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Design of a cobalt-60 fueled thermionic power supply.
Doherty, Brian J.
Massachusetts Institute of Technology
http://hdl.handle.net/10945/11956
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1969
DOHERTY,
B.
DESIGN OF A COBALT-60 FUELED
THERMIONIC POWER SUPPLY
by
Brian
J.
Doherty
.
DUDLEY KNOX LIBRARY
NAVAL POSTGRADUATE SCHOOL
MONTEREY, CA 93943-51 01
DESIGN OF A COBALT-60 FUELED
THERMIONIC POWER SUPPLY
by
Brian
B.
S.
,
J.
Doherty
United States Naval
Academy
(1965)
.Submitted in Partial Fulfillment
•of
Requirements for the
•Degrees of Master of
the
'Science
and
Nuclear Engineer
at the
Massachusetts Institute of
Technology
June, 1969
»e2ts^4;t»34
LI3RARY
NA y/AL POSTGRADUATE SCHOOfc
MONTEREY. CALIF., 93940
DUDLEY KNOX LIBRARY
^OTI^*??**.
MONTEREY, CA
93943-5101
DESIGN OF A COBALT- 60 FUELED
THERMIONIC POWER SUPPLY
by
Brian
J.
Doherty
Submitted to the Department of Nuclear Engineering on June 30, 1969 in
partial fulfillment of the requirements for the degrees of Master of Science
and Nuclear Engineer.
ABSTRACT
The objective of this thesis was to design a practical thermionic
which would use cobalt-60 as a fuel and which would provide
supply
power
500 watts of electric power over a three year operating period.
In order to make the cobalt-60 fuel, which has a low melting point,
compatible with the high temperature required for efficient operation of
a thermionic converter, a low temperature fuel concept was employed.
This meant that the fuel would be insulated from the converter heat source
by a multi-foil thermal insulation. The multi-foil insulation uses refractory
metal foils separated by thin layers of refractory oxide particles to provide
a highly efficient and compact thermal insulation. With this design it was
desirable to minimize the gamma self absorption of the fuel. Most of the
effort in this thesis was directed toward the optimization of the fuel supply.
The final design uses fuel elements which are in the form of hollow
cylinders and which have a thermal efficiency of 75. 6%.
A power flattening device which operates on a moveable fuel concept
was designed to overcome the problems posed by the relatively short half
life of cobalt-60.
The power supply was designed for terrestrial applications;
accordingly it was not subjected to severe weight limitations. Nevertheless,
every effort was made to keep its weight and size within reasonable limits.
The power supply was also designed so that it could operate automatically,
unattended, for the three year lifetime. An additional design criteria was
that no significant advance in the present state of the art be required for
the design to be feasible.
The final design uses five thermionic converters operating at a
fixed power point and a DC -DC regulated converter to provide 500 watts
of electric power at 28 volts. The overall efficiency of the power supply
system is 9. 7%.
Thesis Supervisor: E. P. Gyftopoulos
Title: Professor of Nuclear Engineering
li
TABLE OF CONTENTS
Abstract
Table of Contents
List of Figures and Tables
CHAPTER
1
ii
iii
v
INTRODUCTION
1. 1
Objective
1.2
Design Concept
Fuel Requirements
1. 2. 1
Low Temperature Fuel Concept
1. 2. 2
Preliminary Design Considerations
Further Design Refinements
1. 3
1.4
CHAPTER
2. 1
2. 2
2
1
Intrinsic Efficiency
Emitter And Collector Operating Temperatures
2.2.4 Output Voltage
Thermionic Converter Designs Compatible With Power
Flattening Requirements
2. 2. 3
2. 3
2. 3.
1
2. 3. 2
2. 3. 3
CHAPTER
3
3.
3.
3.
3.
3.
3.
3.
3.
4.
1
4. 2
4. 3
1
5
15
16
Converter Operation With Varying Cesium
Reservoir Temperature
Operation At A Fixed Power Point
18
21
FUEL ELEMENT OPTIMIZATION
26
26
29
30
30
31
31
36
38
40
SHIELDING
General Remarks
Method For Calculation Of Shield Thickness
Shield Design
CHAPTER
5.
4
8
8
8
9
18
18
General Remarks
2
Fuel Element Configuration
3
Energy Losses To The Fuel Elements
4
Fuel Element Efficiency
5
Calculation Of Ea
6
Calculation Of E^ F
7
Calculation Of e£ c And E^t
8
Calculation Of Eg^
9
Calculation Of Qj
10 Evaluation Of Specific Fuel Elements
CHAPTER
5
Power Flattening Requirements
3. 1
3.
2
4
SELECTION OF THEMIONIC CONVERTER DESIGN
General Remarks
Thermionic Converter Performance Characteristics
Performance Characteristics Used As Design Basis
2. 2. 1
2. 2. 2
1
1
50
50
53
POWER CONDITIONING
General Remarks
59
iii
TABLE OF CONTENTS (CONT.
5. 2
5. 3
5.4
5. 5
Operating Principle Of The Power Flattening Mechanism
Fuel Rod Positioning Mechanism
Initial Fuel Rod Position
Operation Of The Fuel Positioning Mechanism
CHAPTER
6.
1
6. 2
6. 3
6. 4
6. 5
6. 6
7. 1
6
61
61
62
63
ADDITIONAL DESIGN CONSIDERATIONS
General Remarks
Lead Losses
Insulation And Support Of The Emitter Heat Source
Modifications Requires To Fuel Element Design
Electrical Insulation Of Emitter And Collector
Radiator Design
CHAPTER
7. 2
)
7
65
65
66
67
68
70
SUMMARY AND CONCLUSIONS
Design Summary
Conclusions
73
73
BIBLIOGRAPHY
.
IV
78
LIST
OF FIGURES AND TABLES
Figure 1. 2. 2. 1
Schematic Power Supply Design
Figure 2. 2. 1. 1
Thermionic Converter Output Voltage Characteristics
Figure 2. 2. 1. 2
Thermionic Converter Intrinsic Efficiency Characteristics
Figure 2. 2. 1. 3
Thermionic Converter Output Power Characteristics
Figure 2. 2. 1. 4
Thermionic Converter Intrinsic Efficiency Characteristics
Figure 2. 2. 1.
Thermionic Converter Output Power Characteristics
Figure 2. 2.4. 1
Representative DC-DC Converter Efficiencies
Table 2. 3. 2. 1
Characteristics Of Converter With Variable Cesium
Reservoir Temperature
Table 2. 3. 3. 1
Characteristics Of A Converter Operating At A Constant
Power Point
Figure
3. 2.
Solid Fuel
3. 6.
Self Absorption
3. 7. 1
Geometry Used
Element
In
Factor
17
22
28
32
The Calculation Of
3^ 7.
LP
34
35
37
3. 9. 1
W-ThO^
Multi-Foil Insulation Thermal Conductivity
Figure ^.10.
3. 10.
Solid Fuel
Element Efficiencies
41
1
Components Of Heat Loss
3.
39
1
Comparison Of
Table
14
27
Normalized Intensity Of Absorbed Radiation
Figure 3. 8. 1
Isotropic Source Gamma Albedo For Tungsten
Table
13
1
Figure
Figure
12
3. 2. 2
Gamma
Figure
11
24
Cross Section Of Tubular Fuel Element
Figure
10
1
Cross Section Of
Figure
3
In Solid
Cylinder Fuel Elements
43
10.2
Components Of Heat Loss For Different Fuel Element
44
Configurations
Table
3. 10. 3
Components Of Heat Loss
Figure
In
Tubular Fuel Elements
45
3. 10.
Comparison Of
Solid and Tubular Fuel Element Efficiencies
Figure 3. 10.
Tubular Fuel Element Efficiency
46
47
LIST
Figure
4. 2.
OF FIGURES AND TABLES (CONT.
)
1
Geometry Used
In
The Calculation Of Shielding
Figure 4. 3. 1
Emitter Heat Source
Table 4. 3. 1
Required Shiel Thicknesses
Figure 4. 3. 2
Cross Section Of Shield Assembly
Figure 5. 1. 1
51
54
55
57
Power Flattening Mechanism
60
Figure 6. 5. 1
Thermionic Converter Configuration
Table 7. 1. 1
Final Design Summary
VI
69
75
CHAPTER
1
INTRODUCTION
1. 1
OBJECTIVE
The objective
of this thesis is to design a
thermionic power supply
which will be fueled with cobalt- 60 and which will provide 500 watts of
electric
power over
of three years
a three year operating period.
was chosen because the required
radioisotope power supplies
Most
is
between one and
of the effort in this thesis
The design lifetime
life of
many
five years.
operational
(Reference
I. 1]
has been directed toward the opti-
mization of the fuel supply and toward the power flattening requirements.
The
final design
has been formulated so that no significant advances
the present state of the art are required for
The power supply was designed
ingly
it
is not
effort has
it
to
be feasible.
for terrestrial applications, accord-
subjected to severe weight limitations.
been made
to
in
Nevertheless every
keep weight and size within reasonable limits.
The power supply was also designed so
that
it
could operate automatically,
unattended, for the three year lifetime.
1. 2
DESIGN CONCEPT
1. 2. 1
FUEL REQUIREMENTS
In
order
to
operate a thermionic converter efficiently the tempera-
ture of the thermionic emitter must be at least 1500°C.
Most design
concepts for radioisotope power generators require that the isotope fuel
operate at temperatures higher than the thermionic emitter temperature
in
order for heat transfer
to
occur.
Difficulties associated with the
operation of isotope fuel at these high temperatures have proven to be
the
primary deterrent
use of isotope fueled thermionic converters.
to the
The relative low cost and high power density
make
ed to other isotope fuels such as strontium- 90,
fuel.
(Reference
and that
is
However, the melting point
1. 2)
compar-
of cobalt- 60,
it
attractive as a
of cobalt-60 is
MQS^,
significantly below the melting point required for a useful
thermionic converter
To make
fuel.
this isotope
compatible with ther-
mionic converter requirements, alloys of cobalt and rhenium have been
tested in an attempt to produce an isotopic fuel
form with
This approach has not been entirely successful.
point.
drawbacks
is that
the alloy
must be formed after
a high melting
One
of its
major
the cobalt has been ir-
radiated.
1. 2. 2
LOW TEMPERATURE FUEL CONCEPT
Considering the facts mentioned above the choice of cobalt-60 as
a fuel for a thermionic
power supply appears
at
best to be illadvised.
However, an interesting concept has been proposed which
isotope which emits energetic
(Reference
radiation to be used as a fuel.
1. 3)
This design concept
The design proposes
fuel,
gamma
to
presented schematically
is
thermally insulate the
The gamma radiation from
gamma
converted into heat by the
in
gamma
cobalt-60 in this case) from a surrounding
absorber.
will allow an
Figure
1. 2. 2. 1.
source (the isotope
medium
of
gamma
the fuel would be absorbed and
absorber.
