at the core walls which must be

reduced by substantial wall cooling.

b) Radial fuel temperature distributions are normally so nonuniform
in character that the highest mixed-mean fuel temperatures at the
core outlets cannot be realized.

c) Nonuniform radial fuel temperature distributions generate hot
spots and significant temperature fluctuations if the fluid flow
is asymmetrical and unstable in character.

d) Complex moderator-cooling components are required to cool low-
temperature moderators.

In order to remedy problems a, b, and c listed above, it is necessary
to develop a circulating-fuel reactor core whose fuel temperature distri-
bution is nearly uniform with respect to radius. This can be achieved in
two ways: 1) generate a high turbulence level within the fuel by mechani-
cal means and 2) control the fuel velocity distribution so that very little

radial heat flow occurs.

 
- -

3. New Core Configurations

 

One method of generating a high turbulence level within the fuel 1is
to’ £11l a fraction of the core volume with packing such as screens; this
configuration would destroy thermal boundary layers. The hydrodynamic
studies describing this method will be repqrted in ORNL-2199, Two prob-
lems associated with such a core would be the increase in the effective
absorption cross-section of the reactor and the cooling of the packing,
particularly under zero fuel flow conditions.

It has recently been shown that the stabilizing effect of a forced
vortex within a circular tube permits the generation of axial fluid ve-
locity distributions of many desired forms. A unique tubular fuel element
based on this principle has been developed (reference 20) which makes it
possible to control the velocity structure so that a nearly uniform radial
temperature distribution can be obtained. A reactor core utilizing this
fuel element would have the following advantages:

a) A separate core-wall cooling system is not required.

b) An optimum thermodynamic efficiency can be achieved.

c) Hot spot and thermal cycling problems would be greatly reduced.

d) If a high-temperature reflector-moderator is used in the system,

the fuel veloclty structure can be so controlled at the core walls

so that "fuel cooling” of the moderator can be achieved.

 

 
 

— -

ACKNOWLEDGEMENTS

A number of people played important roles in making the half-scale
ART volume-heat-source experiment a success. The authors are indebted

to the following people:

J. M. Cornwell and his colleagues were responsible for carrying

out the design work for the half-scale model.

R. J. Pox and his associates in the X-10 machine shop constructed

the complicated platinum-plastic core model.

E. R. Baxter and other Y-12 craftsmen assembled the volume-heat-

source experiment.

G. W. Greene and J. A. Russell, Jr., designed the control and

- instrumentation circuits of the experiment.

R. T. Guice was responsible for the proper functioning of all

the recording equipment.

F. E. Lynch and R, M. Burnett assisted in assembling the compli-

cated thermocouple system and in the reduction of the data.

The authors also wish to thenk M. D, Eden, M. B. Arnold, and S. E.

Wassom who typed the manuscript and prepared the 11lustrations.

 

 
— -

APPENDIX 1

 

Electrolysis Research

An experiment was conducted to determine separately the effects of
voltage, current density, frequency, electrode materials, and tempera-
ture on electrolytic gas evolution. The results of this experiment in-
dicated that current density, frequency, and electrode materials were
significant. Faraday's law (the proportionality between liberated gas
and current) was verified at bare electrode surfaces. Further, for a
glven amount of gas liberation at an electrode surface,vthe amount of
gas liberafed per unit surface area decreases as the total electrode
area increases,

During the search for electrode materials, it was found that platinum
possessed the unique property of forming a finely divided platinum surface
film, which materially reduced electrolytic gas liberation. This is the
result of the recombination of oxygen and hydrogen due to the catalytic
action of the film. Measurements were made with time of the 60 cycle cur-
rent required to initiate gas liberation at the surface of a platinum elec-
trode of known area. As a result of the surface film accumulation, the
current was observed to increase with time and eventually level off at ap-
pProximately 12 amps/ine. When this value was reached, the surface was con-
sidered fully passivised. However, 6 am.ps/in2 was used conservatively as
a design criterion.

