ORNL-CF-53-9-84.txt

 
ORNL
m FAES Wl

OAK RIDGE SCHOOL OF REACTOR TECHNOLOGY 5 g /

   

F. C, Vonderlage, Director

’ [_—’
"This document consists of &5 —_pages,

No..":..;."":i__ ofgfi._l_Zchcpies, Series,*fi.;..‘_"

 

Reactor Deasign and Feasibility Problem

¥ A REFLECTOR MODERATED, CIRCULATING FUEL, AIRCRAFT REACTOR"

Prepared by:
J. H. MacMillan, Group Chairman
C. B. Anthony
K. Guttmann
C. P, Martin
J. L. Munier

R. D. Worley

August 1k, 1953

 
# A REFIECTOR MDIERATE

Digtribution:

1. J. 3. MacMillian
2. B, Anthony
3. Futitmann

b, P, ¥artin
50 L. Munler
6o D. Worley
Mo Fox

8. Mills

9. Mann

10, . Welnberg
11. Zmola
12, ., Blizard
13. . Briggs

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17.
15,

19. . B. Larson
20. . N. Lyon

21. . C. Briant
22, . ¥, Frasas
23. . A, Swartoub

=
il OoHEER P E QR WO

W riters
Poppendisk
Cole
Livingston
Rickover
Bussard
Yonderlags
Boyis
Covayou

E{f';? e R
Marakle
Mpghreblian
Alexander

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REACTOR"

hO-41 DLViSlO Raactor Development, AEC, Washingion

L2-45 Central Reseavch Idbravy
h6-51 CRSORT Files
52-132 Laroratory Racords

 
PREFACE

The program which has evolved at the Jak Ridge School of
Reactor Technoiogy consiste of two eemesteré of formal course instruc-
tion, followed by ten weeks given to reactor design studies. These
gtudies provide each student an opportunity of applying to a specific
but representative problem the principles and technfilogy which the
school attempts to impart. Individual student groups are chosen so as
to include men of the various engineering professions and scientific
fields in much the same pattern found in a typical reactor project.

This report is based on the study made by its authors while
they were studente in the 1952-53 session of QRSQRT@ It was made and
the report prepared in ten weeks. Obviocusly those weeks wvere diligently
spent. Even so 1t would be unreasonable to expect that the study
reported here is either definitive or free of defect in judgement. The
faculty and meny, perhaps all of the studente are convinced that the
project well served its pedagogical purpose. The report is published
for the value 1t has to those who are professionally engeged in the field,

Ag the authors have noted, several members of the Oak Ridge
National Laboratory gave generougly of their time and,knmwledgé” The
faculty Joins with the authors iu appreciation of that help. Most
particularly is acknowledged the adwvice and inspiration which the group

recelved from ite consultant, E. R. Mamn.

~ F. C, Vonderlage

e ‘
flgk‘for

-
 

ACKNOWLEDGEMENT S

This group wishes to express its appreciation to the members
of the CRSCRT faculty who presented the information which served as
the technical background for this study. Thanks are also extended to
all members of the Oak Ridge ANP group for their invaluable
assistance, patient consultation and cordial hospitality.

For his guidance and assistance. this group expresses its
appreciation to the group advisor, E. R, Mann, Particular thanks
are also extended to H. F. Poppendiek who made the flow experiment
possible and to A. H. Fox for his guidance on the nuclear aspecte

of the reactor,

 

;nf!ca
 

 

Acknowledgements

Tible AT Contents

List of Figures

Section 1

Section 11

hol
b3
A
L
section V
5.1

o R

W

5.3

Introduction
Summary
General Plent Design

Greneral Descriplion

t‘:j

esilgn Philosophy

T

Materis

€3
-

Yot

ffuel

Reflector

Moderator

Intermediate Heat Transfer Mediumr
Fabrication

Reactor Physics

Cross Sections

Sell-snielding

One Group, Two Regilon, Critiecslity Calculation
Two Group, Three flegion Calculation
Temperature Ceefficilent of Heactivity
Fission Product Handling

Excess Pael Reguirements

Einetics

 

4

o

N0 s 3

12
5

9

- Controls

5,10 ~ Btart Up

5.11 « Shut Down

Section VI - Reactor Englnesring

6.1
60

6.

Section VII

2

3

- Optimization
- Heat Transfer
6.2.1 = Germa Heating
6.2.2 - Internal Heat Transfer
6,2.3 - Reflector Cooling
6.2.4 - Primary Heat Exchanger
6.2.5 - NaOD Heat Exchanger
-~ Fuel Flow Experiment

- Shielding

Section VIII ~ Conclusions end Recommendations

Sectlion I -

Section X -

om0 W

10

References

Appendices

- Design Data

-

One Group, Two Reglion Data

Two Group Cross Section Weighting
Two Group, Three Region Data
Optimization

(ramma Heating

Core Heal Transfer

Primary Hesat Exchanger

NaCD Heat Exchangsr

Nomenciature

38
39
39
40
Lo
40
40
Ly
k9
53
5k
25
o7
29
61
63
63
67

10
n
73
76
71
78

 
Figure Number
1

2

O

10
11
12
13
14

 

LI15T OF FIGURES

Title

General Plant Layout

Schematic Drawing of the Fuel Tubes
Typical kgpe vs. Uranium Mass Curve
Characteristic Self-shielding Factors
Thermal Utilization Curves for Cylindrical
Fuel Tubes

Nuclear Approximation of the Screwball
Gamma Heating Distrifiution

Over-all Heat Transfer Coeffiecient vs,
NeOD Velocity

N20D lieat Transfer Coefficient vs, NaQD
Velocity

Temperature Variations Through the Core
Reflector Power Absorption Curve
Photograph of the Flow Experiment Apparatus
Shield Weight Curve

Ciyitical Determinant

 

oo

25
45
L7

48

50
52
56
58

30
 

I  INTRODUGTION
The objective of this project was to apply the theoretical
information presented at ORSORT to the design of a reflector-
moderated, circulating fuel, aircraft reactor.
The scope of the investigation was limited primarily to
an analytical evaluation, although a minor flow experimeni was
performed .
This design study has been limited to the reactor; the

propulsion system has not been considered.

 
IT SUMMARY

A preliminary feasibility study of a 200 MW reflector moderated,
circulating fuel, aircraft reactor is presented. The Screwballm core
configuration as presently conceived consists of:

1) A spherical shell beryllium reflector

2) ARE tybe fluoride fuel in helical tubes arranged in

annular form

3) NaOD moderator and reflector coolant

In an attempt to justify the use of fuel tubes, an experimental
investigation of the flow in a model helical tube was conducted.

The reactor analysis was conducted on a two group, three region
basis. The nuclear cross sections were appropriaztely weighted and
judiciously applied so that the results compared favorably with the
multi-group machine calculations.

The reactor presented is believed to be conservative and appears
to be feasible, The fundamental limitation is the 1250°F maximum wall
temperature tor prevent excessive NaOD corrosion. Large NaOD flow rates
and ample flow guidance are required to minimize corrosion. If the
corrosion limit can be raised, the use of NaQOD as moderator and
coolant has greater potential.

Helical fuel tubes ares recommended to reduce the uncertainties
of unstable flow in high power-=density reactors. The engilneering

complexities introduced by their use are justified for controlled flow.

 

* The resctor described in this report will be called the "Screwball®
(the Fireball with = new twist). .

 
ITIT GENEBAL PLANT DESIGN
3.1 General Description

The Screwball is a spherical, reflector moderated, eirculating
fuel reactor. The fuel enters the gore at the north pole and flows
downward through six 3.5 inch I.D. inconel tubes. Five of these tubes
are wrapped in a variable pitch helix to form a spherical annulus of
fuel and the sixth tube passes through the center of the sphere forming
a helix of smaller diameter, See Figures 1 and 2. In returning the
fuel flows over NsK cooled tubes in the primary heat exchanger which is
wrapped in a spherical annulus surrounding the beryllium reflector.

The beryliium reflector has the form of a spherical shell with holes at
the north and south poles for entry of the fuel tubes. Sodium deuteroxide
flows downward through the spherical cavity in the beryllium and surrounds
the fuel tubes, hence functioning as a moderator "island". The NaQOD
returns to the top through 0.23 inch diemeter holes drilled in the
reflector and through a spherical cavity outside the reflector thereby
removing the heat preduced in the reflector., The NaOD then passes through
& heat exchanger and is pumped back through the core,

The intermediate heat transfer medium, NaK, returning from the
propulsion system passes through the sodium deuteroxide heat exchanger
and then through the primary heat exchanger. This system uses only one
intermediate heat transfer medium and eliminates the necessity of
additional radiators for subcooling a portion of the NaK as proposed for
the Fireball. However, a control system is required which will keep the
return NaK temperature constant., If the temperature rises, the NaOD will

be insufficlently cooled and excessive corrcsion may result. At return
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

FUEL TUBES

 

- GUIDE YANES

 

 

 

 

 

 

 

 

| = ==

 

 

 

 

 

 

 

 

 

 

GAS CPESSURE

?
I{g
DEUTERIUM L_jl_— ;.\i\

 

 

 

 

MAK INLET O :
i
1

 

 

 

 

 

 

 

 

 

’L

 

EXCHANGER

FIGURE |

SCREWBALL
GENERAL LAYOUT

APBPROKIMATE SCALE ~ 4 SIRE
30~

/o
NaQD HEAT __/

 

- AA

 

L~ BB

BORON LAYERS

~_ 7

 

 

 

 

 
 

’_KPRESSUEE SHELL

 

      
 
   
     
      

( =—FUEL DRAIN

- NaOD DENN

Dwm'n, Hamre

- 0

 
UNCLASSIEIED

 

DW7.#2—3M"7
FUEL IN
FUEL OQUT
OWG, BY C.PM.