The
gamma
absorber would
then act as the heat source for the thermionic emitter.
Since the cobalt-60
source
(gamma
is
absorber),
thermally insulated from the emitter heat
it
can operate
at a
temperature lower than
the temperature of the emitter heat source and lower than its
ing point.
own melt-
This design concept has recently become feasible due
to the
VAC
HOD
COLLECTOR
RADIATOR
SCHEMATIC POWER SUPPLY DESIGN
FIGURE
1. 2.
2.1
develop^ment
of a high
temperature multi-foil insulation which uses
refractory metal foils separated by thin layers of refractory oxide particles to provide a highly efficient and
(Reference
1. 3
compact thermal insulation.
4)
1.
PRELIMINARY DESIGN CONSIDERATIONS
Several additional design requirements are illustrated in Figure
Some
1. 2. 2. 1.
of these
have been selected for convenience, others
are required by the operating conditions.
Since the high operating temperature of the emitter heat source
required the use of a refractory material, tungsten was selected as the
The high atomic number
material to be used.
gamma
of tungsten gives
it
good
absorption properties.
The high temperature
of the
thermionic converter and
its
heat
source imposes a requirement that the system operate in a vacuum
order
to
Thus
the
design
in
prevent rapid oxidation of the high temperature components.
vacuum housing, shown
in
order
to
in
Figure
1. 2. 2. 1,
was included
in the
maintain a vacuum around the high temperature com-
ponents.
In
order
to facilitate fabrication of the
heat source assembly
it
is
thermionic converter and
desirable to delay loading of the isotope fuel
until all other steps in the fabrication
process have been completed.
This procedure will minimize the work which must be performed re-
motely
in a hot cell
and thus greatly simplify assembly of the unit.
was therefore decided
to locate the fuel outside of the
Approximately one
to the collector of the
power.
It
is
fifth of the
It
vacuum housing.
energy transfered from the emitter
thermionic converter
thus necessary to provide a
is
removed as electric
means
of
removing the remainder
order
of this
energy
ture.
A
in the
atmosphere.
in
maintain the collector
to
constant tempera-
at a
radiator is provided so that the excess energy can be dissipated
Since the radiator area remains constant throughout
the operating period, the collector temperature will be determined by
the heat flux to
it
from the emitter and the output power.
The hard gamma radiation from
Mev
and
1.
33
per disintegration) requires that the power supply be shielded
in
order
the cobalt-60
(1. 17
personnel from the ionizing radiation.
to protect
Since there will be
some heat generated
in the fuel a
means must
be provided to remove the heat so that the fuel will remain at a low
temperature.
In
Figure
1. 2. 2. 1
As
conduction through the shield.
necessary
to
the heat
removal
this design
accomplished by
is
was modified,
it
provide the fuel with a radiator assembly similar
became
to the
collector radiator.
1.4
FURTHER DESIGN REFINEMENTS
The basic design
matically
in
be modified
Figure
in
is
now
qualitatively set and is represented sche-
1. 2. 2. 1.
In the following
an attempt to both optimize
chapters the design will
performance and
its
to
remain
within limits set by materials and the state of the art.
The thermionic converter design
practical output voltage for the
obtaining
output
mine
it
A
In
Chapter
of
3
power
the fuel
is
in
to fix the
Power
Chapter
2.
A
selected and methods of
thermionic converter design
the required input power.
mode
considered
power supply
power requirements are used
ted and the
imum
discussed.
is
is
selected and the
operating point and deter-
flattening concepts are investiga-
flattening selected.
element design
is
optimized so that the max-
useful energy will be delieverd to the emitter heat source.
An
optimized fuel element design
is
selected to meet the converter input
power requirements which were determined
in
Chapter
The shielding requirements are discussed
in
2.
Chapter
4.
The
shielding calculations are explained and the shield design is finalized.
Since no power flattening device found was compatible with this
design's needs, one was designed.
discussed
in
Chapter
Chapter
6
The power
flattening
mechanism
5.
contains an explanation of numerous heat losses which
degrade the performance of the thermionic converter and cause
operate
at less
is
than the intrinsic efficiency.
losses on the fuel element design
is
The
it
to
effect of these heat
Several additional
also treated.
design problems which were not treated in detail are summarized.
The
drawn.
final design is
summarized
in
Chapter
7
and conclusions are
REFERENCES
1. 1
1. 2
W. R. and Harvey, D. G.
Englewood Cliffs: Prentice Hall,
Corliss,
,
Radioisotopic
Inc.
,
Power Generation,
1964.
Hilbom, H. S. "Savannah River Laboratory Isotopic Power and
Heat Sources, Part I Co-60, " Quarterly Progress Report, July
September, 1967, DP-1129-1.
,
"Description of a Cobalt-60 Fueled Thermionic
Generator Experiment, " Conference Record of the Thermionic
Conversion Specialist Conference, October, 1967.
1. 3
Dunlay,
1.4
"Quarterly Progress Report of
Carvalho, J. and Dunlay, J. B.
Research and Development of Vacuum Foil Type Insulation for
Radioisotope Power Systems," Thermo Electron Corp., Report
No. 4059-109-69, January 20, 1969.
J.
B.
,
,
-
CHAPTER
2
SELECTION OF THERMIONIC CONVERTER DESIGN
2. 1
GENERAL REMARKS
Thermionic converter performance characteristics
(i. e.
,
output
current density, output power density and intrinsic efficiency) are functions
of several
that the desired
different
These parameters can be varied
parameters.
in a
power output can be obtained using any one
parameter combinations.
In this
manner such
of several
chapter a set of performance
characteristics, which has been extracted from the literature, is discussed
and the reasoning used
in fixing the
converter operating parameters
is
explained.
Methods
of obtaining a practical voltage output and their effects on
converter design are explained.
this
power supply design
The problem
of
The choice
method
to
be used
in
made.
is
power
flattening is also treated.
ing concepts are proposed and discussed.
to operate using
of the
Two power
flatten-
Thermionic converters designed
each of the power flattening concepts are discussed and
compared.
Finally the thermionic converter design to be used in this power
supply
2. 2
is selected.
THERMIONIC CONVERTER PERFORMANCE CHARACTERISTICS
2. 2. 1
PERFORMANCE CHARACTERISTICS USED
The performance characteristics
output
power density and
reservoirtemperature T
(i.
e.
,
AS DESIGN BASIS
output current density,
intrinsic efficiency) are functions of the
,
emitter temperature T
Tq, interelectrode spacing and electrode material.
,
cesium
collector temperature
In
order
to select the
operating values of these parameter
shows the functional dependence
it
is
desirable to have data which
of the thermionic converter
performance
characteristics on each of the variable parameters.
Figures
2. 2. 1.
1
through 2.2.1.5 show the thermionic converter
performance characteristics
of a converter with tungsten emitter at
2000°K, molybdenium collector and an interelectrode spacing of
mils
7.
as a function of cesium reservoir temperature and collector temperature.
These performance characteristics were calculated using an analytical
These theoretical characteristics are
converter model.
with corresponding experimental characteristics.
in
The method used
calculate these characteristics is explained in References
Although the data presented
in
Figures
2. 2. 1. 1
for an emitter temperature of 2000°K, Reference
good agreement
2.
1
2.
and
1
through
to
2. 2.
2. 2. 1. 5 is
provides similar
data for emitter temperatures ranging from 1600°K to 2100°K.
As
explained below, however, 2000°K is the emitter operating temperature
K
and 1000
is
the proposed
the collector operating temperature which
were selected for
power supply.
INTRINSIC EFFICIENCY
2.2.2
The
Figures
intrinsic efficiency appears as the ordinate on the graph in
2. 2. 1. 2
and
2. 2. 1. 4;
it
intrinsic efficiency
fl-
is
defined here so that no confusion will
arise.
The
of a thermionic converter is defined as
the efficiency in the absence of electrode, lead, and structural support
losses.
This efficiency
considerations and
^i
=
is
is
independent of detailed converter design
given by
P/(Q e + Q t + Q r + Q
g
)
(2.2.2.1)
10
THERMIONIC CONVERTER OUTPUT VOLTAGE CHARACTERISTICS
0.4
0.8
1.2
1.6
OUTPUT VOLTAGE (VOLTS)
FIGURE
2. 2. 1.
1
2.
11
THERMIONIC CONVERTER INTRINSIC EFFICIENCY CHARACTERISTICS
24.
20.
^
16.
O
u
—
I
12.
w
o
I—
w
I—
8.
4.
0.
4
0.8
1. 2
OUTPUT VOLTAGE (VOLTS)
FIGURE
2. 2. 1. 2
TO
12
THERMIONIC CONVERTER OUTPUT POWER CHARACTERISTICS
24.
20.
K
Tn =64C
TE = 2000
I
Tq = 1000
I
D
i\
=
MI
7.
_,S
630
Y<
6:
<>]
O
16.
H
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610
i—
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A
o
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8.
P-i
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H
-
ID
O
4.
^*****™^^^i
0.4
1.2
0.8
OUTPUT VOLTAGE (VOLTS)
FIGURE
2. 2. 1. 3
1.6
2.
13
THERMIONIC CONVERTER INTRINSIC EFFICIENCY CHARACTERISTICS
24.
0.4
0.8
1.2
OUTPUT VOLTAGE (VOLTS)
FIGURE
2. 2. 1. 4
1.6
2.
14
THERMIONIC CONVERTER OUTPUT POWER CHARACTERISTICS
24.
20.
CV)
O
16.
>i
H
i—
CO
W
Q
12.
o
PL,
Ph
H
O
ID
4.
0.4
0.8
1.2
OUTPUT VOLTAGE (VOLTS)
FIGURE
2. 2. 1. 5
1.6
2.
15
where P
fluxes
is the
output
removed from
power density and Q
c
,
QX
Q.,
X
and
Q
are the heat
g
the emitter due to electrons, ions, radiation, and
gas conduction, respectively.
Q
flux
is
which
2. 2. 3
by far the most important term and
Qr
the only other heat
is
is significant.
EMITTER AND COLLECTOR OPERATING TEMPERATURES
It
is
generally true that the efficiency of an optimized thermionic
converter increases monotonically with increasing emitter temperature.
It
is
thus desirable to operate the converter at the highest allowable
emitter temperature.
The highest temperature allowed
in the
system
is
limited to 2270°K by the tungsten multi-foil insulation which is used to
insulate the fuel elements and the emitter heat source. (Reference
The highest temperature
to
which the multi-foil insulation will be
subjected occurs at a point on the emitter heat source
from the emitter.
Using
it
was determined
that the
emitter temperature would be approximately 2100 K.
that further
refinement of the design
the emitter
from
of
end farthest
(i. e.
necessity
maximum
Since
it
allowable
was expected
to electrically insulate
heat source) would lead to a larger temperature drop
across the heat source,
the
at the
first design iteration values for heat fluxes and
emitter heat source size,
its
2. 3)
it
was decided
performance characteristics
that the design would be
of a converter with an emitter
based on
temperature
2000°K.
