nps archive 1969 ewers, b. - connecting repositorieshalf-life composition meltingpoint...
TRANSCRIPT
N PS ARCHIVE1969EWERS, B.
A PARAMETRIC ANALYSIS OF ADEEP SEA RADIOISOTOPIC THER-
MOELECTRIC GENERATOR EMPLOY-
ING A HEAT PIPE
by
Benjamin James Ewers
C
DUDLEY KNOX LIBRARYNAVAL POSTGRADUATE SCHOOLMONTEREY, CA 93943-5101
United Stat
Naval Postgraduate School
THESISA PARAMETRIC ANALYSIS OF A DEEP SEA
RADIOISOTOPIC THERMOELECTRIC GENERATOR
EMPLOYING A HEAT PIPE
by
Benjamin James Ewers, Jr.
June 1969
TkU document ha& bzzn appnjovtd fan pubLLa ie-£eoae and 6atz; it& dUt/Cibvutlon Zt> [xnJLbnitzd.
*4~"
A Parametric Analysis of a Deep Sea Radioisotopic
Thermoelectric Generator Employing a Heat Pipe
by
Benjamin James ^Ewers, Jr.
Lieutenant (junior grade), United States NavyB.S. in Nuc.E., Rensselaer Polytechnic Institute, 1968
Submitted in partial fulfillment of therequirements for the degree of
MASTER OF SCIENCE IN MECHANICAL ENGINEERING
from the
NAVAL POSTGRADUATE SCHOOLJune 1969
£,InJ££%3.ABSTRACT
A parametric design analysis was performed using a heat pipe in an
existing deep sea Radioisotopic Thermoelectric Generator (SNAP-21). Heat
is transferred from an annular fuel pellet to an annular thermoelectric
generator through a connecting heat pipe. The fuel pellet is fully
shielded so that the thermoelectric generator is easily removable.
Overall efficiency and the weight of major components were determined
for varying fuel radii of from 1.3 inches to 1.7 inches and for varying
insulation thicknesses of from 1.0 inch to 2.0 inch.
The analysis indicates that there is a particular fuel radius (at
constant insulation thickness) at which minimum weight is reached,
while the maximum overall efficiency is obtained at a larger fuel radius.
The median design has an overall efficiency (at the beginning of life)
of 5.4% and a total weight of 570 lbs. These design results, when com-
pared to the existing SNAP-21 design gives an increase in overall ef-
ficiency of at least 77», and a reduction in total weight of 127o.
library
j s Naval Postgraduate Softool
Jonterey, California 93940-^ DUDLEY KNOX LIBRARYNAVAL POSTGRADUATEMONTEREY, CA 939434191