SCHEMATIC DRAWING
OF FUEL TUBES

-11-
temperatures below 200°F,, the fuel will freeze in the primary heat
exchanger, With its inherent simplicity, the use of a single transfer
medium warrants further investigation. Figure 1 is & drawing of the
Screwball system, and a tabulation of design dasta is contained in the
Appendix 1.,
3.2 Desipn FPhilosophy

A brief survey of NEPA, ANP, H, K. Ferguson, and Technical Advisory
Board reports indicated that homogeneous reactors held the greatest
potential for efficient nuclear propelled flight. Since little information
is available on a combined hydroxide of lithium and sodium (the most obvious
candidate for a high temperature homogeneous reactor fuel)} the circulating
fuel type reactor was chosen as an intermediate step between fixed fuel
elements and the homogeneous type fuel. The large heal tranzfer surface
required in fixed fuel reactors is removed from the core in circulating
fuel reactors and the potential simplicity of homogeneous reactors is
retained., The moderating propertlies of the uranium bearing, fused salts
are generally poor, but employing thick, . efficient reflectors enables the
construction of a small high power reactor.

Having chosen a reflector moderated, circulating fuel type reactor,
a nore detailed investigation was initiated on the Fireball as described in
Referenca 2, Investigation of the Fireball design parameters yielded the
following five problems which appeared to warrant basic design changes or
modifications:

1. Eigh power density
2. Questionable fuel flow patterns

3. VPossibility of pressure surges

12
L. Cooling the Be "igland"
5. Self-shielding in the fuel

The Screwball eliminates or reduces the magnitude of each of
these problems except pressure surges. To achieve these ends compromises
in simplicity and resctor size have been medes however, the increase in
shield weight over the 22.5 inch core is less tham 10%. It is believed
that this reactor has a real potential for alreraft application, and as
such warrants further investigation.

The controllability of a high power density reactor has been neither
proven nor disproven. E. R, Mann states that controlling a reactor in which
the fuel temperature rise in the core exceeds 2000°F. per second will be
difficult and somewhat doubiful. To be more conservative, a power density
of 2.5 K¥/cc (1070°F. per second) has been chosen for this reactor.

With such rapid increases in fuel temperature only short lived flow
instabilities or eddies can be tolerated in the fuel., The use of fuel
tubes in the Screwball has greatly reduceé the uncertainty of sustained
instabilities in the fuel region. Aabrief gqualitive experiment varifying
stable flow through helical pipes is described in Section 6.3.

Pressure surges result from rapid density changes due to temperature
variations which occur in eddies of lengthy duration, or from the
instentaneous introduction of a cold slug of fuel. A step decrease in
temperature is difficult to visualize in a cireculating fuel reactoer,
Pressure surge calculations have been made on the Fireball assuming stagnant
fuel in the core and a step increase in k of 1% throughout the core.

These assumptions are both conservative since neither condition is likely to

oceur in the reactor. Based on these assumptions the resulting pressure

-] 3w
surge is not expected to exceed 150 psi.. As a result of the more
tortuous expansion path out of the core, pressure surges in the
Screwball are expected to be larger. However, the fuel tubes in the
Serewball will withstand pressures of 200 psi and no difficulty from
this phenomenon is antieipated.,

The beryllium central "island" in the Fireball reactor requires
ccoling to remove the heat generated by neutron moderation and gamma ray
attenuation. The density of heat generation is 100 to 200 watts/cc, and
its removal will require a large number of coolant tubes. The beryllium
hes been replaced in the Screwball by a circulating "island® of NaOD,
However, the problem of NaOD corrosion has been introduced. As indicated
in Section 6.2.2, no stagnant or low velocity layers in NaOD can be
tolerated next to the hot fuel tubes or containing shell.

The self-shielding effect, as described in Section 5.2, for the
3.5 inch diameter tubes of the Screwball should be less severe than for

the spherical fuel annulus in the Fireball.

] Lo
IV MATERIALS
4.1 Fuel

The proposed fuel for the Screwball is a fused salt containing
50 mole percent NaF, A7 mole percent ZrFA, and 3 mole percent enriched
UF&. This fuel is similar to that prqposed for the ARE and was chosen
because considerable information is availsble on its
physical and chemical properties. To relax the limitation on the
temperature of the returning NaK (Section 3.1}, a fuel with a lower melting
point would be desirable. Inconel will be used as the fuel containing
material.
4.2 Reflector

The reflector has two functions; moderation and shielding., Be is
a good moderator. Its moderating ratio is 159 compared to 170 for carbon,
In addition, it serves as an excellent shield due to its high atomic
density and small age. The fast neutron leakage for a given reflector
thickness is much smaller for beryllium than for sybstances. such as NaOD,
BeC, graphite and BeO apgregate. (Reference 2, Figure 7). Hence,
beryllium has been chosen for the Screwball reflector.
4.3 Moderator

A fluid moderator with 2 low vapor pressure al elevated temperature
was desired., Their high wapor pressures eliminated the possibility of
using light or heavy water. Hydroxides were then considered,

The diffusion length of a hydroxide is very small relative to its
age. Hencé, a hydroxide in the core of the Screwball would serve &s a

sink for fast neutrons rather than as a moderator, Deuteroxides do not

have this undesirable nuclear property and should exhibit similar physical

-] 5
and corrosive properties. Therefore, 110D ; NaOD and combinations of
both were considered., The double isotopic separation eliminated LiOD
from serious considerationi NaOD was chosen for the core moderstor,
Na0D also serves as the coolant for the reflector., It is a better
moderator than sodium (the proposed Fireball reflector coolant) so that
the Screwball reflector should be a more effective shield. However, the
macroscopic cross section for thermal neutrons is larger for NaOD than for
godium, The slight difference in absorption does not warrant cohsidering
the additional complexity of a separate sodium system for the Serewball,
BMI has made a survey of containing materials for NaOH at
elevated temperatures (Reference 23). Graphite, silver and nickel were
the most salisfactory of the materials tested, Nickel was chosen for the
Screwball on the basis of ease of cladding and electroplating and tolerable
neutron cross section. The corrosion mechanism of NeOH on nickel is
reported in Reference 4.

2 NaOH + Ni = NephiOp H,
N&2O @Ni()

The reaction equilibrium is temperature sensitive resulting in
mass transfer of nickel from hot regions to adjacent colder surfaces,
The corrosion can be suppressed by hydrogen pressure over the NaOH,

The corrosion mechanism for NaOD is expected to be gimilar to
that for NaOH, but the degree and temperature dependance of the corrosion
are unknown, For this study, the temperature Ilimitation for NaOb
corrosion of nickel is assumed the same as for NaOH,

According to Reference 3, corrosion of nickel by stagnant NaCH is,

~16~
1) not néticable at 1000°F

2) small at 1250°F and would be tolerable for
alireraft applications

3) excessive at 1500°F

A 1imiting wall temperature of 1250°F and a deuterium gas
pressure in the NaOD expansion tank of two to three atmospheres are
proposed for this reactor.
4oL Intermediate Heat Transfer Medium

A near eutectic alloy of sodium and potassium, 56 weight percent
Na and 44 weight percent K, has been chosen as the intermediate heat
transfer medium. As is typical of liquid metals, this alloy has excellent
heat transfer properties and also has a low melting point (66°F), The
main disadvantage of NaK is the induced radiation resulting from neutron
bombardment in the primary heat exchanger.

4.5 Fabrication

The proposed methods for fabricating the primary heat exchanger,
punps and beryllium reflector are the same as those described in
Reference 2, Ni will be substituted for chromium in the reflector.

Bending the fuel tubes is possible (Reference 5), with the use
of a cermet internal mandrel.

The NaOD heat exchanger is standard, welded shell and tube
construction.

The entire system will be welded, Reference 6 states that welds
in nickel for 1000°F NaOH corrosion tests were made with no unusual
difficulty. Inconel welding presents no major e¢omplications.

The fabrication sequence has not been fully considered in the layout

of Pigure 1. Modifications may be required to facilitate assembly of parts.

=17
V REACIOR PHYSICS
5.1 Cross Sections

The cross sections used for nuclear calculations in this report
are based on current ANP data.
5.2 3elf-shielding

The application of diffusion theory in Reactor design, yields at
best only a reasonable gpproximetion of the nuclear characteristics of
homogeneous systems. The Screwball is a heterogeneous rezctor which has
been homogenized for the purpose of expediting the nuclear calculations.
This fact makes it necessary to correct the diffusion eguations by lntroducing
a parameter commonly referred tc as the self-shielding factor, F. This
factor accounts for the local depression of the neutron flux within the fuel
region, which in turn results in decreased thermal utilization of the fuel
Two major disadvanbtages result from self-shielding. First, more fuel is
required than for a homogeneous reactor of the same proportions: and
second, the negative temperature coefficient is not as large. As seen in
Filgure 3, a smaller change in k pe results from the removal of an equal
mass of uranium for a reactor with a greater uranium investment.

Figure /4 depicts estimated values of F vs. fuel tube diameter at
various reactor operating temperatures., The calculations were based on
the method set forth in Reference 7. To apply the method one must know
2 and % of each constituent, the atomic densities in the fuel tube and
its diameter, and the variation of f with 2By as shown in Figure5~

From these data calculate,

18-
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

_fi:’—"rc;r LEH s U atim Maoss  Cloeve
fo _ANP Coocunring _VFoee| £xg cries
Y i
N L
S e
3 /
8 /
g 3 /
M
/
¥
S
g /
b /
g
U‘H ;WAJ,F
2319w
g, 2 #
 

20
 
F= % opp = momt
PR R W
a Tt

as a function of lethargy, which i1s then used as a multiplying constant
on the macroscopic cross section of uranium,

The self-shielding factors which were incorporated in the Screwball
configuration were Ffast = 0.8, and Fgp = 0.5. It is believed that these
figures resulted in a conservative value for the critical mass.

5.3 Oneg Group, Two Begion, Criticality Calculation

As & basis for advanced engineering and nuclear calculations, an
estimate of the Screwhall criticsgl mass was necessary. For this purpose a
one group, two reglon calculation was made of the proposed configuration.