The operating temperature
of the collector
was selected as 1000
K
since this gives the highest intrinsic efficiency for an emitter temperature
of 2000°K.
Since the collector radiator
the emitter to the collector
is fixed in size,
must be constant
in
the heat flux from
order to maintain a constant
1G
collector temperature for a given electric
power
output.
OUTPUT VOLTAGE
2.2.4
Much
of the
equipment which power supplies of this type are
designed to power require input voltages on the order of 28 volts. (Refer-
ence
2. 4)
It
was therefore decided
that in
order to be practical this power
supply should have an output voltage of 28 volts.
Thermionic converters are classified as low voltage, high current
devices.
volt.
The output
of a single thermionic diode is on the
Thus, in order to furnish power
mionic diodes must be connected
must be stepped up using
more
attractive since
it
a
desired 28 volts,
many
ther-
series or the output from a few diodes
in
DC-DC
at the
order of one
converter.
The second alternative
is
requires fewer diodes and, moreover, the
electronics for the step up process are relatively simple.
The circuitry
and operating characteristics of low voltage input, regulated, current
drive
DC-DC
described
in
Figure
DC-DC
in
converters suitable for use with thermionic converters are
References
2.4.
2.
1
2. 5,
2. 6
and
2. 7.
shows representative efficiencies
of current drive
converters for various voltage inputs and power levels.
Figure
2. 2. 4.
1
The data
indicates that there is little to be gained by using an
input voltage greater than 5 volts, but that the efficiency falls off rapidly
for input voltages less than 5 volts.
At a power level of 500 watts and an input voltage of
representative
DC-DC
converter efficiency of 89%
2.2.4.1.
Thus,
necessary
to supply 560 watts to the
in
order
is
a
found from Figure
to obtain 500 watts of useful
DC-DC
5 volts,
power
converter.
it
will be
Therefore the
thermionic converters will be designed so that several connected
in
series
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u
1—
i
u
Q
PS
Eh
o
>
CM
i—
<
Eh
u
w
H
Eh
p
W
Ph
CO
1
H
o
o
PL,
H
//
PS
o
o
o
o
CO
A0NHI0MJ3
o
1—
fe
18
DC-DC
will provide 560 watts at 5 volts to a
Now
converter.
that the thermionic converter output
requirements have been
established the power flattening problem must be investigated to determine
whether or not
it
restricts the selection of the thermionic converter
operating point.
2. 3
THERMIONIC CONVERTER DESIGNS COMPATIBLE WITH POWER
FLATTENING REQUIREMENTS
2.3.1
POWER FLATTENING REQUIREMENTS
Since the half
life of
cobalt- 60 is
5.
25 years, the energy supplied to
the emitter heat source will decrease significantly over the three year
life of
the
power supply.
must be employed so
This means that .some form of power flattening
that constant
power can be supplied
to the load.
Since a constant emitter operating temperature of 2000°K has been
chosen for this design, the power flattening problem reduces
maintaining the emitter heat source
at a
to
one of
constant temperature while the
energy available from the cobalt-60 decreases.
approaches to this power flattening problem.
There are two general
The
first is to
remove
all
the energy deposited in the emitter heat source through the thermionic
This approach necessitates operating with a variable cesium
converter.
reservoir temperature.
verter to operate
current).
In
The second approach allows the thermionic con-
at a fixed
power point
(i. e.
constant output voltage and
order to do this a variable heat removal system
to the emitter heat
source and operates
in parallel with the
is
connected
thermionic
converters.
2. 3. 2
CONVERTER OPERATION WITH VARYING CESIUM RESERVOIR
TEMPERATURE
When operating near maximum
efficiency the
major fraction
of the
19
heat transferred
electrons.
If
from the emitter
to the collector is carried
by the
the emitter is maintained at a constant temperature
the
only other significant heat transfer, that due to radiation, remains constant.
Thus,
order
in
be varied.
to
vary the emitter cooling rate, the output current must
Figure
2. 2. 1.
1
shows
that the output current can be varied by
varying the cesium reservoir temperature.
In
order to maintain a constant power output the output voltage would
also have to be varied.
the current density and
As can be seen from Figures 2.2.1.2 and
power output are both functions
2..
2. 1. 3
of the converter
output voltage and cesium reservoir temperature.
Over
a three year period the energy released by the cobalt-60
decreases by 33%.
to
vary by 33% and
This means that the current density would also have
in
order to maintain a constant power output the output
voltage must also be varied by 33%.
References
Thus
it
2. 5
and
2. 6
can accomodate a
-
14% variation
in
in input voltage.
would be desirable to employ a system that would decrease the
variation in output voltage so that a
not have to be designed.
thermionic converter
In
The DC-DC converters described
at a
It
more complex DC-DC converter does
was therefore decided
that the operation of a
constant output voltage would be investigated.
order to maintain a constant emitter temperature while operating
at a constant output voltage,
it
is
necessary to control both the cesium
reservoir temperature and the voltage regulator shunt resistance.
range of voltage outputs over which a variation
temperature can cause a 33% variation
decrease
in the
in the
in
In the
cesium reservoir
current output density a
cesium reservoir temperature causes
a
decrease
in
output current density.
Therefore the thermionic converter would be designed to provide the
20
desired power level with a low cesium reservoir temperature
In
life.
order to cool the emitter
end of
at the
beginning of
at a faster rate at the
life,
the converter would be operated at a higher cesium reservoir temperature
and consequently a high current density.
power output
constant, the
will
of design lifetime is reached.
would have
This means that the thermionic converter
2. 5)
which would maintain a constant
to the load.
Figures
2. 2. 1. 2
and
power density as functions
The data
performance
held
always be higher than required until the end
(such as described in Reference
ature.
is
be coupled to the load with a dissipative shunt regulator
to
power output
Since the output voltage
in
of a
2. 2. I. 3
show the intrinsic efficiency and output
cesium reservoir temper-
of output voltage- and
these figures was used to predict the beginning of
thermionic converter designed
to
operate
at a
life
constant
output voltage and variable cesium reservoir temperature.
Even though the emitter would be maintained
ture
its
at a
constant tempera
-
the exponentially decreasing heat flux to the collector w ould cause
r
,
temperature to decrease because of the fixed heat transfer area
collector radiation.
Therefore Figures 2.2.1.4 and 2.2. 1.5, which show
intrinsic efficiency and output
power density as
temperature and output voltage, were used
performance
It
of the
a function of collector
to predict the end of life
of the thermionic converter.
was found
that at output voltages higher than
0. 7
volts variation of
the cesium reservoir temperature could not cause enough change in the
output
power density
to
provide the desired three year lifetime and
maintain a reasonable efficiency.
Thus
0. 7
volts
was selected as the oper-
ating output voltage for the individual thermionic converters.
that seven thermionic converters
still
would have to be connected
This means
in
series to
21
provide a
life
4. 9 volt
input to the
DC-DC
The beginning and end
converter.
of
characteristics of the thermionic converter designed to operate at a
constant output voltage and with variable cesium reservoir temperature
are summarized
Table
2. 3. 3
2. 3. 2. 1
at a
Table
2. 3. 2. 1.
The
were calculated using the
input
power requirements
listed in
intrinsic efficiency.
OPERATION AT A FIXED POWER POINT
In
point,
in
a
order to allow the thermionic converter
to operate at a fixed
power
system must be provided which maintains the emitter heat source
constant temperature while the thermionic converter
constant amount of heat.
system which operates
parameter
of the heat
The usual approach
in parallel with the
is to
removes
a
provide a heat removal
thermionic converters.
Some
removal system, such as heat transfer area,
is
varied such that the excess heat removed decreases with the same time
constant as the exponential decay of the isotope fuel.
an excellent review of
some
of the
Reference
more promising methods
Unfortunately the only concept discussed that
flattening.
is
of
gives
2. 7
power
neither beyond
the present state of the art nor too complex to be simply automated is one
which employs a variable radiator area.
This method provides only
approximate power flattening since the radiating surface
finite steps
by ejecting parts of the radiator.
33% variation
in
In
is
reduced
order to provide for the
the heat input to the emitter heat source and maintain
a relatively constant temperature, the radiator would have to be
of
of these
proposed power flattening schemes seem
particularly well suited to this design's requirement of a three year
lifetime.
it
made up
many segments and would be very cumbersome.
Thus none
in
Therefore, a power flattening mechanism was designed to
at
22
CHARACTERISTICS OF CONVERTER WITH VARIABLE
CESIUM RESERVOIR TEMPERATURE
Beginning of Life End of Life
Tungsten
Emitter Material
Emitter Temperature
(
2000
K)
lybdenum
Collector Material
Collector Temperature (°K)
1000
Interelectrode Spacing
7
Output Voltage (Volts)
Output Power Density (Watts/ cm
)
Cesium Reservoir Temperature (°K)
Total Emitter Area
Total
Power Output
(cm 2 )
(Watts)
Required Heat Input (Watts)
Intrinsic Efficiency
mils
10
630
608
56
5G
975
560
4820
3150
3. 2
TABLE
7
2.3.2.1
-
17.4
Design Lifetime (Years)
Converters Required
750
0. 7
20. 2
of
-
0. 7
(%)
Number
2000
17. 8
-
_
23
This mechanism
maintain a constant emitter temperature.
in
Chapter
This power flattening mechanism
5.
mionic converter operating
at a
made
is
described
the design of a ther-
constant power point feasible.
converter would operate with the characteristics listed
This
Table
in
2. 3. 3. 1.
The converter was also designed using the performance characteristics
presented
in
Figures
2. 2. 1. 2
and
2. 2. 1. 3.
Again, the input power
requirements were calculated using the intrinsic efficiency.
A
converter operating with this
mode
of
power
flattening has the
following advantages over a converter using a variable cesium reservoir
temperature (Table 2.3.2.1) for power flattening.
thermal power input requirement results
fuel costs
920 watt lower
saving of $12, 900 on initial
based on a cost of $14 per thermal watt (Reference
five thermionic diodes are
the
in a
Its
DC-DC
needed to provide the desired
5
1. 2).
Only-
volt input to
converter instead of the seven required by the system using
the variable cesium reservoir temperature
mode
of
power
flattening.
Since
the cesium reservoir temperature remains constant over the entire
operating period, an internal adsorption type reservoir of the type
described in Reference
2. 9
can be used.