TABLE OF CONTENTS
I. INTRODUCTION . . . 11
II. BASIC DESIGN OF PROPOSED RADIOISOTOPETHERMOELECTRIC GENERATOR 16
A. COMPONENTS OF DESIGN 16
B. IMPOSED DESIGN RESTRICTIONS 18
C. DESIGN VARIABLES 20
III. ANALYSIS OF PROPOSED RTG DESIGN 21
A. NUCLEAR RADIATION ANALYSIS 21
B. HEAT LOSS THROUGH INSULATION 24
C. GENERATOR COLD FRAME HEAT TRANSFER 27
D. DERIVATION OF COMPUTER PROGRAM 30
IV. RESULTS AND DISCUSSION ........ 33
V. CONCLUSIONS 48
VI. RECOMMENDATIONS 49
APPENDIX A NUCLEAR RADIATION EXAMPLE ..... 50
APPENDIX B HEAT LOSS DERIVATION 54
APPENDIX C CRITICAL DIMENSIONS AND VOLUME DERIVATIONS 58
APPENDIX D COMPUTER PROGRAM 63
BIBLIOGRAPHY 68
INITIAL DISTRIBUTION LIST 69
FORM DD 1473 70
VffAfiaUXOWtYSb
LIST OF TABLES
Table Page
1. SNAP-21 system parameters 13
2. Materials used in SNAP-21 design and proposedsystem 19
3. Geometrical and material data for nuclearshielding calculations 51
4. Sample calculations of nuclear radiationdose rate 52
LIST OF ILLUSTRATIONS
Figure Page
1. Basic features of the SNAP-21 design 12
2. Basic components of a heat pipe 15
3. Basic features of the proposed design 17
4. Model employed to calculate dose rate due tonuclear radiation 22
5. Cross section of proposed design 26
6. Cross section of generator cold frame 28
7. Geometry assumed for heat transfer throughgenerator cold frame 28
8. Efficiencies vs. hot end temperature of
SNAP-21 thermoelements 29
9. Computer program flow chart 32
10. Weight of major components vs. fuel radiusat 1.0" insulation thickness 36
11. Weight of major components vs. fuel radiusat 1.2" insulation thickness 37
12. Weight of major components vs. fuel radiusat 1.4" insulation thickness 38
13. Weight of major components vs. fuel radiusat 1.6" insulation thickness 39
14. Weight of major components vs. fuel radiusat 1.8" insulation thickness 40
15. Weight of major components vs. fuel radiusat 2.0" insulation thickness 41
16. Weight of major components vs. insulationthickness at constant values of fuel radius 42
17. Fuel radius at which minimum weight is reached vs.
insulation thickness 43
18. Overall efficiency vs. fuel radius at constantvalues of insulation thickness 44
19. Overall efficiency vs. insulation thickness atconstant values of fuel radius 45
20. Minimum weight of major components and efficiencyat minimum weight vs. insulation thickness 46
21. Percentage increase in minimum weight of majorcomponents and overall efficiency vs. insulation 47
thickness
22. Dimensions of example used in sample dose ratedetermination 50
23. Length dimensions of annular generator 59
24. Volume derivation of annular generator 60
25. Volume derivation of pressure vessel 60
26. Volume derivation of shield 61
27. Volume derivation of fuel capsule 62
NOMENCLATURE
Symbol
B nuclear radiation buildup factor
D dose rate due to nuclear radiation (mr/hr)
E energy of nuclear radiation (ev)
k thermal conductivity of the fuel capsule (BTU/hr-f t-°F)c
k thermal conductivity of the fuel (BTU/hr-f t-°F)
k thermal conductivity of the insulation (BTU/hr-f t-°F)
k thermal conductivity of the biological shield (BTU/hr-f t-°F)s
LF length of fuel (in)
P source strength for volume source (Curies)
( —r-). heat transfer rate to heat pipe from fuel/unitJ? 'in
VY^m
yUi
length (BTU/hr-ft)
( —jr- ) heat transfer rate through insulation from fuel/unit* OUt
length (BTU/hr-ft)
RF outer radius of the fuel (in)
RI outer radius of the insulation (in)
RS outer radius of the shield (in)
t self absorption thickness (in)
t. shield thickness (in)1
T hot end temperature of thermoelements (°F)H
Z distance from source to where dose due to nuclearradiation is to be measured (in)
Carnot efficiency (7e )
material efficiency
overall efficiency (7»)
attenuation coefficient of shields (1/in)
attenuation coefficient of source (1/in)
ACKNOWLEDGEMENTS
The author wishes to express his sincere appreciation to Professors
Paul J. Marto and Paul F, Pucci for their original thoughts that started
this project and for their help and guidance throughout the course of the
investigation. The author is also indebted to the 3-M Company for their
cooperation in providing information on the SNAP-21 program.
I. INTRODUCTION
Future demands for measurements of oceanographic data needed to
support scientific, commercial, and military operations necessitates
the development of reliable power sources for deep sea use. For these
undersea missions that require continuous, relatively low levels of
electrical power for a few years, radioisotope powered systems are
needed. Because isotope fueled themoelectric generators do not require
oxygen and have no continuously discardable waste (i.e., no exhaust),
the performance of these systems are independent of the environment in
which they operate [14] , These advantages make them the ideal source
of power for this application.