The general method of caleulation is discussed in Reference 8,

equation 8,31.1

 

1
Pt P 1 7 Bo R (1m %_ag] - or o coth L.
© DC BC ' Ly
Bc = -.;l:-m & DC = 1 ) },'{ _
~} 3 Zir, TS r, core radius
Ly =| f-2- s T = Reflector Thickness
: 5
& r

Note: Edquation €.31.1 is im error in the first edition of Reference 8

The item K}m Eg should read 1o 2;
Dy De

The effective reflector thickness was computed for ANP Reactor
121 for which the critical mass had been calculated by the 32 group IEM
technique. Assuming the same effective reflector thickness, the critical

mass was detgrmined for the proposed Screwball,

DD
For the purpose of cross section weighting both reactors were
assumed 50% fast and the fast fraction to be equally distributed among
the lethargy groups. A salif-ghielding factor of 0.7 was applied to the
resulting one group crose saction. Thermal base 92 was used., Dats used
in the calculation are contained in Appendix 2.

A critical mass of 36.4 pounds was obtained for an effective
reflector thickness of 4,04 ¢m. This corresponds to 3.05 mole percent

UFh in the fuel.

5.4 Twe Group, Three Region Calculation

 

The problem of calculating the critical mass and flux distribution
of intermediate reactors is wmore difficult than for thermal reactors. The
ong group approximation is unsatisfactory because of the wide variation in
epithermal cross secticns, Furthermore, the comparatively small size of
intermediate reactors increases the lmportance of the reflector. This
fact holds particularly in connection with reflector moderated reactors as
axemplified by the Fireball and the Screwball, In these reactors the
nuclear aharact@riatjcé are strongly 1nfluenced by reflector composition
and its thickness.

Because of the uncertainties in cross sections in the intermediate
energy range, it is not anticipated that calculations willl lsad te accurate
prediction regarding the critical mass and flux distributions., It appesars
that these calculations willl at beat be a reassonsble approximation of the
nuslear characteristics of the reactor. In order to conduct the reactor

analysis expsditiously, the two groups, thres region method was used.

-23w
is schematically depicted in Figure 6.

sphere
1T and

region

are:s

Region

Region

Region

The avproximation of the Screwball used for nuclear calculation

Ry is the radius of the inner

(I), with Rp and R3 representing the radii of spherical shells

IIT. As applied to this rsactor, region 1 is the moderator,

II the fuel bearing medium and region 11l the reflector.

The diffusion equations which were used in the reactor analysis

I -szlvz,GIl + zfill fr, 0

»
nd -DI, <7< 5 = 5

> =D, + 2 =
Ix -Dyp V%) + R f1ny arr Prr,

” zfllzfillz

R ,
end D1y VoI, * Yaqpfir, - Zfinlfilxl

e Dror 2 .
Iz -Dryp, ¥*rin * 2Riin, 4111,

and

o Do 2 v
111, V%111, + 2

S fri,

—

i

0

R #.
IIII 1111

* VZgn

gIIl

where subscripts I1 indicates fast group region I and where subscripts I2

indicates thermal group region I, etc.

In the sbove

Zfi =

3’2% fi&l

0
in

b

The above equations arc¢ founded »n the following assumptions:

(1)
(2)

(3)

There are no fast absorptions in the reflector

There are no scattering collisions with the

uranium in the fuel

A1l fast absorption in the fuel region is due to

uranium

-2 f
3191
Drawmg ;{::'/ F7 s
Cl 8

 

25~

o T
(1) The use of 'f Z% in place of ¥ Zj is a valid

approximation providing 24 <K'l

5
(5) The nentron energy spectrum, from source to thermal,
can be divided into two representative energy groups.
(6) Neutrons do not Jeak before the first collision.
(7) The Doppler Effect is neglected.
(8) Crystal effects are neglected.
(9) Moderation essentially takes place in the reflector-
moderator region.
The applicable boundary conditions for bhoth groups are:
(1) Symmetry or nonsingulsrity of flux at the center of
region T.
(2) Egual fluxes at the interfaces.
(3) Equal currents at the interfaces.
(4) Fluxes vanish at the extrapolated boundary.
Solving the diffusion equations and applying the first and fourth

boundary conditions yields the following expressions for the flux:

fr = Ay siph I

 

 

1 L
=
hy
sy T
WI? = 02 S17in le . T
= o Sj Al ilflh LIZ

T

 

 

1 = 43 5in gr A, cosgr + Ag simhlr 4 pg coshhr
1 T T g T

 

 

p = 854 Ay 8In gP &+ S48, ©0S gTy g4, sinh hr 4 g, cosh hy
I 2 3 - 2 e - ’ e
2 g £ - 375 e 34 -
&.
#

 

el
IIT, _iwL:tz:fl
I
~ e
= R R
finz? G sinh.f?.:%l sinh 3=
: I 4 Syhy Lr11q
T r

The constants in the above equaltions are defined as follows:

(1) LIl: Dll (2) L ) =
zhl
1

(3) g =102 (Zfi T, 4% J
IIz . IIl+ IIlw 1T

D11, Dlll

 

o

+

 

 

 

e 45 2 (= 5. A Iz
;?112 (Zhiz + aIIlm fII) ) 3112(Zfile+ aIlq~ fIIl)- fIizzfiIIl

 

 

 

 

 

 

 

1
D, D | D, D
11, 1T, 11,711,
2 _1 s | 5 A=
(/1) =h" = = ac a (ZR & )
2 oo o \ 711, + 11, - flil )
D D
112 111
5 (3, +3, -9z 2 (% (ZR + 5, =z }-«)z* %,
3112 +( 1, 1L ffil 4 9 1\ -frrq frn YIL J'-Hz 11,
D Drq Dor”
P11, 11, 11, 11,
) S, =
(5) 5 % .
1
)
5
6) S, = D e + % . %
(6) 8y = "1 *zflzzl + arp, ~f 11
4z
F o

L
 

 

 

(7Y 84 = T >, D 5
> zfilxl + 87, - 9111 - I kb
Y3
f i1
2
(8) s =
& zfiIII
1
D 1 1
II1 (:m-
21 L-+-2 -~ L 2)
111, 1112
~?
(9) Ry= Ry 4+ 2 DIII2

8.
Eight equations with eight unknowns result from applying
the remaining boundary conditions. A non-trivial solution for
these equations is obtained if the coefficients of the determinant
(figure 14) vanish; this then establishes the critical equation.

The two group calculation method requires accurate and
Judicious application of nuclear cross sections. Thermal base 92
values were used for determining thermal group cross seetions and
an average over lethargy groups 1 through 26 for the fast group.
0r< vs. r curves were plotted for ANP reactor 129 and normalized
area fractions (Appendix 3) determined for each letharmy group and
reglon, These areas are proportional to the fraction of neutrons
in each group. The same neutron versus lethargy distribution was
assumed for the proposed Screwball reachor,

It is possible to solve the criticality determinant after
calculating the nuclear constants (L, D, and £ ) from the specified
dimensions and material constituents for each region. The critical mass
is obtained by iteration and is that uranium mass which results in the
zero value of the determinant. The method for sclving the determinant
is presented in Reference 9.

To check the validity of the method of analysis, a2 ealculation
was conducted on the Fireball Reactor 1293 its critical mass as
determined by a 32 group IBM calculation was 23 pounds of 8235. The two
group three region calculation of reactor 129 predicted 23./ pounds of
0235,  This indicated excellent correlation between gnalytical methods

and choice of cross sections.

w2
CRITICAL DETERMINANT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

AQ AB Aq— AS A;, CQ_ A-, C‘i
! | | l
ginh {?T\_\ . —sin (g?l) — co% (%B) - sinh (h ?1\ ] - Cosh {h’?\) \ © © ©
=1, ! 5 I
S !?.\ s, s (g®) lae) | ! L e nh (B l o O
S | =) =S5 (g%) | =5, ws QR - S5 sinh (k,??‘\ ~ Sy cost (1)) s (T l
3,/ = ta
: |
‘ E ! ’ ‘ ! k — sint lm\
0 sin {%Ql} 1 cos (61?2)  sion (kR . cosh (hRy) C smn\ = O
|
| | | |
| ; - \ N | 1 %=\ [Re—%2)\
O S,3n (8)’9?2_\, ] S, cos \8‘21) Sa s (M?l) Sz coch (Wi, ) C i -S4 smh\ 2 mz’. ~ sinh . SL-m‘_L
- Di,, ___L C-Oih \ ’LDE‘ [‘2.8 cos {Efie,) ‘ Dfl P(j s (2)? ) ‘D’il r?,i?\. cosh (h?n\ ‘L DXL‘EE‘h 5m¥»(h?.\) k ‘} p
| ; | O
- ;. B’ . ; - ‘ O
- s, _\ ).l - SN (5&"\‘ ‘( + 08§ (8?, 3 —~ S i 1-?.,\_] -;‘Cosh. (h?.)! l ¢
— e e Tonen YR AN
! ’D.I < [*? cosh (E’{\) Difl S, [?.a cos “(D?' S L;?,;bm.(BE B S I—”E?hco&r [th"‘\ Dj.zsa [?.h Sinh (r\P./: %A 5,_4—'12. " (':l’ ‘
| 7 . Y ' [ 1 ) O
- SN 3 .i_x ] T (5 E‘}‘l -;r COS {8?1>j I" - S\nh' (H?) I : ~ COSIn (h.‘?ij-}’ ‘_S‘Y\h :{KffLL\ C
- [
~ T /. _ Ns n X {té R \
i—'DnJ_'Eg?)cas(?sz) iDH\LKQES‘“{g)EZL\) Pt [h cosh | r'Ef\ 5 L? %“5“"}‘\‘”?}’ T ka\___l___m_li o
O : . ~ - ’ i o E’l
— S (?)EIZ).: + CoS (8??.5:1 —_ SW\}\; (W‘E2_>l “ - COS‘T\ '\I"l \Z}J [ O : ~ SPT"‘L ( ,_I[;‘ )_l r %
- i £. RN I 5 T - o ' Y ‘S %z B2\ |-y | o2, ~ R\
"" DizgztEggfor (f)'?l% DIL.;Sl I.EJ;Z) 5w (@ :?\/:.”'DI;H-Sg L?zh Cosh (;\22\1 Dizsa l‘th Sian '{\’\?z E Dflnl.:fi CO‘SKL > ) J*J;LL_ cosh ! L Lmn.
0 B ¢ | _owh (R 0 o RBem R\
— Swm {(Z\EZ\}J + oS (Z]R’z)j sk (nE’zll —cash \h? '{ +smh | L meifii i +Smk’( L )E
UVCLAS S/FrED
Tieoee |4

-
30 -

TOTLE # Buimsag
The value of the determinant veries radically with small change
in uranium mass, The determinent for the Serewball was zero for two
assuned uranium masses, 3/.8 pounds and 49 pounds. The curve of
determinant velue versus uranium mass 'is similar to reactor 129 for
messes around 3.8 pounds, Hence, the mess of thé screwball is
approximately 34.8 pounds of U235a This results in the following
fluoride fuel'compositicn:

2.9 mole percent UFA
47,1 mole percent ZrF&
50.0 mole percent NaF
Several efforts to calculate the spatial distribution of the flux

yielded results of questionable validity. Very small changes in the nuclear

constants produce major changes in the flux distribution. With such a

sensitive relationship no significant conclusions have been obtalined.