Since these advantages strongly favor a thermionic converter
operating
at a
constant power point, a thermionic converter with the
operating characteristics given
this
power supply design.
in
Table 2.3.3.1 was selected for use
in
24
CHARACTERISTICS OF A CONVERTER OPERATING AT A
CONSTANT POWER POINT
Beginning of Life End of Life
Tungsten
Emitter Material
Emitter Temperature
(
2000
K)
Molybdenum
Collector Material
Collector Temperature
(
K)
1000
Interelectrode Spacing
7
Output Voltage (volts)
Output Power Density
(watts/
cm
Cesium Reservoir Temperature
Total Emitter Area
Power Output
(cm
(
K)
100(
-
1.0
1.0
610
63. 5
)
-
mils
8. 8
)
2000
8.8
610
63. 5
(watts)
560
560
Required Heat Input (watts)
2540
2540
Excess Fuel Required
1360
Total
Intrinsic Efficiency
(watts)
Design Lifetime (Years)
Number
of
22
22
3. 2
-
(%)
Converters Required
5
TABLE
2.3.
3.
1
_
25
REFERENCES
2.
1
2. 2
"An Improved Theoretical Description of Thermionic
Converter Performance Characteristics, " Procedings: 27th
Annual Physical Electronics Conference, Cambridge, Mass.:, March,
___
Wilkins, D.R.
,
Wilkins, D.R.
,
"A
Unified Theoretical Description of Thermionic
" Journal of Applied
39, number 5, April, 1968,
Converter Performance Characteristics,
Physics, vol.
2. 3
2.4
Paquin, M. L.
"High Te_mperature Multi-Foil Thermal Insulation,
Thermo Electron Corp.
Corliss,
W. R. and Harvey, D.
Englewood
2. 5
"
,
C.
Prentice Hall,
Cliffs:
Radioisotopic
,
Inc.
,
Power Generation,
1964.
Low
Voltage Converter Regulator
J. T. , "Thermionic
"
Conference Record of the Thermionic Conversion
Systems,
Lingle,
Specialist Conference,
November, 1966.
2. 6
Lingle, J. T.
"Low Input Voltage Conversion, " Procedings of the
18th Annual Power Sources Conference, May, 1964.
2. 7
Lingle,
2.8
Rush, R. E. and Belofsky, H.
"Power Flattening Studies for
Radioisotope Thermoelectric Generators, " General Instruments
Corp., NYO-9783 1963.
,
"Energy Source - Low Voltage Conversion System,
T.
Procedings of the 19th Annual Power Sources Conference. 1965.
J.
"
,
,
,
2. 9
Harbaugh, W. E. and Basiulis, A. 'The Development of a HighTemperature Reservoir for Automatic Control of Cesium Pressure,
Conference Record of the Thermionic Convers ion Specialist
Conference, November, 1966.
,
"
26
CHAPTER
•FUEL
3.
1
3
ELEMENT OPTIMIZATION
GENERAL REMARKS
This chapter explains. in detail the methods used to optimize the
the fuel element design.
Limitations placed on the fuel element geometry
are discussed and two practical fuel element configurations, which were
selected for study, are described.
The heat losses which contribute
to fuel
element inefficiencies
are defined and the methods used to calculate these heat losses are
Heat losses and efficiencies, calculated for fuel
explained in detail.
elements of various lengths, diameters and strengths, are compared.
Based on
this
for use in this
3. 2
comparison the optimum
fuel
element design
is
selected
power supply design.
FUEL ELEMENT CONFIGURATION
The major supplier
of cobalt- 60 is the
Savannah River Laboratory.
The cobalt
is
Atomic Energy Commission's
obtainable in the form of
i
wafers which are 40 mils thick and up
wafer
is
to 3.5
inches in diameter.
Each
plated with approximately one mil of nickel in order to prevent
contamination of the equipment used to handle
irradiated.
(Reference 3.1) Due
it
once
it
to the size limitations
has been
placed on the
cobalt wafers any fuel element large enough to be of interest will have to
be composed of a large number of wafers.
The two
fuel
element configurations which were considered for
power supply design are shown
element
is
composed
cylinder; the other is
in
Figures 3.2.1 and
of a stack of cobalt
composed
of
3. 2. 2.
One
this
fuel
wafers which form a solid
washer
like cobalt wafers and takes a
27
CROSS SECTION OF SOLID FUEL ELEMENT
COPPER ROD
OPPER HEAT
REMOVAL PATH
COBAL
WAFERS
MULTI-FOIL
SULATION
TUNGSTE
EMITTER HEAT SO
FIGURE
3. 2. 1
28
CROSS SECTION OF TUBULAR FUEL ELEMENT
-COPPER ROD
.COPPER HEAT
REMOVAL PATH
MULTI-FOIL
INSULATION
TUNGSTEN
EMITTER HEATJSOUR(
FIGURE
3. 2. 2
29
The
tubular form.
insulated
from
fuel
at
They are
copper.
low temperatures.
order to insure that the fuel
any heat generated
in
it
any heat which reaches
When
removed.
in
the emitter heat source with multi-foil insulation and are
designed to operate
In
elements are both clad
due
it
to the self
maintained
at a
absorption of
low temperature
gamma
radiation or
through the thermal insulation must be
stacked to form a fuel element, the cobalt wafers offer a
very poor heat transfer path due
wafer interfaces.
is
Thus the
fuel
removing any heat generated
to the
low thermal conductance across the
element design must provide a means of
in the fuel
element.
In this
case the stack
which provides a path of high thermal
of fuel wafers is clad in copper
conductance for heat removal.
For future reference
the copper heat
the fuel element is defined as the cobalt wafers,
removal path (cladding) and the surrounding multi-foil
The cobalt wafers and copper cladding
insulation.
will be referred to as
the fuel rod.
Since the fuel element
source
it
is
heat which
is
obvious that any energy which
is
is
absorbed
in the fuel
or any
transmitted through the insulation to the fuel canjiot be used
by the thermionic converter.
fuel
thermally insulated from the emitter heat
element so that the
total
It
will therefore be benificial to design the
energy which the system loses
to
it
will
be
minimized.
3. 3
ENERGY LOSSES TO THE FUEL ELEMENTS
In
order
necessary
to
to
minimize the
total
energy loss
know what the losses are and how
to the fuel
to calculate
the energy loss rates are defined in this section.
calculate
them are then explained
elements
them.
is
Thus,
The methods used
in the following sections.
it
to
30
Eg
energy loss due to absorption of beta particles
copper per unit time.
Er
Ey^rr energy loss due to self absorption of
per unit time.
Ey
=
Ew=
gamma
radiation in the cobalt
energy loss due to absorption of
removal path per unit time.
gamma
radiation in the copper heat
energy loss due
per unit time.
gamma
radiation in the insulation
absorption of
to
E„jr= energy loss due to the absorption of backscattered
in the fuel element per unit time.
Q H energy
loss due to heat flux
to the fuel element.
T
3.4
gamma
radiation
through the insulation from the tungsten
FUEL ELEMENT EFFICIENCY
The efficiency
(E
%
where E
1-
=
of the fuel element, f1p
t.+
F
E
C
+
E T + E SQ
+
Q*
T
is
defined as
+ E ft
)
(3.4.1)
g
T
is
defined as the total energy released during radioactive decay
of the fuel per unit time
This definition
power density
3. 5
and
in the cobalt
is
minus any energy carried away by neutrinos.
compatible with the convention used when calculating the
of the fuel.
CALCULATION OF Ep
Eg
resulting
is the
from
the decay of the cobalt-60 are emitted with an energy
spectrum which has an upper energy limit
most energetic beta particle
of cobalt.
all of
The beta particles
simplest energy loss to calculate.
is 81
Since this distance
is
mg/cm
of 0. 31
which
much shorter
the beta energy is absorbed in the fuel.
Mev.
is
The range
equivalent to
of this beta
decay energy
is
009
cm
than any fuel chord length
This means that
0. 31
are lost to the system for each disintegration of a cobalt-60 atom.
71%
0.
of the
Mev
However,
carried away by neutrinos (Reference
3. 2);
31
thus only
0.
09
Mev's per disintegration are deposited
A sample
in the fuel.
of cobalt- 60 with an activity of 400 curies
release a total of 58.
7
watts/ cm
3
;
52. 4 watts/
cm
per gram
3
is in
form
the
will
of
gamma
o
radiation, 4.4
3
cm appears
watts/cm
V-,-,
r
carried away by the neutrinos and 1.9 watts/
as beta particle energy.
E^
where
is
is the
=
volume
1.9
Thus
Vp
(3.5.1)
of the fuel (cobalt-60) in
cm
o
.
valid only for cobalt with an activity of 400 curies per
3. 6
Equation
3. 5.
is
1
gram.
CALCULATION OF E v
In
order
described
finite
E^p
to calculate
in detail in
,
Reference
the results of calculations
3. 3
v/ere used.
performed and
This reference treats the
source as a series of planes composed of point isotropic sources and
integrates over the volume assuming scattering is straight ahead and
This integral can be performed analytically
attenuation is exponential.
only
if
planes and cylinders of infinite length are considered.
obtained are plotted in Figure
is
3.
The results
6.1 as a self absorption factor,
equal to the fraction of emitted
gamma
f,
which
radiation absorbed in the fuel.
Thus,
E*F
3. 7
CALCULATION OF
Ew-,
Reference
unit
=
f
(E
E.
T"
V
(3.6.1)
AND E^
and E^ T were computed using the following method developed
3. 3.
I
is
in
defined as the intensity of absorbed radiation per
volume per second
at a distance r
from the axis
a plane coincident with the end of the cylinder.
of a cylinder and in
32
tf
CO
CO
1
55
Q
s
U
—
i
E
H
X
n
x
Q
£
—
pq
<
O
H
U
<
CO
i
I
4
2
H
CD
X
CO*
H
O
W
CO
O
i—
<J
H
CO
LO
O
O
00
I>
CD
LO
<#
CO
CM
o
o
O
o
o
o
O
33
£-?
where
is
if
the macroscopic
material surrounding the fuel
radiation and
D
See Figure
D
is
=
z
7
related to
2
(3.7. 1)
h
'0
'o
n
+ r
2
gamma
at the
2
+
-
f>
energy of the emitted
and
,
absorption cross section of the
gamma
by
z
2rp cos ©
(3.7.2)
3. 7. 1.
obtained from equation 3. 7. 1 is one half the value of
P
the radial distribution in any normal plane of an infinite cylinder. There-
The value
fore, a
of
I
new function
is
I
defined where
2L
(3.7.3)
V
I
is the
1
- f
normalized absorbed radiation intensity so that
oo
2L'
r d
5a»
[UaR
(r
-
1
)]
-
(3.7.4)
1
^
where R
is
the radius of the fuel and r
The function
r'
V*
The fraction
shell
between
of the
1
f
/Ja (r
2
-
emerging energy
is
lXa
t
R(r'
-
1) in
Figure
equal to
R)
P
JWaR
R)'
r'
d ff/aR
U
(r'
3. 7. 2.
that is absorbed in an annular
^
1
against
2
2I
/*a (r
egual to r/R.
a^
and r
r.
is plotted
is
-
1)1
J
This integration can be performed graphically on Figure
(3. 7. 5)
3. 7. 2.