The 3-M Company has designed a radioisotopic thermoelectric genera-
tor (RTG) for just such a purpose (SNAP-21). The basic features of the
SNAP-21 design are shown in figure 1 9with the SNAP-21 system capabili-
ties and parameters in table 1 [12]. SNAP-21 is constructed so that
it is a fully shielded device with a removable generator, making the
handling and maintenance easier. The RTG°s predicted reliability and
long life fulfills the requirements for deep sea use. The maximum
temperature of the fuel in the SNAP-21 design is 1700°F (as listed in
table 1) while the hot end temperatures of the thermoelements is 1000°F.
This 700°F temperature drop from the fuel pellet to the themoelectric
generator is due to heat conduction through the biological shield.
A heat pipe can be introduced to the SNAP-21 design to enhance the
Numbers in brackets refer to bibliography
11
PRESSUREVESSEL
POWERCONDITIONER
THERMOELECTRICGENERATOR
INSULATION
FUEL
BIOLOGICALSHIELD
Figure 1
(Basic features of the SNAP-21 design)
12
POWER OUTPUT
EXTERIOR SURFACE MATERIAL
DESIGN LIFE
SYSTEM OUTPUT VOLTAGEwith power conditionerwithout power conditioner
LOAD CURRENTwith power conditionerwithout power conditioner
NET SYSTEM EFFICIENCYend of lifebeginning of life
GENERATOR EFFICIENCY
POWER CONDITIONER EFFICIENCY
FUEL TYPE
FUEL LOADING
FUEL TEMPERATURE MAX
T/E HOT JUNCTION TEMP, MAX
T/E COLD JUNCTION TEMP, MAX
OPERATION DEPTH, MAX
10 watts
Copper on Titanium
5 years
24 VDC4.7 VDC
WATER TEMPERATURE
TOTAL WEIGHT
.42 amp2 . 1 amp
6%
5%
8-97o
90%
SrTi03
33,000 curies
1700 °F
1000 °F
120 °F
20,000 feet
28-41 °F
640 lbs
TABLE 1
(SNAP-21 System Parameters)
13
heat transfer from the heat generated in the fuel pellet to the hot plate
of the generator., The heat pipe consists of essentially a closed evacu-
ated pipe whose inside walls are lined with a capillary structure (called
a wick) saturated with a volatile fluid (see figure 2). The operation of
a heat pipe combines two principles of physics: vapor heat transfer and
capillary action. Vapor heat transfer is used for transporting the heat
energy from the evaporator section to the condensor section. Capillary
action then returns the condensate back to the evaporator section. The
working fluid absorbs the heat energy received at the evaporator section,
transports it through the pipe, and releases it at the condensor end.
Since evaporation and condensation take place at essentially the same
temperature, the heat pipe operates almost isothermally [4], For ex-
ample, a thermal power of 11000 watts was carried 27 inches by a one
inch diameter heat pipe with a temperature loss so small it was diffi-
cult to measure accurately. By way of comparison, a copper block nine
feet in diameter and weighing about 40 tons would be required to pro-
duce the same result. [8]
14
1
I I
HEAT IN
t I ¥ Y
WICK- t t ftHEAT OUT
\ \ \ v v \ v \ \ \ \^ s v v v S v \\
LIQUID VAPOR
'x --^ \ V \ - \ \ \ \ \ V \ \ \ ^
EVAPORATOR SECTION
I
CONDENSER SECTION
Figure 2
(Basic Components of the Heat Pipe)
The objective of this thesis was to parametrically analyze the
feasibility of adapting the heat pipe to a deep sea RTG and to compare
the design results using the heat pipe to an existing RTG design (SNAP-
21).
15
II. BASIC DES IGN OF PROPOSED RAD101510X0PTC THERMOELECTRIC GENERATOR
A. COMPONENTS OF DESIGN
Figure 3 contains a cross section of the proposed RTG system. The
major change made to the SNAP-21 design was the implementation of a heat
pipe to enhance the heat transfer from the heat generated in the annular
fuel pellet to the hot plate of the annular generator. A tubular geo-
metry was used for the heat pipe primarily because experimental data
exists for this configuration. The annular geometry of the fuel pellet
and thermoelectric generator was necessary to provide enough surface area
for efficient heat transfer to and from the heat pipe.