" Based on the results of the ANP 32 group calculations, it is
anticipated that the 3crewball will be approximately 50 percent thermal.
If so, the flux level réquired to produce LQDO\MH.is 1019 neutrons per square
centimeter per second,

5.5 Temperature Coefficient of feactivity

The Screwball has been conceived for possible use in aircraft
applications. It is therefore important that its contreol system te as
simple as possible. Since the use of control rods is not anticipated
and the delayed neutron contributions to the flux are attenuated when
the fuel is circulating, the control of this reactor cén be assumed to e

satisfaetery'ohly if it is provided with a strong negative temperature

w3l
coefficient of reactivity. This coefficient is a function of numerous
nuclear and physical parameters, a few of the more important ones being:

(1) liquid fuel expansion

(2) fuel tube wall expansion

(3) Doppler effect in fuel

(4) moderator expansion

(5) thermal base changes with temperature

There are several reasons why keff is temperature dependent,
the most important one being the thermal expansion of the core materials.
This effect usually resulfs in reactivity decreases with temperature
increase, 1f the over-all temperature coefficient is positive, the
continuous increase 1in temperature relegates the reactor to a short
nonuseful life. The reactor then contains a built-in suicide complex.
A negative coefficient is obtained from the thermal expansion of the fuel
and its loss from the active volume, Moderator expansion, resulting in
increased neutron leakage, is also a large contributor toward a negative
coefficient. The Doppler broadening, which for enriched fuel could
provide a positive component of the temperature coefficient, has not been
consldered in this report. In this connection, it is believed that
addition of U238 «0 the enriched fuel may possibly cancel or overcome the
Doppler effect; the price is a greater fuel investment.
The calculations were conducted on the basis of a two group

thermal reactor. Although the Screwbsll has been estimated to be 50
percent thermsl, it is believed thalt a reasonable estimate of the
temperature coefficient was obtained. It was also assumed that the product
of the resonance escape probability and the fast fission factor rere equal

to unity.

~-32~
The effective multiplication factor based on two group,
thermal reactor theory is:

= e

X .
(1+ Cn B2) (1s IPBR)

eif

This steady state equation is temperatufe dependent as a result
of temperature variation of core geometry, material densities and energy
distribution of the neutrons, The fractian&l change in keff which
accompanies a unit temperature rise 1s the temperature coefficient of
reactivity. This quantity must be negative for stable reactor operation;
it is obtained by taking the logarithmic derivative of the above equation

with respect to the temperature,

 

Gl R [ L) B [ W
The solution of this equation based on the mean operating tempersture of
approximately 1300°F and including cross sectionsappropriately weighted by
the self-zhislding fuctor, yielded the following results:

(S‘k/k

| = 2.1 x 1070y
$T Jtotal

S?/& = -0,7 x 1074/op | (?Ei& = =1.4 x 10™4/op
8T | fuel ? 8T } moderator

The ratio of the moderator to fuel coefficient is two to one.
This ratio has important bearing on the kinetic behavior of the reactor
because of the relaticnship between the temperature response time
congtants for fuel and moderator regions., For the Screwball these time
constants are approximately 1.3 and 9 seconds Tor the fuel and moderator

respectively; the ratic of moderator to fuel constants is: approximeiely

m33-
seven., The combination of the above ratios becomes most important
when the powver increases unless the mean moderator temperature is kept
constant the fuel may freeze. The explanation of this phenomenon is as
followse an increased moderator temperature reduces the reactivity and
causes the fuel temperature to decrease since its negative temperature
coefficient compensates for this reduction in reactivity and maintains
the reactor critical. Since the reactor is without servo=type control rods,
it may be possible to forestall this possibility by maintaining a constant
mean moderator temperature.
5.6 Fission Product Handling

The two major fission products which absorb neutrons
parasitically ere Xe1?? and sml49. m important advantage of circulating
fuel reactors is the possibility of continuwously purging Xe and other
fission product gases from the system, thereby appreciably reducing the
fuel inventory required. Reference 22 proposes bypassing a fraction of
the primary fuel sitream through a turbo-diffuser unlt in which the Xe is
purged with helium., It has been estimated that for an assumed equilibrium

¥e concentration condition of 8k . g 3% , about 6 percent of the
K >
primary flow must be continucusly passed through the separator.

Additional fuel will be added "o account for the reduction of keff

due to absorption by the equilibrium Xe. Samarium poisoning under

s

equilibrium conditions is expected to have 2 8k _ 4 64 o Fuel will
k

have to be added to take care of the equilibrium Sm absorption.

33J+m
5,7 Bxeess Fuel Requirements
In accordance with Reference 2, the change in uranium mass
required for a given change in kgpp (for ANP circulating fluoride fuel

reactore iz given by the relation:

| jiEZEM o 0,22

It was estimated that a kgpe of 1.021 will be required if the
reactor is to operate at 100 MW for 100 hours., Background information
for caleulating this figure was obteined from various ANP, ARE and HEF

reports. A breakdown of the component k,pe is:

Critical 1,000
Equilibrium Xe override 0.003
Equilibrium Sm override 0.006
Fuel depletion ' 0.006
Excess for delayed neutron attemuation 0.005

Excess for instrumentation in the reflector 0,001
kopp = 1.021
The excess reactivity required is obltained by increasing the
critical mass by 3.3 poundsi of this, approximately one pound will be
used to shim the system during operstion.
5.8 Kinetics
The question of inherent stability is extremely important with
high powered, mobile, circulating fuel reactors. Since high power at
high thermodynamic efficiency is required, a reactor temperature approach-

jng the upper permissible 1imit is desirable. The extremely rapid power

=35~
fluctuation possible in reactors of high power density deems manual or
even servo-type conirol impractical. As a result control rods for use
during normal reactor operation were nol considered feasible.

The transit time of the fuel through the rezctor is a fraction
of a second. As a result, the delayed neutron contributions to the flux
are attemuated when the fuel is circulated, Normally, the delayed neutrons
play an important role in conventional reactors; their attenuation ralses
a legitimate worry regarding the stability of the Secrewball.

There are two aspects to inherent stability, (1) statiec, which
means that an increase in reactor temperature causes the reactivity Lo
decrease, and (2), dynsmic, which means that the oscillations in reactor
power are inherently damped. As indicated under Section 5.5 the Screwball
has been calculated to have a strong negative temperature coefficient,

Current data and theoretical studies indicate that the rapid
circulation of the fuel itself provides a powerful damping factor for‘power
oscillations with periods comparable to the transit time of the fuel
through the reactor. This damping factor is presumed te compensale for
the delayed ncutron attenuation. Evidence supporiing this statement

3s ‘et forth under References 10, 11, and 123 it 18 dindicated that the
circulating fuel reactor equation (without reliance on delayed neutrons or
control rods; hes no antidariped solutions for the following, not entirely
realistic conditionss
(1) constant power extraction
(2) large temperature and power excursions where the
steady state power 1s four times design power for

all times

-36-
(2) sudden positive excursions of the power to
ten times design power,

It would seem that a properly designed circulsting fuel reactor is no worse
with respect to dauping oscillations than one in which none of the delayed
neutrons are attenuated,
5.9 Controls

The underlying control philesophy for this reactor is the
"master~slave" relationship, where the power plant is the master and the
reactor the slave. In other words, the power extracted from the reactor
is determined solely by the demand of the propulsion system.

The Screwball econtrol system is basicelly dependent upon its
large negative fuel temperature chbefficient. As stated in Section 5.7,
shim control is obtained by addition of enriched fuel; a possible basic
écheme to zeccomplish this is set forth in Reference 13, There are not
expected to be control rods in the reactor fuel and moderator regions.
Ceonsideration should be given to the possibility of a variable bypass on
the Xe separator to provide fine adjustments in reactivity between batch
additions of enriched fuel.

fn dmportant advantage of the circulating fuel reactor powerplant
combinstion, is that preliminary analysis of controlability of a loosely
coupled system can betpredicted for each separsate ccmpofiento Reactornand
engine stability problems can, therefore, be attacked independently since
surges in either component are admitted to the other after considerable
delay. 4&s indicated in Reference 14, it appears that the mgster-sliave idea

can probably be satisfactorily reduced to practice.

e
5.10 Start Up

A possible procedure for starting the reactor is as follows:

(1) Heat the fluorides, to a mean temperature of 1300°F in an
external system and add the enric:hed fuel.

(2) Using an external heat source, heat the NaK and NaOD.

(3) Bring the fuel, at correct concentration, to 1500CF,

(A) Instsll a strong polonium-beryllium source in the reflector
(perhaps by mixing molten polonium with the beryllium in a separate
reflector tube).

(5) Transfer the fuel into the heated reactor system.

(6) Allow the subceritical fuel to cool. At about 1300°F, with
the moderator temperature closely controlled by the NaK, the core should
be critical,

The reactor should now be ready to supply heat to the propulsion
system. In the event that the temperature of the moderator can not be
precisely controlled, it may be possible to wvary the height of the
moderator level in the core and thereby effect a reasonable degree of
control for start up,

5.11 Shut Down

Driving a reactor suberitical when at idle power without the
use of safety rods may not be a practical possibility. The practicability
of draining the fuel from the core was given lengthy consideration, This
was eliminated on the grounds that the additional weisht, higher radistion
levels and manifold engineecring complexities would be associated with

this systemn.