34
GEOMETRY USED
IN
THE CALCULATION OF
h>
FIGURE
3. 7. 1
35
O
i—
H
Q
W
O
en
CM
ffl
<
00
O
H
>H
H
i—
CO
W
H
Q
W
N
i—i
O
o
CM
a
CM
36
E\/£
equal to
is
,/'a(r
(E
c -R)
-E VF )1
T -E^
2^
r -d[|laR(r'
-
1)]
(3.7.6)
1)]
(3.7.7)
J
where
r
c
is the
outer radius of the copper.
,Ua
(E
Ep
-
T
-
E^ F
(r
rj is the equivalent
is
equal to
R)
21
f
P
)
J/^(r
where
-
Ejj
r
d[/laR(r'
-
-
c -R)
outer radius of the multi-foil insulation.
equivalent radius is defined such that rj
-
r
Q
is
equal to the
sum
The
of the
thicknesses of the individual foils in the insulation.
3.8
CALCULATION OF E ou
E
was approximated
S fr
in the
energy albedo for tungsten for
are shown
in
Figure
where Ej
albedo
at
S
,
AN
is the initial
Ej and
Once
of the fuel
A
N
/j.
aF
is
E
g
E
is
o
—
the
gamma
number albedo
is
evaluated
defined as
(3.8.1)
energy of the
is the
the value of
of the backscaltered radiation
A
Ej x
s
radiation as a function of energy
3. 4.
The average energy
E
gamma
The number and
These curves were found by interpolating
3. 8. 1.
data found in Reference
following mariner.
radiation,
A£
is the
energy
at E,.
obtained the energy absorption cross section
at this
The backscattered radiation
is
average energy.
assumed
isotropic source at the surface of the fuel rod.
to constitute a
plannar
The average distance
that
37
1.0
1
——
— ——-
O
Q
pq
^\
0.
^L
<
V/
y
.
—
/
/
//
/
'
/
VA
fs
E
/
/
0.01
0.
10
1.0
1
GAMMA ENERGY
ISOTROPIC SOURCE
(Mev)
GAMMA ALBEDO FOR TUNGSTEN
FIGURE
3.8.
1
38
the backscattered radiation travels through the fuel rod is equal to the
mean chord
length of the fuel rod r
4 x fuel
-
__
_
.
rod volume
(3.8.2)
area
fuel rod surface
Thus
E
3. 9
=
gy
(E
T
E^
-
-
E^ F
per layer
exp(-UaF r)
-
1
)
(3.8.3)
Two terms
design
C.
layers
at
performance
(Reference
latter arises
watts per
Figure
3. 9.
Qt1
cm
of the foil edges
To
is
is
the
3. 6
degrades the
indicates that
of edge is approximately twice the heat flux
through the insulation.
shows the thermal conductivity
1
2Lk
-T F
=
N
is the total
layer,
The average spacing
the difficulty of matching the
insulation as a function of source temperature.
+
Akj(T S
(T s
)
1
N
of tungsten
3. 5)
Data from Reference
of the insulation.
cm 2
from
The mismatching
corners.
the heat loss in watts per
length,
composed
the heat lost through the insulationjQ
contribute to
The
edge loss.
where A
is
heat lost due to conduction through the insulation and the other
is the
is the
in this
Multi-foil of this composition has given satis-
mils.
is 4.
d,
factory performance at 1900
in
c
mils thick and separated by thorium oxide.
foils 0. 5
foil
E^
CALCULATION OF Qj
The insulation selected for use
One
-
TF
-
L
is
the total insulated edge
of layers of foil, d is the average spacing per
the temperature of the emitter heat source and
rod temperature.
The
(3.9.1)
)
d
insulated surface area,
number
kj of the multi-foil
foil
thermal conductivity
is
evaluated
Tp
at
is the fuel
Tg
39
W-ThQ 2 MULTI-FOIL INSULATION THERMAL CONDUCTIVITY
(k
-4
10
1
1
1
r
""
1
i
1
l
1
l
—
O
o
£
o
+->
3
Eh
i—i
>
—
i
-a
10
h
O
Q
O
O
«
W
X
h
-6
10
!._.
i
.
•
500
JL
.
.!.._.
1
1
1000
l
1500
SOURCE TEMPERATURE
FIGURE
1
3. 9. 1
(°C)
i
i
2000
)
40
3.
EVALUATION OF SPECIFIC FUEL ELEMENTS
10
Once
all
the energy losses could be evaluated, the fuel elements
were compared as follows.
fuel
The selected
length were selected.
its
The
element configuration, strength and
element was then optimized and
fuel
The efficiencies were then compared
efficiency calculated.
in
order
to
determine the optimum fuel element design.
Each
fuel
element evaluated was optimized
in the
Values were selected for E T and fuel element length.
E^j
The number
and Q, were calculated.
selected so that the
assumed
sum
of
E ^ and Q
SI
sum
that heat equal to the
generated uniformly
in the
Ey
,
was
of layers of insulation
was
minimum.
a
,
E
y.^
E^
f
was then
It
and
copper heat removal path.
assumption since the copper
This
Q T was
a good
is
very thin and has a high thermal conductivity.
is
The temperature rise along the length
o
300 C and the outer radius,
Then Eg
I
E^
of
following way.
of the fuel
of the copper
r,
element was limited
to
was calculated using Equation
3. 10. 1.
v2
where At
=
__
(Ep+E yF
300 C,
+
E
yi
+
Ql
R
is the
In
Figure
various values
was then used
3. 10. 1,
of
ET
monotonic increase
fl
Ev^
to calculate
is
(3
of copper,
L
radius of the cobalt fuel.
thickness of the copper was determined,
3. 4. 1
+R 2
At 2TTk c
kp is the thermal conductivity
length of the fuel element and
Equation
)L
fl
and
E^
_
10>1)
is the
Once the
were calculated.
.
plotted against fuel element length for
and a solid cylinder fuel element geometry.
in efficiency with
to the
decrease
in self absorption.
to the
decrease
in the
decreasing E T
The decrease
diameter of the
is
due almost entirely
in self
fuel rods as Erp
The
absorption
decreases.
is
due
41
COMPARISON OF SOLID FUEL ELEMENT EFFICIENCIES
80
f[
F
(%)
^Eji
=
250
- ET
=
500
70
**
60
1
1
I
1
1
1
1
10
5
FUEL ELEMENT LENGTH
FIGURE
3. 10.
1
15
1
(CM)
Erp = 1000
1
42
Figure
In
E
T
=
3. 10. 2,
p
rt
plotted against fuel element length for
is
1000 watts, but for the solid cylinder and tubular fuel element
geometries.
decrease
The higher efficiency
E^ F
in
and
Ef c
The gain
.
not for a significant increase in
compared
of the tubular fuel
E^
in efficiency
element
is
due to a
would be higher were
it
and Qj for the tubular fuel element
to the equivalent solid fuel element.
See Table
3. 10. 2
for a
tabulation of the various energy losses in these two fuel
elements.
Figure
shows n
3. 10. 3
a tubular fuel element with
diameter up
p
ET
as a function of fuel element diameter for
=
cm, then remains relatively constant and then decreases
to 4
as the diameter
becomes very large.
best be seen from Table
since the cobalt
The efficiency increases with
1000.
3. 10. 3.
becomes thinner.
The reasons
E^ decreases with increasing diameter
E^ decreases with increasing diamet-
er since the copper heat removal path can be
in
Ey p
E^ c
and
seen from Table
increase
in
QJ
made
lead to an increase in efficiency.
3.
10. 3,
for this behavior can
thinner.
The decrease
However, as can be
the increasing surface area leads to a
which eventually overrides the decrease
in
marked
E % F and E $ c
and causes the efficiency to decrease.
Table
3. 10.
1
shows the relative importance
ents of the total heat loss and
varied and E
T
how they vary as
held constant at 1000 watts.
along the fuel rod
is
held
must be increased as
at
in
E^ F
;
compon-
the fuel element length is
Since the temperature drop
300°C, the thickness of the copper cladding
the fuel element length is increased.
copper thickness leads to an increase
decrease
of the various
in
E
^c
The increased
which practically offsets the
thus there is little variation in fuel element efficiency
with length.
Based on the data presented
in
Figures
3. 10.
1
through
3.
10. 3
and
43
COMPONENTS OF HEAT LOSS
LENGTH
5
IN
cm
SOLID CYLINDER FUEL ELEMENTS
10
cm
1
cm
5
Erp
1000
1000
1000
H
35
35
35
*F
222
174
145
E fc
27
E
18. 5
21. 2
26.4
E SS
17
14.1
14. 3
Ql
25. 3
26. 6
27.4
E
Sl
V
94.5
58. 5
65. 5
%
66.2
%
65.7
.__
(ALL HEAT LOSSES
IN
WATTS)
TABLE
3. 10. 1
.
—
—~
,—
%
44
COMPONENTS OF HEAT LOSS FOR DIFFERENT FUEL ELEMENT
CONFIGURATIONS
FUEL ELEMENT CONFIGURATION
SOLID CYLINDER
LENGTH
10
cm
TUBULAR
cm
10
DIAMETER
4
cm
ET
1000
1000
Ee
35
35
E &F
174
67. 5
E frC
58. 5
26. 2
E frl
21. 2
48
E sv
14.
Q,
26. 6
66. 2
Of
(ALL LOSSES
IN
1
%
WATTS)
TABLE
3. 10. 2
5. 2
62.
75. 6
1
%
45
COMPONENTS OF HEAT LOSS
-CJrp
DIAMETER
IN
1000
1000
1000
2
TUBULAR FUEL ELEMENTS
cm
4
cm
6
cm
-
Ep
35
35
35
E ifF
125
67. 5
48.2
E SC
50. 5
26. 2
18.3
E
37.4
48
53.6
SI
E Sfr
Qj
If
9.4
62.
34. 7
70. 7
%
TABLE
3.4
5. 2
75. 6
3. 10. 3
%
1
86.6
75. 5
%
4G
COMPARISON OF
SOLID AND TUBULAR FUEL ELEMENT EFFICIENCIES
(E T = 1000)
80
%
<%)
4cm)
70
;olid
1.J
60
I
10
5
FUEL ELEMENT LENGTH
FIGURE
3. 10. 2
15
(CM)
47
TUBULAR FUEL ELEMENT EFFICIENCY
(LENGTH
=
10
CM)
80
Erpf)
F
(%>
70
u
1
/
/
/
Rf>
2
4
6
TUBULAR FUEL ELEMENT DIAMETER
FIGURE
3. 10. 3
8
(CM)
1000
48
the
power requirements
listed in Table
2. 3. 3. 1,
tubular fuel elements would be used, each 4
and with an E
of 1000 watts.
cm
it
in
was decided
diameter, 10
that five
cm
long
49
REFERENCES
3.
1
3.2
Farace, J. P., "Experimental Cobalt-60 Heat Source Capsules,"
Savannah River Laboratory, DP-1 145.