Since the liberation of gas may be considered an effect of polarization,

& stu

y, was also made of the influence of power source frequency on gas

 

 

 
 

E— =

generation. For a constant gas generation rate at a passivised platinum

electrode surface in a 5 per cent Hesoh solution, determinations were
made of the required surface current density with frequency to initiate
gassing. These results are given in Figure 30, where it appears that
the surface current density varies directly as the square root of the

frequency; nemely,
O'N‘/f (18)

This expression is the well-known Warburg law, which relates pola?ization
at electrodes to frequency.

This study indicates that if one employs the resistance heating method

of volume power generation, the following factors must be considered:
| a) Platinum electrodes are superior to other types.

b) High frequencj electric currents make it possible to attain
higher power densities without gas liberation at the electrode.
However, the frequency must not be so great that the "sk;n effect"
becomes important.

c) For é given system with a fixed electrical power frequency, the
volume hea;ing intensity is proportional to the applied voltage,
since the maximum surface current density is established.

d) Electrode arrangements should be such as to distribute the cur-

rent over the greatest electrode area.

 
SURFACE CURRENT DENSITY (amps/in.2)

-84-

  

ORNL-LR-DW

 

60

55

 

 

50

 

45

 

 

40

 

OEXPERIMENTAL VALUES

 

35

30

 

 

:Ti_,2;
0 100

j

ot a Passivised Platinum Electrode in an H, SO,

$4

0

 

 

 

 

 

 

 

 

v

140

180

FREQUENCY (cycles/sec)

220

260

300

340

Fig. 30. Variation of Maximum Surface Current Density with Frequency

Solution,

 

 
I -85-

* APPENDIX 2

* Physical Properties of Electrolyte
‘lfi%?fia
The electrolyte employed in this experiment was a one per cent (by
weight) HQSOu solution. Figures 31, 32, 33, 34, 35, and 36 show respec-
tively the specific heat, thermal conductivity, viscosity, density, elec-

trical conductivity, and Prandtl numbers of the sulphuric acid solution.
3R

_86_

ORNL-LR-DWG, 18011
1.2

 

 

{.1

 

 

1.0

 

 

 

0.9

 

 

0.8

 

SPECIFIC HEAT (Btu/lb-°F)

 

0.7
/

 

 

 

0

 

 

 

 

 

 

0 10 20 30 40 350 60
TEMPERATURE (°C)

Fig. 31. Specific Heat of a 4 Per Cent (By Weight)
Aqueous HpSO4q Solution (Data from Int. Critical Tables)

 

 
THERMAL CONDUCTIVITY

Btu/ hr - f12(°F 7 ft )

ORNL-LR-DWG. 18012
0.50

 

 

0.45

 

 

0.40

 

 

 

0.35 —

...18_

 

0.30

 

 

0.25

¢

 

 

 

 

 

 

 

 

 

 

 

TEMPERATURE (°C)
Fig. 32. Thermal Conductivity of a { Per Cent (By Weight) Aqu%__
Solution (Data from Int. Critical Tables)

 

 
VISCOSITY (Ib/ft -hr)

ORNL-LR-D&G. 18013

| l

 

 

 

 

\.

0 | |

0 20 40 60 80 100
TEMPERATURE (°C)

 

 

 

 

 

 

 

 

Fig. 33. Viscosity of a { Per Cent (By Weight) Aqueous H2S04 Solution (Data
Taken from International Critical Tables) ?a&y}%

_88_
DENSITY (Ib/ft3)

 

ORNL-LR-DWG. 18014

 

66 I I

65

 

64

 

63

 

_68_

62 \\

\

 

 

 

 

 

 

A | |
0 20 40 60 80
TEMPERATURE (°C)

 

Fig.34. Density of a 1 Per Cent (By Weight) Aqueous H»SOg4
Solution (Data Taken from International Critical Tables)

 

 
 

CONDUCTVITY {(ohm ¢m)

ORNL-LR-DWG. 18015

 

 

 

 

 

 

 

 

 

 

 

 

 

0.04
/
/
/
//
0.03 —
//
-

0.02

/oޢ 30 40 50 60 70 80 90 100

TEMPERATURE (°C)

 

Fig.35. Electrical Conductivity of a 1 Per Cent (By Weightfifi Bl us Ho SO4

Solution (Data Taken from International Critical Table)

-06...
 