=38-
To drive the reactor subcritical a shut down rod in the reflector
appears to be necessary. This rod will be completely withdrawn from the
reactor during normal operation; to drive the reactor subcritical it will
be inserted in the reflector either manually or antomaticelly. This rod is

not expected to unduly penalize the shield or reactor design.
VI. REACTOR ENGINEERING
6;1 Optimization

Folliowing the decision to contain the fuel in tubes, a study was
undertaken to ascertain the combinatlon of fuel tube diameters and number
of tubes which would yleld optlmum pe;formance. The factors considered in
the study are described in Appendix 5. The ultimate cholce was =
nompromise between fih@ excessive self-shielding of large diameter tubes
and the large core diameter and pressure drop associated with small
dismeter tubes., Six 3.5 inch diameter tubes were chosen.,
6.2 Heat Transfer
6.2.1 Gamma Heatlng

The heating produced by gamwa radiatlon must be known for the
deslgn of cooling passags to prevent overheatlng of ths reactor etructure.
This heating superimposed on that due to heat transfer determinss the
gsource ussd to calculate cocling holerdistribution, per Reference 15.

For the purpose of this calculation the reactor was resclved as
followss

1. Island ~ NaOD and central fuel tube homogenlzed.
2. OSource Beglon - Rewmalaning fuel tubss and NalCD
in the interstices - Annulus.

3. NalDh sphericsl shell.,

O~
L. Hickel inconel shell
5. Be reflector and an estimated quantity of NaOD and
Hi for cooling.
W. 8. Fammer's method (Reference 16) was used with modifications
suggested by F. H. Abernsthy snd A. H, Fox,
Assumptions inherent in the method are: ..o ..

a. The "straizht shead" theory of gamma absorption
applies, i.e,, compton scattering degrades the photen in energy
but does not change its direction.

b. Mo refraction takes place at boundaries.

c. The source power density is uniform over the
equivalent source annulus.

d., The fission rate is uniform.

Assfimptions used for the Serewball:

a, The Yannulus™ of fuel tubes may be replaced by a
homogeneous annulus of the same thickness.

b. The gammapspgctrum may be idealized as a source
consisting of 1 Mev gammas only. (4 more accurate treatment
would be to use scources of 1, 2, and 3 Mev gammas with the
source strengths adjusted according to the rmamber of gammas
between 0 and 1.5, 1.5 and 2.5, and 2.5 and infinite Mev
energy. )

c. The use of T for both energy deposition probability
and attenmuation factors, rather than uszing p and & buildwup: factor

for attenuation, will not result in serious errors. (The proper

hde
build~up factors for the Screwball configuration are net known.
This assumption will cause an error such that the cooling tubes
will be placed closer than necessary. Accurate results can
only be obtained through the use of critical experiments or
actual mockups. )
d. For calculations in the source region, gemma's
which traverse the island must be considered. Therefore; for
these ealculations, the T for the island (0.117 inches’l)
was assumed equal to that for the source region ( 0.152 inches ™).
In the gource region {  a spherical annulus) where the source and

absorber have the same 't',

R = Ro @ =7
P(r) = Po I ! 27 B2 sin © e‘”‘tfi
R = 6 =o jmp2 d¢edRr (1)

€

}

Eliminating @ with

2:R2+ rzuzrflcosg

< _ po®® (R =Ro =R + T ~T
R = Ri

Q:Rwr Q

Integsrating b arts snd usinpg Reference 1°7.
[w] p oD

P(r) = poT Rg’ - R [El | T (B - f)\ -BE1] T (Ro + 1) ‘]

o .

 

fiedfi (2)

2 2
- 337 = r

[El | T®R -0)] -8 [T (R +r)|]

) {Mfio ! Pm"] > Tfi%’;z@ + [T r)+1] - T';RZ”P)
2

+ [’E(Romr)fl_] 8“:%};:3)% [f(fli\ml”)fli'l] a” f;fi; + I‘) (3)

 

s j’;e_2'm
Close to the source region, an infinite slab source 1s assumed, 1,e.,

P = Po T(r) Y= B "
) ""é“’f‘c"”{E FH T Y tfi)}

2 1
3

(4)
o0

where 52 (x) = J o FE
|

;2

subseriptsy 1 refers to layer(s) of the slab

 

%f (Reference 18)

g refers to the source
Farther from the source region, a surface source is used to
calculate the sttenuation

r R1
P(xW\." i
P(+Yy = (....i—l.)“ L
DBy e w51t e @l B v el
2 r
7 »Ro
P(r) = i_f-éfil ro T () ,
S Ro {El | () (x - Ro) |~ B {(r)(r + Ro) l} (6)
2 r
In the "igland®, the slab source should be used for atienuation
near the fuel amnulus, and the surface system at greater distnace., At the

center of the island, spherical symmeiry reduces the formula toz

r =0

P(o) = [E('Z'l] T (o) o~ TR
; Ry

A fictitious surface source which ylelds reasonable heating
results in the "island" is obtained by matching the power absorption
at 1/2 Ay from the source.

In the reflector region, the slab source is used for about

1/2 »g3 then it is matched to a surface source on the outside of the
nickel - inconel shell. FEquation (6) may be modified by replacing the
Eq functions by g, functions, thus correcting the non-isotropic
emission from the surface source. The second term in the parenthesis
is always negligible and may be deleted,

Equation (&) thus becomes: r » Ro

P(x) = [E%‘l] TG R g, |t (r-m) | (@)
_—SeBe r
2

<o

The gamma heating ecalculatiouns appear in Appendix 6,
By plotting 4w s P(r) vs. r and graphically integrating, the
percentage of the fission energy emitted in gamma rays and neubtrons which

is absorbed in the reactor is determined for each region.

Island 2.8%
Fuel | 54.4%
Ni-Inconel shell 3.9%
Reflector 32.9%

Approximately 300 KW leak out of the reactor.

Figure 7 shows the spatial distribution of heat absorption in
the reactor,
6,2.2 Internal Heat Transfer

Due to the complex flow passage for the NaOD, an exact
prediction or anslysis of the NaOD velocities in the core is impossible.
Hence, the following simplified method has bsen used for determining
the required NaOD flow rate. Since corrosion and-éngineering data are
not available for NaOD, NaOH has heen used in the engineering analysis,

The thermal conductivity of NaCH is small (6,72 Btu/hr £t 9F, at 11000F.)

YA
Drawing # 23193
u!\ ,M..\ n\;h. xmx. h,.q.. £ At

L2

 

7

-
-
£

Iy
compared with liquid metals mnd is approximately half the thermal
conductivity of the fuel. Hence, a large fraction of the temperature
difference between the fuel and hydroxide may occur in the NalOD film
for low velocities.,

To estimate more intelligently the flow rate which results
in & tube wall temperature nol exceeding 12500F, a calculation was made
for a 3.6 inch outside Yiameter fuel tube with a one inch annulus of
NaOH surrounding it. The fuel velocity was assumed to be 20 ft/sec.
and the NaOH velocity was varied. The variation of U with Vy_qp was
determined and is shown in Figure?.

The NaOD flow area perpendicular to the polar axis was
determined at various latitudes., Then the variation of VNaOD with position
in the reactor could be caleulated. A relation between the NalOD velocity
at the equatorial plane (V) and the average velocity was found.

Assuming a velocity normal to the equator, the average U was
calculated and the total temperature rise of the NaOD through the core
was estimated. Since the total temperature rise including that due to
gamma heating was small (10 - 20°F.), a linear temperature rise through
the reactor was assumed.

At one inch intervals along the axis, average velocities, U's,
h's and AT's were estimated. The product of U and AT gave the heat
flux. The temperature rise in the NaOD film, aflfi.NaOD , was calculated
by dividing the heat flux by hy,gp. Figure 9 1s a plot of hy.gp V8.

v The gamma heat which is generated in the tube walls will be

NaOD”®

transferred to the Nz0OD causing an additional temperature rise, ATEQ

by
Drawing # 2319,
UM AASS s FIED

 
Ve o A5 1F7ED

 

 
The sum of AT, ,AT, and the NaOD temperature is the outside tube
wall temperature, which must not exceed 1250°F,

Figure 10 shows the variation of fuel mixed mean temperature,
tube outside wall temperature and the NaOD mixed mean temperature with
position in the core. AV, of 6 ft/éec@ gives a maximum wall temperature
of 1254°F. This calculation establishes the magnitude of the flow rate
based on the simplifiea flow syatem,

6.2.3 Reflector Cooling

The heat generated in the beryllium reflector is removed by the
passage of NaOD through 0.23 inch diameter coolant tubes. The
calculation of coolant tube spacing is based on the following assumptions:

1. Neutron flux distribution from the two group, three region
calculations were not availsble for this calculation. Therefore, the heat
generation due to the neutron moderation was assumed &gqual.uto the gamma
heating. This assumption agrees with work done on the Fireball (Beference
2).

2. Bach coolant tube row is treated as a separate annular cell.

3. A mean, uniform power density is assumed for each cell.

4. The tubes are arranged in an .equilateral matrix.

5. The tube diameter is 0.23 inches.

6. The maximum beryllium temperature will not exceed the
coolant tube wall temperature by more than 50°F,

7. Heating from capture gammas in the inconel shell is neglected.,

8. A11 fission product gammas are emitied in the cofe,

From the basic heat conduction equation it can be shown that

wfigm
  

%%mh‘\\ &P

aUQZ

Frg. /0
(Reference 15)

;&é?T = 52 in (§}2 + a2 - r2 (9)
From geometric eonsiderations,
B =5 %;;2 (10)

To determine the cooling tube spacing, the following iterative
method was used,

1. Assume the row spacing,

2. Calculate unit cell dimensions using equations (2) and (3).

3. BEstimate log. mean power density from figure 11.

4. From equations (1), (2§ and (3). calculate the value § for
vhich AT = 500F, | |

5. Check the caleulated value of 5 with the assumed row spacing
and iterate until egual.

From the row spacing and reflector dimensions, the tube pitch
circle radius is determined. The number of tubes in each row is calculated
from the pitch circle circumference and tube spacing. Non-integral
numbers of tubes were adjusted to the next higher integer snd their
spacing on the pitch circle zltered zccordingly.