Corliss,
W.R. and Harvey,
Englewood
3.3
3.4
Cliffs:
D. G.
,
Radioisotopic
Prentice Hall, Inc.,
Hurwitz Jr. H. and Roe, G. M. 'Gamma Ray
Storm, M. L.
Absorption Distributions for Plane, Spherical and Cylindrical
Geometries, " General Electric Company, Knolls Atomic Power
Laboratory, KAPL-783.
,
,
,
,
Berger, M.J. and Raso, D. J. "Monte Carlo Calculations of
Backscattering, " Radiation Research 12 20-37, 1960.
,
Gamma Ray
3. 5
3. 6
Power Generation,
1964.""
,
"High Temperature Multi-Foil Thermal Insulation,
Paquin, M. L.
Thermo Electron Corp.
"
,
Carvalho,
J.
and Dunlay,
J.
B.
,
"Quarterly Progress Report of
Vacuum Foil-Type Insulation for
Radioisotope Power Systems, " Thermo Electron Corp.
TE Report
Research and Development
of
,
No. 4059-109-69, January 20, 1969.
50
CHAPTER
4
SHIELDING
4.
1
GENERAL REMARKS
Radiosotope fueled generators intended for terrestrial use generally
require considerable shielding since personnel
in contact with
them even though they may be
may
inadvertently
installed in
come
remote locations.
The Interstate Commerce Commission's shipping regulations for
radioactive materials were therefore selected as the design criteria
which the shielding for this power supply must satisfy.
tions specify a
and
10
maximum
dose rate of 200 mr/hr
mr/hr one meter from
The
members
in shielding calculations.
surface
at the shield
the shield surface.
self- shielding of the fuel
and the other structural
These regula-
element structure, the fuel
itself
of the generator is not usually included
(Reference
4. 1)
However
in this design,
these
self shielding effects are significant and the self shielding of the fuel
element and the tungsten emitter heat source are included
in the shielding
calculations.
The shielding calculations are performed assuming
gammas
that two
1.
are emitted for every disintegration of a cobalt-60 atom.
25
Mev
The
bremsstrahlung radiation resulting from the slowing down of the beta
particles
is
mated as
line
4. 2
neglected.
The geometry
sources located
at the
elements
is
approxi-
center of each fuel element.
METHOD FOR CALCULATION OF SHIELD THICKNESS
The geometrical arrangement
is
of the fuel
shown
4.2.1.
in
Figure
4. 2.
1.
of the
gamma
The dose rate D
source and the shielding
at point P^ is given
by equation
51
Ve-
-£.
I
LINE SOURCE
T
^P
L
/
/
/'
/
/
/
/
/
/
/
/
/
e-2
T
.
7/e
1
GEOMETRY USED
IN
THE CALCULATION OF SHIELDING
FIGURE
4. 2.
1
l
52
B
(1-f) S
D=
L
aR4Tf
The dose rate D
D
at point P]_ is
a
is the
emitted
gamma
,
-
F(0 2
,
J
4. 2. 2,
(4. 2. 2)
b)J
4. 2),
f
is the
radiation absorbed in the fuel (Figure 3.6.1),
given in reference
is
it
R
photons/cm-sec.
in
The distance
is the flux to
4. 3
a and the angles Q\ and
b is defined in equation
n
b=
(4.2.1)
b)
dose build up factor. (Reference
conversion factor;
energy.
F(0 2
given by equation
R 4Ty
source strength
line
b) +
[FO^b)
-
where B
F(0 Xj
l
fraction of
Sl
the
dose rate
as a function of
G2
is
are shown
gamma
in figure 4.2.1.
4. 2. 3.
/A*
£>*,
(4.2.3)
1
i=l
tj
is the
P, and W
thickness of the shielding material between the source and point
i
is
the
macroscopic cross section for
gamma
attenuation for
the shield material.
-9
e'
|
b
sec 9"
d0»
(4.
2.4)
'0
F(9b)
is plotted
as a function of b for various values of
9
in
reference
4.3.
All of the quantities in equation
4. 2.
1
and
4. 2. 2
are known with the
exception of b and F(0b). The equations are thus solved for
JFOjb) + F(9 2 b)l or
from
[F^b)
-
F(9 2 bJ] and
the graphs in reference 4.
3.
the value of b is
determined
53
4. 3
SHIELD DESIGN
The components
Each
fuel elements.
has an E
of the
fuel
of 1000 watts.
system which must be shielded are the
element
cm
is 10
The design
long, 4
calls for
cm
them
in
diameter and
be arranged
to
symetrically within the tungsten emitter heat source as shown
4. 3. 1.
They are located exterior
to the
five
vacuum housing
it
Figure
and, with the
exception of one end, are completely surrounded by the tungsten emitter
heat source.
It
thus necessary to contain all components which are
is
located within the
vacuum housing
housing
circular cylinder 23
is a right
inside the shield.
cm
in
The vacuum
diameter and 20
cm
in height.
Using the line source approximation and the method of calculation
described
in section 4. 2,
it
was found
that a value of b of 15. 5 on the
sides of the cylinder and 15 on the ends was required to reduce the dose
rate to the desired levels.
The ends
of the shield will
which are intended
to
each be penetrated by five solid rods
remove heat from
the fuel rods on one end and
the thermionic converter collector on the other end.
4. 3
from
Data from Reference
indicates that irregularities such as small ducts and iron stiffners in
the shield cause the flux in the vicinity of the irregularity to increase by
a factor of 5 to 10 over its value at other areas of the shield.
of b for the ends of the shield
was therefore increased
decrease the flux by an additional factor
an effect similar
Table
4. 3.
1
to the
It
to 17. 5 in
order
to
since the rods will have
above mentioned irregularities.
lists the
values of b before and after they were modified
to account for the self- shielding
source.
of 10,
The value
provided by the tungsten emitter heat
also lists the thicknesses of lead and depleted uranium which
would be needed
to
provide the modified value of
b.
54
EMITTER HEAT SOURCE
T CAVITY
TUN
FIGURE
4. 3.
1
55
-
CO
B
CJ
s
CJ
o
CO
OD
CO
to
B
B
CJ
m
o
I— co
£o
i
5^'
tf
H
P
M
CO
a
o
s
o
bjo
Qw
<j
LO
iH
^
J
CJ
LO
Ci
—
I—
i
CO
CO
i
II
"
SELF
'
O
•—
O
i
CO
C\l
.—1
»—
LDIN
CO
£>
1—1
CXI
02
CO
CO*
W
i—
T—
.
Q
<#
JD CO
i—
W
CO
PQ
<
E-f
i
Q
SELF-
LDING
in
LO
LO
in
i—
NO
I—
HIE
H
JQ co
ti
Q
Q
S
Eh
<
O
o
1
J
W
P
W
Q
Fh
CO
_
«
H
H
tf
H
>
O
U
56
The modified value
of b for the
converter end
the fuel end because there is an additional 4
cm
is
less than that on
of tungsten
between the
fuel and the shield on that end.
Lead was selected as the
uranium would have provided
shielding" material
a lighter and
even though the depleted
more compact
shield.
The
relatively low cost and ease with which the lead shield could be fabricated
were
the basis for this decision.
Due
power
to its
low melting point, the lead was not compatible with the
flattening concept incorporated in this design and described in
Chapter
Thus
5.
of the shield.
it
was decided
to
use depleted uranium for the fuel end
Since wrought depleted uranium has been successfully
used as the shielding materia] for radioisotopic power generators
SNAP
-
7
series, no
problem
The low melting point
4. 1)
tungsten bars
lead.
A
is
anticipated with its fabrication. (Reference
of the lead also necessitated insulating the
which penetrate the converter end of the shield, from the
Aluminum oxide was selected as
the insulating material.
cross section of the shield configuration
The shield
is in
the
form
is
between an inner and outer casing of stainless
made
of
shown
of a right circular cylinder.
and sides of the shield will be composed of lead.
shield will be
steel.
The
total shield
4. 3. 2.
The converter end
The
will be cast
fuel end of the
The lead surface
wrought depleted uranium.
streaming between the surfaces.
Figure
in
The lead
the lead-uranium interface will be offset to prevent
1040 kg.
in the
gamma
weight
is
radiation
at
from
approximately
57
URANIUM TOP
PLUG
STAINLESS STEEL
CASINGS
14. 5
cm
12. 5
CROSS SECTION OF SHIELDED ASSEMBLY
FIGURE
4. 3. 2
cm
58
REFERENCES
4.1
Corliss,
W.R. and Harvey, D.G., Radioisotopic Power Generation,
Englewood
Cliffs:
Prentice Hall, 19M"!
4. 2
Nuclear Engineering Handbook,
Etherington, H.
McGraw Hill, 1958^
New
4. 3
Reactor Shielding Design Manual
Rockwell, T.
Van No strand Co., 1956.
Princeton:
,
,
,
York:
59
CHAPTER
5
POWER CONDITIONING
5. 1
GENERAL REMARKS
The term power conditioning includes power
transformation and regulation.
These topics have been mentioned
power
of
flattening has been discussed in Chapter
2.
mechanism
flattening
The necessity
for
was decided
There
it
power
input.
power
to
in
The design
preceding chapters and are tied together
the
flattening, voltage
is
in this chapter.
treated in detail.
operate the thermionic converters with a constant
This means that the emitter heat source must provide the
thermionic emitters with
from the decay
a constant heat flux as the
of the cobalt- 60 fuel
characteristic half life of
energy available
decreases exponentially with a
25 years.
5.
The thermionic converters can be supplied with a constant power
input in two ways.
The
first
method, mentioned
in
Chapter
2
and the
only one to which reference was found in the literature, allows all the
energy from the fuel
to
be deposited in the emitter heat source.
variable heat transfer path
is
provided
to
emitter heat source to the surroundings.
A
shunt the excess heat from the
As explained
none of the systems which have been designed
were practical for
'
to
in
Chapter
2,
accomplish this objective
this design application.
The second approach,
the one used in this design, is to provide a
constant energy input to the emitter heat source.
the schematic design of a
mechanism which
is
Figure
5. 1.
1
shows
designed to provide the
emitter heat source with a constant power input.
60
RADIATOR
FINS
DRIVE MOTOR
GEAR TRAIN
RELAY
STAINLESS STEEL
CASING
POSITIONING
/// PLATE
DRIVE ROD
in
»—
<
K
U
H
w
H
H
<J
ft
o
ER HEAT
SOURCE
ROD CAVITY
O
i—
61
OPERATING PRINCIPLE OF THE POWER FLATTENING MECHANISM
5. 2
vacuum housing,
Since the fuel elements are located outside of the
they can be partially withdrawn
As
heat source.
will be
from
the fuel rod is
from
the fuel rod cavity in the emitter
withdrawn from the
surrounded by the uranium shield.