PRANDTL NUMBER

e
'bfidmfifi'

 

 

 

 

 

 

 

 

 

 

 

-9]~
ORNL-LR-DWG. 18016
10
[ |

8

6 \

* \\\;\\‘\\\\\ssmfifi

2

0 | |

0 20 40 60 80

Fig. 36. Prandtl

H?_SO4 Solution.

TEMPERATURE (°C)

Number of a1 Per Cent (By Weight) Aqueous

 

 
— -52-
APPENDIX 3

Materials of Construction and Flow System Components

-

s

r

a. Ma%erf;iS“of Construction

The materials directly in contact with the stou solution were
Carpenter 20 alloy, platinum, Micarta plastic, Boltaron plastic, Araldite
resin, Plexiglas, Pyrex, Teflon, and Neoprene. The pumps, heat exchanger,
and flow regulator valves were also constructed of Carpenter 20 alloy.
The core model (see Figure 8 for cross section) was made primarily of
close-grain Micarta and platinum.
b. The Half-Scale Core Model

The exact half-scale model of the proposbd ART core was constructed
of laminated Micarta sheets in which were imbedded platinum rings of the )
desired shape. Bus bars contacting the electrodes conducted the current
radially outward. The thermocouples, which were in contact with the elec-
trolyte between the electrodes, were composed of platinmum-platinum + 10%
rhodium.
¢. System Components

Two 20-h.p. Carpenter 20 single-stage centrifugal pumps withdrew the
electrolyte from a glass-lined, 300-gallon reservoir. Carpenter 20 alloy
globe valves regulated the electrolyte flow rates to a maximum of 200
gal/min at a 200-foot head. A thin plate VDI-type 2-inch diasmeter orifice

in conjunction with a 50-inch manometer was used to measure electrolyte

flow rates. The high resistance external electrical curcuit was insured

e

 
- ~93- t_,. R

by means of Boltaron plastic piping in the flow system ducting electrolyte
to and from the core.

The Carpenter 20 alloy heat exchénger was of the cross-counter flow
type having 50 one-half-inch tubes on three-fourth-inch centers in a tri-
angular array. The outer diameter was 12 inches, with a total length of
12 feet, including the headers.

The electrolyte temperature level was maintained by means of a 2-inch
pneumatic valve, which controlled the flow rate of cooling water through

the heat exchanger in conjunction with an automatic regulator.

 

 
o ~oh- R

APPENDIX 4
Calibrations

Calibration curves for the Hathaway galvanometer and Brush recorder
systems appear in Figures 37 and 38. The flow metering orifice coefficient
versus the manometer deflection appears in Figure 39. The variation of the

mean axial Reynolds number within the core is plotted with the manometer

deflection in Figure 40.

 
FRACTION OF D.C. RESPONSE

 

 

ORNL-LR-DWG, 18017

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.0 1 T T T T [ [ ! T T
\VINNER WALL
0.8 N\
UTER WALL
0.6 \
0.4 ‘
INNER WALL THERMOCOUPLE EXTERNAL RESISTANCE =13 OHMS
OUTER WALL THERMOCOUPLE EXTERNAL RESISTANCE = 4 OHMS \
0.2 N
\
0 | I [ | ] | | ] | |
0.01 O.1 1.0 10
FREQUENCY (cycles/sec)
Fig. 37. Freqency Response of Galvanometer 4036-2 ‘?413

 

 

 

 

 

 

_96_
FRACTION OF D.C. RESPONSE

ORNL-LR-DWG, 18018

 

1.0 ! | l

 

i

T

!

 

0.8

 

0.6

 

0.4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.01 0.1

FREQUENCY (cycles/sec)

 

10

_96-
ORIFICE COEFFICIENTS

0.8

0.7

0.6

0.5

 

ORNL~-LR-DWG, 18019

 

 

 

 

_£6u

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2 3 4 5 6 7 8 9 10 20 30 40 50 60
TOTAL MANOMETER DEFLECTION (in. of Hg)

Fig. 39. Volume -Heat-Source Experiment Orifice Calibration (2in. Dia. Orifice in a 3in. Pipe)

 
 

MEAN AXIAL REYNOLDS NUMBER

ORNL-LR-DWG. 18020

AVG. CORE TEMP.
50°C

 

 

40°C

30°C

 

\
\
U

10° ///

 

 

 

 

 