The results for the Screwball reflector are listed below,

 

Row Spacing Pitch Cifcle Radius  No, of Tubes
1 0,788 in 15.69 in. 125
2 0.976 16,52 103
3 1.23 17.63 90
4 1.62 19.05 74
(Cor'd)

51
U/
e LASS JFIED

 

Frg. 1

52
Row gel Pitch Circle BRadius No., of Tubes

5 2.32 21.04 | 57
6 412 24,27 37

In calculating the gamms heating, M was used as the
attenuation factor rather than p, resulting in more rapid attenuation
and hence larger heat generation., Therefore, the above results should
be eonservative.

A1 fission préduet garmas were sssunod bo be enitted in the
core, In reality a fraction will be emitted in the core snd the remaining
gammas will be emitted in the ewternsal el circuit. The hest
generation at the outside of the reflector is removed by the NaCD in the
by~-pass annulus.

The NaOD velocity in‘the reflector was determined by calculating
the heat flux, heat transfer AT, and temperature rise of the Na0OD at
various assumed velocitles, Calculations were made for the tube row in the
highesat power density region.

At & veloeity of 7 ft/zec, the temperature rise of the NalD is
156°F, h is 2600, snd the heat transfer AT is 80°F, This gives a total
temperature at the end of the coolant tube of 1251 “F, which is
approximately the maximun temperature allowable from a corrosion étandpointa
6e2,A,Primary Heat Exchanger

The primary heat exchanger for the Serewbsll reactor is a
spherical shell which will wrap around a 53 inch diameter sphere. This
shell will be 4 inches thick and will begin snd end on the sphere at
45° North Latitude and 60° South Latitude, respectively, Within the

shell the fuel and NaK coclant will flow counter-currently; the NaK flows

=53
down within the tubes in the heat exchanger. The tubes will be wrapped
in such a way that there is a constant clearance between tubes of 0,035
inch. Two spacers per foot of length of tubing appear to be adequate.

| The fuel will enter at the botton of the heat exchanger at
1550°F and will leave at the top at 1150°F, On the NzK side the entrance
temperature is 940°F and the temperature rise will be 510°F. The
velocities and pressure drops for the Tuel and NaK are, respectively,
6.95 fi/sec., 36.3 ft/sec., 32.9 psi and 31 psi. The material of
construction will be inconel.

The primary heat exchanger design for the Screwball is based on
the method presented in Reference 19; a summary of the calculations for
this exchanger appear in Appendix 8,

This heat exchanger represents a feasible design and no major
attempt has been made to optimize it., It is anticipated that the fuel
volume in the heat exchanger can be reduced to approach that of the
Fireball design and further effort in this direction is recommended.

£.2.5 NaOD Heat Exchanger

 

The NaGD heat exchanger has the form of a right, circular
cylindrical annulus six inches thick and 15 inches tall, The NaK flows
downward through 1/2 inch 0. D, inconel tubes which have a wall
thickness of 50 mils, including an externsl 10 mil cladding of nickel.
These tubes form a lattice in the form of an equilateral triangle with a
ninimum clearance of 0,125 inches between the tubes. The NaOD flows
across the bottom of the anmulus, up the outside and back down the
inside of the anpulus ag indicated in Figure 1. For this calculation elght

percent

w5 fie
( 16 MW ) of the reactor heat was assumed to be removed by the NaOD,

The heat transfer calculations are based on relations presented
in Beference 20. Two pass, parallel flow of NaOD and single pass
downward flow of NaK were assumed. Preésure loss caleulations for the
NalD assumed mixed parallel and cross flow. A sample calculation and
tabulation of design data are contained in Appendix 9 and Appendix 1,
respectively.

The NaQD heat exchanger is a conservative designi more heat
transfer area is provided than is actually required since the higher rates
of heat transfer in cross flow have been neglected to simplify the
analysis,

6.3 Fuel Flow Experiment

As mentioned in Section 3.2 it is assumed that the flow patterns
in the tubes of constant cross section are more predictable than the
variable area passage emploved in the Fireball. This experiment was
conducted to verify flew stabllity in helical tubes.

FPipure 12 1s a photograph.of the apparatus. The one inch glass
tube 1s geometrically similar te the Screwbali fuel tubes; - no flow
irregularities were observed., The fluid is an aniline dye.

A secondary flow typical of that generated in smooth tube bends
was observed; this added turbulence should increase fuel mixing s
preoduce & more uniform velocity profile and imcresase pressure losses.

This experiment supports the assumption of fuel flow stability

in the Screwball,
 

 

™
 

M

hclassified
Photo # 20590

 

 

 
ViI. SHIELDING

Figure 13 is taken from the report of the 1953 Shielding Board
meeting. The shield consist of lead and borated water. Lead was used
adjacent to the pressure shell and in a 20° shadow shield which is
incorporated in those shield designs requiring selective reduction of
external dose.

The curves ghown are for reactor core diameters of 28.5"
(Screwbell) and 22.5". Details of the calculations can be found in the

reference report.

-58-
 

Drawing # 23198

£r 3

4y 0 ¥ A/

~58a-
VIII CONCLUSIONS AND RECOMMENDATIONS

On the basis of the work presented in thils report, the Screwball
reactor appears to be feasible., However, a considerable quantity of
detailed analysis and experiment is required before its practicability is
established,

Based on the work covered by the report, the conclusions and
recommendations are:

1) The use of NaOD as a moderator and reflector coolant, as
proposed, has great potentiality; thowever. with the assumed corrocsion
limitation on thbe wall temperature (1250°F), very large flow rates and
adequate flow guidance are required to attain marginal performance.

2) The uncertainty about flow instabilities is less severe in
helical fuel tubes than in spherical., annular flow passages. Hence, the
uge of helical tubes is recommended until stebility in spherical annulii
has been confirmed experimentally.

3) For design point operation, preheating the NaK with the
moderator heat lends itself to a simple resctor and propulsion system
design, The desirability of this scheme increases as the melting-point
of fused salt fuels is decreased. Further investigation of NaK preheat
is recommended, particularly for operation off the design point,

4} Although the fuel volume external to the core is large, by
optinmizing the primary heat exchanger for minimum fuel wvolume while
maintaining reasonable pressure dropsz, the fuel wvolume reported should
approach that of the Fireball, With an external fuel volume equal to

that in the Pireball (5.7 ecubic feet), the Screwball core will contain

-hO.
33 percent of the total fuel volume. The higher delayed neutron
concentration in the core and a more conservative power density make
control of the Screwball more practicable than the Fireball,

5) Despite the larger size and the use of tubes for fuel
conbainers, the critical mess of the Serewball (35 pounds - based on
conservative self-shielding factors) compares favorably with the Fireball
critical mass (30 pounds) as reported in Reference 1. In addition, the
ratio of total fuel volume to core volume for the Screwball may be
reduced by optimizing the primary heat exchanger, thus yielding a smaller
total fuel mass for the Secrewball,

6) The NaOD flow pattern in the core is unknown. The assumption
that NaODh will flow between the tubes may not be realistic and more positive
ruidance of flow may be required.

7) Support of the thin-walled fuel tubes at such close tolerances
may be difficult, particularly since the thermal expansion patterns are
analytically unpredictable. Any support structure contacting the tubes in
the core presents a poltential NaOD stagnation point and hence, a corrosion
center,

8) The assumption of quantitatively similar physical and chemical
properties for NaOD and NaOH is unfounded ,

The major, fundamental limitation of the 3crewball ia the RalObD

corrosion,

60~
IX REFERENCES

Ref, HNo,

‘13

HW

10.

il.

Iitle
ORNWL 1556, W. B. Cottrell, "ANP Quarterly Progress Report®”,
for period ending June 10, 1953.
CF-53-3-210, A. P.Frass., G. B. Mills, "A Reflector Moderated
Circulating Fuel Réactor For an Aircraft Power Planth,
March 27, 1953.‘
The Reactor Handbook, RH~3, Technicsl Information Service, AEC
NRL-Memo Report No. 130, R. R, Miller, "Fourth Progress Report
on the Thermal Properties of Sodium Hydroxide and Lithium
Metal®; March 1953.
Conversation with Leo Hemphill -~ Y=-12 Engineer.
TAB-20, D. 3, Bloom, "Report of Trip to BMI, Internaticnal
Nickel Company and M,I.T.", June 29 to July 3, 1950.
Y-F10-102, C. B. Mills, "An Outline, of the General Methods
of Reactor Inalysis used by the ANP Physics Group®.
Glasstome and Edlund, "The Elagents of Reactor Theory".
MM-182, P; D, Crout, "A Short Method for Evaluating Deter-
ninants and Solutions of Systems of Linear Equations With
Beal and Complex Coefficients”.
CF-53-3.231, W. K. Ergen, "Finetics of Circulating Fuel
Kueclear Reactors", March 30, 1953.
Y-F10-98, W, K. Ergen, "Physics Consideration of Circulating

Fuel Reactors"”, April 16, 1952,

61~
12,

13.

14.

15.

16.

17.

18,

12.

20.

2L.

22.

23.

Y-F10-109, S. Tamor, "Note on the Non-linear Kineties of
Circulating Fuel Reactors”, fag. 15, 1952,

ORNL 1234, W. B. Cottrell, "Reactor Program for the AMreraft
Nuclear Propulsion Project", June 2, 1952.

MM-92, E, R, Mann, "Controls and Instrumentetion™, 1951.
CF-52-9-201, W, 3. Farmer, "Cooling Hole Distribution for
Reactor Reflectors', Sept. 3, 1952.

ORNL 1517, M. P. Frass et.-al., "Fireball Reactor Moderator
Cooling 3ystem',

"Pgbles of Sine , Cosine and Exponential Integrals®, WPA,

New York, 1940, Vols, I and II,
o0
XU N W

MT-1, G. Phaczek, Part I, "The Functions Ep(x) = J e W du
Part II, "Table of En(x)" 7

ORNL LBBQ, A. P. Fraass M. E. LaVerne, "Heat Exchanger Design

Charts™.