Most
fuel rod cavity
of the
gamma
it
radiation
the portion of the fuel rod outside of the emitter heat source will
be absorbed by the uranium shield.
It
is
thus possible to vary the energy
input to the emitter heat source by varying the position of the fuel rod.
A maximum
Most
shield.
It
uranium
of 1200 watts of heat will be deposited in the
of the heat will be deposited in the vicinity of the fuel rods.
will be conducted to the surface of the
uranium with
tempera-
a small
ture drop since the uranium provides a path of high thermal conductivity
due
cross section.
to its large
will allow
it
to
The high melting point
of the
operate at a temperature high enough to allow
uranium
be
to
it
cooled by natural convection.
FUEL ROD POSITIONING MECHANISM
5. 3
The
Each
fuel rod positioning
of the five
mechanism
is
shown
is
Figure
5. 1. 1.
copper rods used to conduct heat generated within the
fuel rods to the cooling radiators penetrates the
through and
in
uranium
attached to a movable positioning plate.
passes
shield,
The rod
is
then
finned to provide sufficient heat transfer area to maintain the fuel rod
at a
low temperature.
The movable positioning plate
and
It
is
is
is
circular in shape, 10
cm
in radius,
attached to each of the five fuel rods as shown in Figure
positioned by a threaded drive rod located at
drive rod
is
its
center.
turned the positioning plate travels up or down on
5. 1. 1.
As
it.
the
There
62
are two guide rods which prevent the positioning plate from exerting a
This torque could cause the fuel rods
torque on the fuel rods.
to bind
as they were being moved.
Although the temperature of the fuel rod
the emitter heat source,
would
The bellows seals shown
air.
fuel
it
rods can be maintained
fuel
rods
to
be
which
is
is
if
exposed
to
are employed so that the
These
an inert atmosphere.
vacuum system valves and allow
moved without disturbing
The drive rod
5. 1. 1
vacuum or
seals are similar to those used on
considerably lower than
oxidize quite rapidly
Figure
in
in a
still
is
the
the actual seal.
driven through a gear train by an electric motor
located on the centerline of the assembly as shown in Figure
5. 1. 1.
5.
is
4
INITIAL
FUEL ROD POSITION
The
rods are initially positioned so that the output of the system
fuel
500 watts.
position since
gamma
It
would be very difficult
it
would be difficult
radiation emitted
from
to
to calculate the
exact initial
determine exactly how much of the
the portion of the fuel located outside of
the tungsten emitter heat source eventually reaches the heat source.
However, Figure 3.7.2
indicates that
most
of the
gamma
energy
is
absorbed within the first three mean free paths of the material through
which
it
is
passing.
Therefore
a
good approximation
position can be obtained by assuming that none of the
to the initial
gamma
radiation
emitted from the fuel outside of the tungsten emitter heat source reaches
it.
The error caused by
slight
this
approximation can be corrected by a
adjustment of the fuel rod position once the power supply
operating.
is
63
From
Table
2. 3. 3. 2 it is
seen that each of the five thermionic
The
converters requires 510 watts of thermal power.
an
ET
of 1000 watts,
that each fuel
cm
element supplies
Therefore,
of length.
6% and are
an n F of 75.
6.
75
10
cm
cm
of the fuel rod
thermal energy per
must be inserted
The remaining
the fuel rod cavity in the emitter heat source.
of fuel rod will be initially positioned in the
This means
long.
75. 6 watts of useful
elements have
fuel
3.
25
uranium shield above
into
cm
the
emitter and will gradually be lowered into the fuel rod cavity as the fuel
This procedure will allow the energy input
decays.
source
5. 5
to
be maintained
at a
emitter heat
to the
constant level.
OPERATION OF THE FUEL POSITIONING MECHANISM
If
the thermionic converter
power output
is
allowed to vary 1% the
power
input can vary 4.
22%.
This means that the energy input to each thermionic converter
can vary by 23.
With this
2
in
watts which
mind the
When
as follows.
5% since
the
is
the thermionic converter efficiency is
equivalent to
fuel rod positioning
0. 3
cm
of fuel rod length.
mechanism
power output drops below 500 watts
circuit will close a relay and activate the drive
will operate
a sensing
motor which
will drive
the gear train and in turn start lowering the fuel into the fuel rod cavity.
One element
of the
gear train
revolution during the time
which time
it
it
is
geared so that
it
completes one
takes to lower the fuel rod
mechanically opens the relay and shuts
0. 3
cm,
at
off the drive
motor.
This action will be repeated anytime the power output drops below 500
watts.
The frequency with which the
determined.
The fraction
fuel will be repositioned can be easily
of fuel which has
decaved f^,
is
given by
64
equation
5. 5. 1,
f
where
A
F
=
-
1
e"
At
(5. 5. 1)
=
=
0.
132 yrs
fuel half life
and
is the
t
For
f
F
elapsed time in years.
=
0.
0454, equation
fuel will be repositioned
time.
If
a
fuel can be
is
gives
t
as
once every 4 months
smaller variation
moved
5. 5. 1
in
power output
0.
if it
is
35 years;
is
moved
thus the
0. 3
cm
each
required or desired the
a shorter distance at a shorter time interval.
This
accomplished simply by modifying the timing of the gear train element
which opens the drive motor relay.
VOLTAGE TRANSFORMATION AND REGULATION
5. 6
The
series
is
5 volt
output of the five thermionic converters operating in
transformed
to 28 volts
as explained in Chapter
2.
by a current drive
DC-DC
The DC-DC converter output
the load through a shunt type voltage regulator.
will maintain a constant voltage output
is
converter
coupled to
The voltage regulator
regardless of slight variations
in the
thermionic converter output caused by the non continuous form of
power
flattening.
The voltage regulator
with a constant load;
point even though the
vary.
will also provide the
this will allow
them
to
thermionic converters
operate
at a
constant power
power required by the equipment they supply may
65
CHAPTER
6
ADDITIONAL DESIGN CONSIDERATIONS
6.
1
GENERAL REMARKS
chapter heat loss through the insulation and structural sup-
In this
port
members
of the emitter heat
the electrical leads are treated..
power
is
source are discussed.
Due
to
The
intrinsic efficiency.
at
to
these heat losses a higher input
required for the same power output.
converter effectively operates
Losses due
Thus
an efficiency which
the thermionic
is
lower than the
effect of these heat losses on the fuel
design and the power flattening mechanism
is
element
also discussed.
Several additional problems related to the electrical insulation of
the thermionic converters and radiator design, which are peculiar to
this design are discussed.
These problems are not treated as extensive-
element optimization or the power flattening design.
ly as the fuel
ever, they were persued until
it
was determined
How-
that a practical solution
did exist and that they would not prevent construction of a practical
thermionic power supply based on this design.
6. 2
LEAD LOSSES
Since the thermionic converters in this power supply are connected
in series, the
emitter of one converter must be connected to the collector
of another converter.
The heat conducted through the lead from the emit-
ter to the collector is designated
Q
T
.
This heat loss by the emitter
one of two contributing factors to the lead losses.
buting factor
losses
which
is to
is
is the
Joulean heating
in the lead,
cause the thermionic converter
lower than
its intrinsic efficiency.
to
Qj.
is
The second contri-
The
operate
at
effect of these
an efficiency
66
The optimum design
to
is not to
minimize the sum
of
Or and
Q
T
but
have
Qj
where
(6.2.1)
^.(Q L + Qj)
=
is the intrinsic efficiency.
tl
The lead losses
will
depend on
the lead material, the lead length to lead area rates and the
temperature
difference between the emitter and collector.
In this
design T
E
2000 °K and T
=
chosen for the lead material due
found that equation
was
ratio
means
From
was
Figure
cm
2.2. 1. 3 the
watts/cm
9.
2
order
in
Joulean heating
=
to
when
2
,
was
It
the lead length to lead area
42. 5 watts and
Q =12
watts, which
J
must be supplied
emitter output power density
to the emitter.
at 1.
volt is
thus the area of each emitter must be increased
provide the additional 12 watts disipated as
in the lead.
INSULATION AND SUPPORT OF THE EMITTER HEAT SOURCE
The emitter heat source
It
E
Tungsten was
1000 °K.
temperature requirements.
satisfied
that an additional 54. 5 watts
1. 3
6. 3
1
The losses are Q
30.
found to be
by
6. 2.
to
=
C
is 21
cm
in
diameter, 14
cm
is a right
in height
circular cylinder of tungsten.
and weighs 85 kg.
The thermal insulation for the emitter heat source consists
of
80 layers of multi-foil insulation similar to that used in the fuel elements.
The insulation
source surface
is 0. 9
cm
thick and reduces the heat loss
to 110 watts.
This insulation
is
from
the heat
placed inside of the
vacuum housing.
If
the weight of the emitter heat source
foil insulation,
was supported by the multi-
the foils would be forced together and their insulating
properties would be seriously degraded.
Therefore pins of zirconium
oxide are inserted in holes drilled through the insulation in order to
67
support the weight that would otherwise rest on the insulation.
Con-
duction by the pins constitutes only a fraction of the total thermal
losses associated with the holes
in the insulation.
The remainder
of
the heat loss is associated with the thermal short circuiting of the in-
sulation surrounding the pin. (Reference
6. 1)
The exact value
of the
heat loss due to the pins would have to be determined experimentally,
but Reference
6.
indicates that for small pins the losses will be on
1
the order of 4 watts per pin.
In this
design 40 watts
allowed for these
is
pin losses.
Figure
6. 3.
The pins on the
1
fuel end of the heat
by disc springs.
in
which the pins will be mounted.
source are held tightly
in position
This mounting technique allows for thermal expansion
of the tungsten and
By inserting
shows the manner
keeps the emitter end of the heat source
the pins into recesses in the tungsten,
it
is
in position.
possible to
prevent any sideways motion of the heat source.
Another heat loss, that due
to
conduction through the structure of
the thermionic converter, has not been calculated since
sitive to the materials
converter casing.
A
used
in
it
is
very sen-
and the configuration of the thermionic
value of 40 watts per converter is used as an
estimate of this heat loss.
6.4
MODIFICATIONS REQUIRED TO FUEL ELEMENT DESIGN
The additional heat loss from
the emitter heat source due to lead
losses and insulation losses totals 622 watts.
Thus
in
order
to
produce
560 watts of electric power 3162 watts of thermal power must be supplied
emitter heat source instead of the
to the
quired
if
2
540 watts that would be re-
the actual converter operated at the intrinsic efficiency.
The
initial fuel loading,
F
for the design life of
t
years
is
given
by equation
p-
6. 4. 1.
FT
where Pt
=
3
is the
years,
F
ET
(6.4.1)
required thermal power input.
is
found to be 6250 watts.
of the five fuel rods
ual
=
must be increased
For P^ =3162 and
Therefore the length of each
to 12. 5
cm
giving
them an
of 1250 watts.