 

20°C
= 1 A
8 — ////
/
5 ,// A // ~
/// /,/ ///
. = -~ pre
- 7 T
—
_—

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

H

4
10 { 2 6 8 20 40 60 %

10 100
TOTAL MANOMETER DEFLECTION
(INCHES OF Hg)

Fig. 40. Axial Reynolds Number Based on Mean Core Perimeter

_86_
Iy | -99- $ .ol

REFERENCES

 

1. Fraas, A. P., ANP Quarterly Progress Report, June 1954, ORNL-1729, p. 28.

2. Poppendiek, H. F. and Palmer, L. D., "Forced Convection Heat Transfer
Between Parallel Plates and in Annuli with Volume Heat Sources Within
the Fluids," ORNL-1701, May 1954.

3. Poppendiek, H. F. and Palmer, L. D., ANP Quarterly Progress Report,
September 1954, ORNL-1771, p. 131 end,

Bradfute, J. 0. et al, ANP Quarterly Progress Report, December 1954,
ORNL-1816, p. 11k,

4. TNikuradse, Johann, "Untersuchungen Uber Die Stromungen Des Wassers In
Konvergenten Und Divergenten Kanalen," Forschungsarbeiten, V. D.-I.,
Volume 289, pp. 1-49, 1929. :

5. Poppendiek, H. F. and Palmer, L. D., ANP Quarterly Progress Report,
September 1954, ORNL-1771, p. 131.

6. Wattendorf, F. L., "A Study of the Effect of Curvature on Fully Developed
Turbulent Flow," Proc. Roy. Soc., Vol. 148, 1935, pp. 565-598.

7. Poppendiek, H. F. and Muller, G. L., ANP Quarterly Progress Report,
December 1955, ORNL~2012, Parts 1-3, p. 177.

8. Bradfute, J. 0., "Qualitative Velocity Information Regarding the ART
Core," CF 54-12-110.

 

9. Muller, G. L. and Bradfute, J. 0., "Qualitative Velocity Profiles with
Rotation in 18-Inch ART Core," CF 55-3-15.

10. Bradfute, J. 0., Lynch, F. E., and Muller, G. L., "Fluid Velocity Meas-
ured in the 18-Inch ART Core by a Particle-Photographic Technique, "
CF 55-6-137.

 

11. Poppendiek, H. F. and Palmer, L. D., "Application of Temperature Solu-
tiong for Forced Convection Systems with Volume Heat Sources to
General Convection Problems," ORNL-1933, September 1955.

12. Poppendiék, H. F. and Palmer, L. D., ANP Quarterly Progress Report,
March 1956, ORNL-2061, Parts 1-3, p. 176.

e
% ST
ey oy

 
 

13.

1k,
15.
16.
17.
18.

19.

20.

21.

e
:afifif

e - e
Greene, N. D. et al, ANP Quarterly Progress Report, June 1956,

ORNL-2106, Parts 1-5, p. 222. "

Greene, N. D. et al, ANP Quarterly Progress Report September 1956,
ORNL-2157, Parts l -5, p. 227. -

 

Churchill, R. V., "Modern Operational Mathematics in Engineering,”
First Edition, McGraw-Hill Book Co., New York, 1944, p. 125,

Latzko, H., "Der Warmeubergang an einen’ ‘Turbulenten Flussigkeits
oder Gasstrom," Zeit. fur Ang. Math. und Mech., Vol. 1, No. 4,
Auvg. 1921.

 

Furgerson, W. T., Stelzman, W. J., Whitman, G. D., personal com-
munication of unpublished velocity data.

Stelzman, W. J, and Whitman, G. D., personal communication of
photographic records.

Copenhaver, C. M. and Lynch, F, E., "ART Reflector Sodium Annulus
Study," CF 56-7-155.

Poppendiek, H. F., Greene, N. D., and Palmer, L. D., ANP Quarterl
Progress Report, December 1956, ORNL~-2221, Chapter 4.1, '"Heat
Transfer and Physical Properties: Heat Transfer in Reflector- -
Moderated Reactor Cores."

 

Perry, A. M., "Core Power and Temperature Distribution,” ART Design v
Memo No. 8-B-1, Add. 2, Feb. 17, 1956.