W. H. Mcflflams, "Heat Transmlssion®, McGraw-Hill Book Co., Inc.i

New York and London, 1942.

ORNL 1395, H, F. Poppendiek, and L. D. Palwmer, "Heat Transfer

in Pipes With Volume Heat Source Within the Fluids".

HEKF-~109, Karl Cohen, "Homogeneous Reactor for Subsonic

AMreraft®, Dec., 15, 1950.

BMI-706, C. M. Craighead, L. A. Smith and R. I. Jaffee,

"Sereening Tests on Metals and Alloys inm Contact With Sodium

Fydroxide at 1000 and 15000F",
X APTENDIXES
Aopendix 1, Desipn Deta
1) General
Power - 200 MW
Power density - 2.5 kw/cc
Critical mass - 34.8 pounds of yR35
Bstimated additional fuel required for poisons, burn-up, etc.,
2.3 pounds,
Bstimated (not optimized) total uranium investment - 175 pounds.
Temperature coefficient of reactivity - 2.1lx 10"4’/DF. negative
Estimated fast flux - 1.06 x 10°7 n/(cmlsec)
Estimated thermsl flux - 1.06 x 10%° n/(cm2sec). (These are
assuming the reactor is 50 percent thermal.)
Dimensions:
Pressure shell diameter - 68,5 in,
Height to ocutside of pressure shell -~ 84 in.
Flow rates d
Fuel - 1410 pounds/sec.
NaQOD - 1890 pounds/sec.
NaX - 1640 pounds/sec.
2} Materials
Fuel - 50 mole percent NaF
47 mole percent ZTFA

3 mole percent UFA

e
Moderator and reflector coolant - NalD.

Teflector - beryllium.

Intermediate heat transfer medium - NaK (56 weisht percent Na).

Structural material - inconel, with nickel plating or cladding
vhere it is in contact with NaOD

3) Core

1880 cubic inches

1

Fuel volume

NaOD volume = 7200 cublc inches
Dimensions:
Mcderator "island" diameter = 21.5 inches
Fuel region outside diameter = 28.5 inches
Fuel tube inside diameter = 3.5 inches
Tube wall thickness = 50 mils of inconel with 10 mil
nickel cladding
Number of fuel tubes = six, including central tube
Turns in core = 1,5

Fuel temperature rise = AOQCF

Maximum fuel temperature = 1550°F

i

Maximum NaOD temperature = 100QCF
Maximum wall temperature om NaOD side = 1254°F
Fuel pressure drop = 10 psi including expansicn and contraction
losses at tube entrance and exit
4) Reflector

Thickness = 11 inches of Be and 2 inches of NalD

Number of cocling tubes = 486
f

GCooling tube diameter = (.23 inches

6

H

Rows of cooling tubes
NaOD velocity in cooling tubes = 3.4 fi/sec
5} Primary hesat exchanger

Healt removal = 185 MW

Fuel volume = 7.45 cubic feet

NaK volume = 7,54 cubic feet

Spherical shell thickness = 4 inches

Tube inside diameter = 3/16 inches

Tube wall thickness = 0.017 inches

Minimum tube spacing = 0.035 inches

Number of tubes = 5220

Letitude of entrance header = 45°

Latitude of exit header = 60°

Fuel pressure drop = 33 psi

NaK pressure drop = 31 psi

Average tube length = 7,35 feet

Equatorial crossing angle = 30€

Exit NaK température = 1450°F

Heat transfer area = 2280 square feet, based on tube outside
diameter

&) NaOD heat exchanger
Heat removal = 16 MW
Dimensions:

Cylindrical anmulus with radii of 21 and 27 inches

B
Height = 15 inches

NeK volume = 5030 éubic inches
NaOD volume = 5700 cubic inches
Tube outside diameter = 1/2 inch
Tube wall thickress = 0,050 inches
Minimum tube spacing (equilateral triangular piteh)} = 0.125 inches
Number of tubes = 2675
NaX temperature rise = AQ°F
NaOD temperature decrease = 20°F
NaK pressure drop = 3 psi
NaOD pressure drop = 20 psi

7} Pumps
Type - mixed flow, sump pumps
Number - 4 fuel pumps

4, NaQGD pumps
Seals -~ gas seals for the fuel pumps
either gas or frozen seals for the NalD pumps

Punp horsepower - undetermined

8) Shield
Estimated weight - undetermined
External dose at 50 feet = 10 r/h

9) Total weight

Reactor, shield and crew compartment shield = 96,000 pounds

Lo
Appendix 2. One Group. Two Hegion Data

ANP Reactor 121.

Beryllium Reflector and Structure

Two Region, 22 inch diameter core, A8 inch diameter reflector,

ATOMIC DENSITIES

 

 

 

 

 

 

 

 

gR25 __F Inconel {vol, fraction)
core _ ,
0.0004150 | 0,035374 0.0277
reflector|Be e
-10.1180 0.0009859

 

 

Screwball 6 Tubes - 3 1/2 inches Dianeter.
Be reflector, HaOD coocled; core fuel 20 and NalD

TWC) He iOl’l 27 ifl@h didflfit@f corg, 31 inch diameter reflector
%
- N

0.000321 {0,0211 0.00402 | 0.01558

inconel (vol fraction)! D
02

He N 0 4D
reflectar |

0.1085 0.0022 0.00221 0.000226 {0.000718

 

Notes All the vwalues are %tamg/cc X 1Dm2£‘unless otherwize indicated.

~67
Appendix 3, Two Group Crossg Section Weighing

The following relations were the basis for weighting the cross

sections for the two proup, three region analysis.

region

The flux in each lethargy group was averaged over each reactor

2
d;)i = fl”egion(bi(r) r~ dr

J( . r2 dr
region

The fraction of the total fast flux (Efihi) was determined for

 

each lethargy group. Then,

the cross

50; =2
The values of &%_afe tabulated below,
The cross sections for the fast group were obtained by multiplying

sections in each lethargy group by its flux fraction and summing.

Yoderator Core Reflector Group
0.0064 0.0055 0.0019 1
0.0199 0.0307 0.0081 2
0.0571 0.0792 0.0260 3
0.0051 0.0127 0.0033 L
0.0802 0.1354 0.0492 5
00944 0.1342 00,0486 6
0.1128 0.1360 0.0571 T
0.0923 00,1170 0.0543 8
0.0873 0.0876 0.0546 9
0.06456 0.0581 0,0537 10
(Con'd)
Moderator

0.0532
0.,0518
0.0326
0.0312
00277
00,0262
0.0234
0,0199
0.0184
0.0170
0.0163
0.0156
0.0149
0.0135
00,0128
0,0144

0.9999

Core
0.0415
0,0282
0,0215
0.0168
0.0133
0.0132
0,012/
0.011/
0.0087
0.0072
0.0058
0.005,
0.,0050
0.0047

0.0042

0.0038

b9

Reflector

0.0476
00497
0.0483
0.0461
0.0434
0.0403

©.0398

0.0392

.0381
0.0372
0.0361
0.035¢8
0.0356
0.0355
G.0353

0.0352

1.0000 -~ Total

Group
”ii' g
12
13
1k

16
17
18
19
20
21
22
23
2k
25
26
Appendix A, Two Group. Three Region Data

In performing a criticality calculation on the Screwball
reactor, the three regions were chosen to approximate most accurately
the actual reactor.

The dimensions of the three regions are shown in Figure 6,

The constituent volumes in each region are as follows:

 

Element Region 1 Repgion 11 Region 111
NaOD 5117.10 1936.3 6975 .20
Fuel 0 2890 .,00 0
Inconel 0 275,03 145.77
Nickel 0 56.14 236.27
Beryllium 0. 0 56134.93
Totals 5117.10 in®  7157.5 in®  63/92.17 in?

Total volume of all regions -- 75766.6 in 3

~70-
Appendix 5, Optimization
1. Bgsic Assugpiions:

In nrder to extract 200 MW of heat at 2.5 KW/cc, a fixed volume
of fuel in the reactor core is necessary. Using this volume the system
was optimized from the nuclear and engineering standpoint by varying the
number of tubes and the tube diameters. |
2. Factors Considered afld Their Associated Parameters;

a, 3elf Shielding: The self shielding factor F 1is discussed
in Section 5.2. It can be shown that F depends dirsctly upon the
diameter of the tube.

b, Pressure Surge: Thls criterion requires further investigation.
However, the larger the ratio of central flow area to the exit flow area

the more severe the problem will be. Thus we wish to minimize (2. where

) = central flow area
exit flow area ’

¢. Heat Transfer: The amount of heat transferred, @, can be

nO‘ZL , where n is the number of tubes of

shoym to be proportional to

of length, L, and Diameter, D, It is desirable to minimize the heat
transferred to the NalD,

d. Pressure Loss: The pressure drop in the fuel tubes will be
much lower than that in the heat exchanger, hence this factor is noct of
major importance. The parameter used was,

AP & VAL
D

7]
e. Fabrication: An index of fabricability is tube lengtih;
the longer Lhe tube, the more turns made, and hence greater fabrication
problems.

f. Poisons: Since for a fixed dismeter the total tube length
is constant, the ratio of poison to fuel added 1s independent of the
nunber of tubes. lHowever, the poison. increases as the tube diameter

decreases. The pearaneter is,

W - Volume of inconel
Volume of fuel

g, Core Diameter:  The reactor weight increases with core
diameter. It is seen that the diameter increases with decreasing tube
diszmeter,

3, Table of ibove Factors for Various Combinstions:

 

In the table there are two values given for the self-shielding
factor F, the first being for the fast neutrons and the second figure

for the thermal neutrons.