The increased input power requirement makes
initially position the fuel rod
necessary
it
cm
so that an additional 1.65
of
it
contained within the fuel rod cavity in the emitter heat source.
8. 4
cm
to
are
Thus
of the fuel rod will be initially inserted into the fuel rod cavity.
Other than a slight increase
in the
frequency with which the fuel rod
repositioned, the increase in required input
power
will
cant effect on the design or operation of the
power
flattening
6. 5
individ-
have no
is
signifi-
mechanism.
ELECTRICAL INSULATION OF EMITTER AND COLLECTOR
Since the five thermionic converters mounted on the emitter
heat source are electrically connected in series,
it
is
necessary
to in-
sure that the only electrical conduction paths between them are the leads
connecting the emitters and collectors.
cally insulated
insulated
The emitters must be
from the emitter heat source and
from the vacuum housing.
Figure
6. 5.
the collectors
1
electri-
must be
shows where the
insulation will be placed in order to accomplish this.
The material used
for the electrical insulation
ably good thermal conductivity.
must have
a
reason-
Beryllium oxide was selected as the
insulating material because of its relatively high thermal conductivity
and high electrical resistivity.
vacuum atmosphere
to
Beryllium oxide
temperatures of
at least
is stable in
an air or
2000 °C. (Reference
6. 2)
69
URANIUM
SHIELD
•NGSTEN
MITTER
LEAD
SHIELD
MOLYBDENUM
COLLECTOR
TUNGSTEN HEAT
TRANSFER ROD
A1 2°3,
INSULATION
THERMIONIC CONVERTER CONFIGURATION
FIGURE
6. 5.
1
70
6. 6
RADIATOR DESIGN
The radiator used
to dissipate the
heat deposited
converter
at the
The
collector must be designed to maintain the collector at 1000°K.
temperature drop
rod conducting the heat from the collector
in the
minimized
the radiator should be
in
order
to allow the radiator to op-
The higher the radiator
erate at the highest possible temperature.
temperature the smaller
its
The heat transfer rod
end and copper
of the rod as the operating
6. 5. 1.
and the rod
270 C.
is 4
If
copper
cm
will be
tion are the
The copper
will
be used for as much
order
in
is
used once the temperature
diameter the temperature drop
in
In this
modes
of tungsten at the collector
temperature allows
The collector radiator
ature of 460 C.
composed
will therefore
have a
minimize
to
The composite heat transfer rod
the temperature drop.
Figure
size for a given heat transfer rate.
radiator end.
at the
to
is
in
below 550°C
is
in
shown
it
will be
maximum temper-
temperature range radiation and natural convec-
of heat transfer
temperature distribution
in the
which must be considered.
radiator
is difficult to
Since the
predict, the final
radiator design must be determined experimentally.
The design
of the radiators associated with the fuel
less critical since
perature but only
is not
it
to
necessary
to
maintain them
insure that they remain
the temperature of the fuel.
mechanism
rods and fuel radiator are shown
remove
a
maximum
of 286 watts
in
Figure
from each
much
at a specific
to
tem-
conduct heat from
same rods used by
to position the fuel rods.
is
temperature well below
The copper rods used
the fuel rods to the fuel radiators are the
flattening
at a
rods
the
power
The heat conduction
5. 1. 1.
These rods must
fuel element.
The rods
71
are 20
cm
long and have an average diameter of
ature drop along the rod will therefore be 150^.
on the fuel rod
is to
3. 5
If
be maintained below 6009^, the
radiator temperature will be 150 C.
cm.
The temper-
the hottest point
maximum
fuel
72
REFERENCES
6.
1
Paquin, M.J-.., "High Temperature Multi-Foil Thermal Insulation,"
Thermo Electron Corp. Waltham, Mass.
,
6. 2
Hove, J. E. and Riley, W. C. Ceramics for Advanced Technologies
New York: John Wiley and Sons, Inc. 1965.
,
,
,
73
CHAPTER
7
SUMMARY AND CONCLUSIONS
7. 1
DESIGN SUMMARY
The
final
power supply design
is
summarized
in
Table
The
rational for this design has been given in the preceding chapters.
final
design uses five thermionic converters operating
point and a
power
DC-DC
decrease
power
Although the intrinsic efficiency of the thermionic
is
22%, the overall system efficiency
is
only
9.
7%.
This
due to lead losses, heat lost from the emitter
in efficiency is
heat source, fuel rod and
7.2
at a fixed
regulated converter to provide 500 watts of electric
at 28 volts.
converters used
The
7. 1. 1.
DC-DC
converter inefficiencies.
CONCLUSIONS
This design shows that
it
is feasible to build a
power supply fueled with cobalt- 60.
system incorporated
power supply
The
to
fuel
in the
In addition,
the
practical thermionic
power
flattening
design enables the operational lifetime of the
be comparable to the half
element design shows that
life of
it
is
cobalt-60.
possible to obtain
significant savings by using a tubular fuel element instead of a solid fuel
rod.
In this
case there
an Erp of 1000 watts.
a 10% increase in the fuel element efficiency, for
is
Greater savings can be realized for larger values of
Erp.
The major advantage of the cobalt-60
At present strontium-90
is
the
most popular
fuel is its relatively
fuel
low cost.
used for terrestrial
radioisotope power supplies with operating periods between one and five
years.
in this
If it
were used
design and
if
in
a fuel
conjunction with the thermionic converters used
element efficiency of 95% were realized, 4950
74
watts of thermal power would have to be provided by the strontium fuel.
At a cost of $77 per thermal watt (Reference
7. 1)
the total fuel cost would
be $380, 000, as opposed to a cost of $37, 500 for the cobalt-60 fuel.
price differential of $292, 500
is a
This
strong incentive to use cobalt-60 fuel.
TABLE
7.1.1
FINAL DESIGN SUMMARY
I
THERMIONIC CONVERTERS
High Pressure Cesium Diode
Type
Number
of
Converters
Emitter Material
Tungsten
Emitter Temperature
2000°
Collector Material
Molybdenum
Collector Temperature
1000°
Interelectrode Spacing
7
Cesium Reservoir
Internal Adsorption
Cesium Reservoir Temp.
610
Output Voltage
1.
volts
Output Power Density
8. 8
watts/cm
Intrinsic Efficiency
22%
Total
Power Generated
Rea uired Thermal Power
x
Total Emitter Area
II
5
K
K
mils
o
K
620 watts
Input
2820 watts
70. 5
cm 2
FUEL ELEMENTS
Fuel
Cobalt- 60
Form
Metal Wafers
Specific Activity
400 curies/g
Fuel
Number
Type
of Fuel
of Fuel
Rods
Element
5
Tubular
Fuel Rod Lenght
12.5
Fuel Rod Diameter
4
cm
cm
76
TABLE
III
7.
1.1
(CONT.
)
ADDITIONAL HEAT LOSSES
From Emitter Heat
Source
Through Mult -Foil
Insulation
110 watts
Through ZK>2 Pins
40 watts
From Thermionic Converters
Lead Losses
272 watts
Structural Support Losses
200 watts
TOTAL
IV
V
622 watts
BIOLOGICAL SHIELD
Material
Lead and Depleted Uranium
Total Weight
1040 kg
POWER CONDITIONING
Power Flattening
Movable Fuel
Power
-
Constant
Input
Voltage Converter
VI
Type
DC-DC
Voltage Input
5 volts
Voltage Output
28 volts
Voltage Regulation
Dissipative Shunt
Efficiency
89%
Current Drive
POWER SUPPLY
Power Output
500 watts
Operational Lifetime
3
System Weight
1200 kg
Overall Efficiency
9.
years
7%
77
REFERENCES
7.1
W. R. and Harvey, D. G.
Englewood Cliffs: Prentice Hall,
Corliss,
,
Radioisotopic
Inc.,
1964.
Power Generation,
78
BIBLIOGRAPHY
Berger, M.J. and Raso, D.J. "Monte Carlo Calculations of Gamma
Ray Backscattering. " Radiation Research 12 20-37. 1960.
.
Carvalho, J. and Dunlay, J. B. "Quarterly Progress Report of Research
and Development of Vacuum Foil Type Insulation for Radioisotope
Power Systems. " Thermo Electron Corp. Report No. 4059-109-69.
January
1969.
20,
D. G. Radioisotopic Power Generation.
Prentice Hall, Inc. 1964.
W.R. and Harvey,
Corliss,
Englewood
Cliffs:
J. B. "Description of a Cobalt-60 Fueled Thermionic Generator
Experiment. " Conference Record of the Thermionic Conversion
Specialist Conference. October, 1967.
Dunlay,
Etherington, H. Nuclear Engineerin g Handbook.
Hill.
New York: McGraw
1958.
Farace, J. P. "Experimental Cobalt-60 Heat Source Capsules.
River Laboratory. DP- 1145.
"
Savannah
Harbaugh, W. E. and Basiulis, A. "The Development of a High-Temperature Reservoir for Automatic Control of Cesium Pressure. "
Conferen ce Record of the Thermionic Conversion Specialist
Conference November, 1966.
.
Hilbom, H. S. "Savannah River Laboratory Isotopic Power and Heat
Sources, Part I Co-60. " Quarterly Progress Report July September, 1967. DP-1129-1.
.
Hove,
J.
E. and Riley,
New
W.
C.
Ceramics
York: John Wiley and Sons,
for
Inc.
Ad vanc ed Techn ologies
.
T965.
"Energy Source - Low Voltage Conversion System. "
Procedings of the 19th An nual Power Sources Conference. 1965.
Lingle,
J.
T.
Lingle,
J.
T.
Annual
"Low Input Voltage Conversion." Procedings
Pow er Sources Conference. May, 1964.
of the 18th
"Thermionic Low Voltage Converter Regulator Systems.
Conference Record of the Thermionic Conversion Specialist
Conference. November, 1966.
Lingle,
J.
T.
Paquin, M. L. "High Temperature Multi-Foil Thermal Insulation.
Thermo Electron Corp.
"
"
Rockwell, T. Reactor Shielding Design Manual. Princeton: Van Nostrand
Company!
1956.
79
BIBLIOGRAPHY
(cent.)
Rush, R. E. and Belofsky, H. "Power Flattening Studies for Radioisotope
Thermoelectric Generators." General Instruments Corp. NYO-9783.
"
1963.
Hurwitz Jr. H. and Roe, G. M. "Gamma Ray Absorption
Distributions for Plane, Spherical and Cylindrical Geometries. "
General Electric Company, Knolls Atomic Power Laboratory.
Storm, M. L.
,
KAPL-783
,
.
"A Unified Theoretical Description of Thermionic Converter
Performance Characteristics. " Journal of Applied Physics, vol. 39.
number 5. April, 1968.
Wilkins, D.R.
Wilkins, D.R. "An Improved Theoretical Description of Thermionic
Converter Performance Characteristics. " Procedings: 27th Annual
Physical Electronics Conference. Cambridge, Mass. March, 1967.
ibk.