 

Factor Symbol 7 -~.2.-inh ‘¥~ 3.3in 623 1/2 in 5 - /4 in

. Self~shielding F 0.61 0.50 0.46 G.42
0.88 0,273 0.80 0,78

b. Pressure surge L 5.5 3.8 3.5 - 3.5

¢. Heat transfer q 211 66 8.5 39

d. Pressure loss AP 96 6 3.2 2.2

e. Fabrication L 249 108 Q2.4 86

f. Polisons qy - 0.069 0.055 0.0L8

g. Core diameter D 3/ 29 28 27

As a eompromise between nuclear and engineering considerations,

six three and one-half inch tubes were selected,

7D
fppendix 5, Gamms Heating
Calculations:
Source (fuel) Region:
The power absorption was caleulated according to formula ( 3)
vielding:

r (in P /P(2) P(r) §ngin3}

10.469 0.379 0,603
11 0.438 0.697
12 0.529 0.840
13 0.546 0,969
14 0.492 0,782
14.3 0,460 0,771

NeOD fnnulus:
The power absorption was calculated according te ( 4)
yielding:

r (in} P(r}/P(o} P(r) (KW/in3)

14.31 0,269 0427
14.4 0.252 0,400
14.8 0,207 0.329
15.13 0,183 0,291

Nickel-Inconel Shell:
The power absorbed in the shell was cazlculated using the slab

case, i.,e,, formala ( 4).
Beflector:

r (in)

 

15.13
15.19

15,25

equations (4) and (8)

[

3
R=0

Using this

r (in}
15.25
16

17

18

19
20
21
22
23
24
25

26

P(r)/P(o)

0.872
0,789

0.715

P(r) (KW/in’)

1.387
1.255

1,137

-

The power absorbed in the reflector was calculated using

and matching the two forms at r = 17 inches,

= PO! = 4.96 M
.2

source throughout and (8)

P(r)/Po_(in~1)

=S4

in

0.161

0,080/,
0.0424
0.0240
0,0142

0.00862

0.00534

0,00298
C.00213
0.,00140
0.00103

0,00095

the power absorption is:

P(r) fKWéinB}

0.798
0.39%
0.210
0.119
0.0704
0.0427
0.0264
0.0148
0.0106
0.00695
0,00508

0.00471
Izland:
(4) and (5).

The power was evaluated using equations

The curves were matched at r = 6 in, vielding a fictitious source on

 

the inside of the fuel anmulus ofs {Efigl] - P: = 2.22 Ki/in?
Ts R, 1
r (in) P(r)/Pi (in-l)  P(g) (KW/1n?)
O+ 0.0336 O.07L7
1 0.0337 0.0749
2 0.0346 0,0791
3 0.0362 C.0805
4 0.0386 0.0858
5 0.0421 0.0937
6 00,0473 0.105
P(r}/Plo)
7 O.QSES 0.131
g 60,1055 0,168
2 0.1377 0,219
10 0,191 0,304
10,69 0.269 0,428

+ Czleulated from ( 7)

 
 

Mppendix 7/, Core Heatl Transfer
The following is & sample calculation of the tube wall

tenperature at x = 19.

Vo (NaOD) = 6 feet per second

v = 1,57 x 6 = 9,42 fect per second

T = 1012 Btu/hr. £1% OF from Figure 8.
T = 3,5°F (estimated)

The total heat transfer area calculated is 36.6 £%°.
qg= U AAT =1.,28x 10’ Btu/hr.
The average temperature rlse of the NaOD in the core is then obtained,
The gamma heat flux from. the inconel tube is estimated to be
5,61 x 10% Btu/hr. £2.
ATy= 1.29F due to gamma heabting.
Since the heat addition to the NaOD results in such a small temperature
rise, the temperature increase through ihe core was assumed linesr and the
tempeféture rise to point x = 19 was 6°F,
At x =19, V = 7,08 £t./sec.
U = 900 Btu/hr. ft.2 OF
the temperature difference betwsen the NalD and
fuel = 405° F
The heat flux is thus, % = -UXATX*—'-: 3.65 x 10° Btu/ hr. £4.°
The temperature rise through the NfibD is found by dividing the heat fluxes
due to heat transfer and gamma heating by the local heat trasfer coefficient
for NaOD. Heat transfer AT, = 215°F Gamma heating ATs = 33°F
Adding these temperature rises to the NaOD temperature of 1000°F gives a

wall temperature of 125/CF,

w76

 
  

fppendix 8, Primary Heat
The design procedure for the primary heat exchanrer is presented
in Reference 19, The following assumptions were mades

1. HNumber of tubes = 5220

H

2. Inside diameter = 3/16 ", 17 mil wall and 35 mil spacing

3. Exchanger wrapped around a 530 diameter sphere.

4o Exchanger to extend from 45° W. Ilatitude te 60° 8. latitude.

5. Tube crossing angle at the equator = 30°

6, Tube bundle thickness = 4"
Applying these assumptions to the curves and eguations in Reference 19,
the following results were obitained:

1. For @ - 459, (i') = 4509 a '72;’

®=. 0o, ¢ = 90°, &= 90°

Total angle of rfiyolution = 164°
2. Fuel volume = 7,45 £t.7

i

NaK volume = 7,54 ft.”
3. Fuel velocity = 6.95 ft./sec.
/. NaK velocity = 36.3 ft./sec
L. Fuel pressure loss = 33 psi
NaK pressure loss = 31 psi
5. Tube length = 7.35 ft,
6. Heat transfer ecoefficients ; Fuel = 3110 Btu/hr, 47 OF
NeK = 16,600 Btu/he, £t2 OF
7. Log mean temperature difference = 1/8°F
8. Cgleulated heat transfer = 198 MW
The heat transfer required for the primary heat exchanger is approximately
185 MW, lesving a margin of 13 MW to allow for inaccuracies in the heat
- transfer calculations,

B Lot 77~

 
  

Appendiz 9, NaOD Heat

The equations nsed for these calculations are found in Refercnce

20. The following assumplions were nmade:
1. Required heat transfer = 16 MW

2. Flow rates

Na0D = 1595 1bs/sec (preliminsry

eatimate)
HaK * 160 1bs./sec
3. Temperatures - (OF) Entrance Exit
NaOD 980 1000
NeX 200 940
A drawing of the heat exchanger and a wnit cell with

the appropriate dimcnsions is shown at the right,

hAreas in the unit co l:

NaOD 142 inz, Area ratios:
Nak .126 120D
Totlal
ak Tubes_,070 -
Falk
Total 0,338 in? Total

Total Area = 204 in<.

Flow Velocities:

Unit Cell

 

General Configuration

 

7

/"

 

 

keZJ“«

< 27—

 

 

V= _u =0D = 11.7 ft./sec. (for two parallel passes)
PS

Golo= 15,3 £u./sen,
Equivalent diameter for NalD:

D. = 4L x Floy Ares

e = 362 in,
e Wetted Ferinmeter 3 '

 

 

 

 

/

 
 

Heat Transfer Coefficientsi:

D gvgaa O
—a oz Y s
v = 0023 (G2 ()

Na0D = 3580 Ptu/br, £t.° °F
HeE = 139,000 Btu/he, T2 oF
For inconel, h s-% = 4080 Btu/hr. 2 Op

The over-all heat tranafer coefficient for the outside tube area

= 1780 Btu/hr £t2 Op

Heat transfer greas:

Humber of NzK tubes =2675
hetual area = 437 £2

Area required for transfer »f 16 MW = 1438 £t2

These calculations have been based on two parallel flow passes, The

additional heat transfer due to cross flow will compensate for the

inaccuracies in heat transfer caleulsations,

Pressure

NaOD -

Loss Calculations:

HaK -

thE
AN .é.m:d.;.fij:': 0.7 psi

Dynamic head = 1.2 psi

i

Summary: Tube loss = 0,7 psi

Entrance loss= 6.6

 

Bxit loss = 1.2
Total 2.5 (approximately 3 psi)
72
Parallel paszses, D :*駧£%~¥L— = 2 psi
&,ge )
Cross flow, p = b T TR R A 12 psi
2g

Total loss = 20 psi

28 . |

  
 

Appendix 10, Nomenclaturs

 

Nuclear
Symbols
A -  nunerical constant
B - buckling
C -  numerical constant
D - diffusion coefficient
E - eneTrgy

f - thermal utilization

F - self-shielding
g ~ nuclear constant
n - nuclear conatant

k -~ maltiplication constant

L - diffusion length

M - nass

T -  radius

R ~ radius to a reglion boundary
S -  Coupling coefficient

t -  reflector thicknsss

T - temparatures

- differential operator
-  Laplacian operator

- average nunber of neutrons produced per absorption in fissilonable
material

- average logarithmic energy decrsment per collision

2
V
<) - average number of peutrons produced per fisslon
s - microscople cross section

2

- macroscopic cross section

~80-

  
 
v -
¢ -

Subscripte

&

Cc

eff

11T

1l

Superscripts

U

s

~J

Engineering
Symbols

a

1

2

 

Fermi age

neutron flux

absorption
core

effective

- figsion

lethargy group

mean

reflector

removal

scattering

total

transport

fast group, region 1
thermal group, region I
fast group, region Il
thermal group, region I
fast group;, region IIT

thermal group, region III

uranium
average value

extrapolated boundary

radius of cooling tube

w81 -

 
3

£ o oo 2w

™

 

heat transfer area

length of one side of the cell
specific heat at constant pressure
tube dlameter

friction factor

self-shlelding factor
acceleration of gravity

heat transfer coefficient

thermal conductivity

tube length

number of tubses

number of tube rows

prespure difference

heat sbsorption per unit volume
sourca power density

heat tranafer

heat per unit volume

radius or radius to absorber
radius to source

tube spacing

flov arsa

wall thickness

temperature difference

reflector thickness or temperature
overall heat transfer coefflciant
velocity

weight fiow

vertical distance from north pole of sphere

_,82_, - -

 
- Subscripts

o

1

2

Superscripts

1
111

c—

i

wen

1

 

engie of longitude
radiue of circle having area equal to hexagonal cell

angle between r and R

angle of latitude

relaxation length

vixcosity or gamma absorpition coefficient

variable of integration

distance between r and R

density

sfimmation

gamma energy deposition coefficienty

entrance angle between tubes and hinge of constant longitude
polison parameter

pressure surge parameter

refers to equator
equivalent

refers to layers of the slab
island

maximan

sodium deuteroxide

outside fuel region
refli=zctor

refers to source

heat transfer component

gamma heat component

fictitious surface source
croes fiow friction factor
average value