In order to get a meaningful comparison between designs, this
analysis used the same materials as used in the SNAP-21 design. The bio-
logical shield is made of depleted Uranium with 87, Molybdenum added to
shift the crystalline phase change of Uranium from 1300°F to 1800°F. De-
pleted Uranium is also a much better shield per weight than any other
shielding material exhibiting similar strength. Safety requires that the
fuel does not rupture its container under any accident. Thus, Hastelloy
C is used as the fuel capsule due to its weldability and high tensile
and yield strengths. Strontium-90 is the fuel used because of its rela-
tively cheap cost and availability. The pressure vessel is made of 721
Titanium because of its high strength per weight. The heat pipe is made
with stainless steel containing sodium as a working fluid because of the
expected operating temperature of 1300°F. To make the heat pipe as ef-
fective as possible [4], a small capillary pore radius of .02 inch was
chosen. From figure 5 of reference [4], the pressure head developed in
16
PRESSUREVESSELPOWERCONDITIONER
THERMOELECTRICGENERATOR
HEAT PIPE
INSULATION
FUELCAPSULE
FUEL
BIOLOGICALSHIELD
Figure 3
(Basic features of the proposed design)
17
the sodium heat pipe was estimated to be .09 psi. These material speci-
fications are given in table 2 [12].
B. IMPOSED DESIGN RESTRICTIONS
Due to its environment, a deep sea RTG has specified conditions of
operation, design, and fabrication not ordinarily required of such a
device. These conditions as listed in SNAP-21 B Program quarterly re-
port #1 [12] are:
Temperature of surrounding water. 34.5°F + 6.5°FExternal pressure. ... 10,000 psi or 22,500 feet (ocean depth)Humidity ....... 100% max in salt atmosphereShock. ...... .an excursion producing 6 g'sVibration ....an excursion producing 3 g's
In addition to the above environmental restrictions, the desired mechani-
cal properties of a deep sea RTG are:
Fully shielded deviceRemovable thermoelectric generatorLife of five years
The Atomic Energy Commission (AEC) has specified in its safety stand-
ards the condition required for a fully shielded device. This condi-
tion states that the external dose rate due to nuclear radiation must
be less than 200 milli Roentgen per hour (MR/hr) [13].
There were no attempts made to redesign the generator thermocouple
elements so the specifications as presented by the SNAP-21 design were
those used in this analysis. The hot end temperature of the thermo-
elements (T ) was held constant because the SNAP-21 design specificationsH
for the thermoelements were not available for temperatures higher than
1100°F. These thermocouple element materials are listed in table 2.
Those factors held constant in this analysis were: the materials
and their properties, the generator specifications (output at beginning
18
FUEL.
FUEL CAPSULE..
HOUSING .
.
compositionchemical formmelting pointmax. operating tempdensityspecific activityspecific powerpower densityspecific heatthermal conductivityradiationhalf-life
compositionmelting pointthermal conductivitydensitytensile strengthyield strength
compositiondensity
SR-90SrTi031900°C
1425°F3.7 gm/cc @ 70°F33 curies/gm0.21 watt/gm0.8 watt/cc0.143 BTU/gm°F0.0132 cal/sec-cm°Cgamma due to brerasstrahlung
28 years
Haste Hoy Alloy C
2400°F10.0 BTU/hr-ft-°F @1150°F0.323 pounds /inch3 @ 72°F121,000 psi @ 72°F81,000 psi @ 72°F
721 Titanium _
0.16 pounds/inch
GENERATOR COLDFRAME composition
densitythermal conductivity
SHIELD compositiondensitythermal conductivity
INSULATION compositionthermal conductivity
Tellurium Copper0.32 pounds/inch^209. BTU/hr-ft-°F
depleted Uranium 8% Mc-ly
.629 pounds/inch^
19 BTU/hr-ft-°F
Linde Super Insulation0.0008 BTU/hr-ft°F
THERMOELEMENTS
,
HEAT PIPE
N-typeP-type
wallfluidoperating temperaturecapillary pore radiuspressure head developed
PbTe segmented(BiSb) Te and PbTe-SnTe
Stainless SteelSodium1300°F0.02 inch0.09 psi
TABLE 2
(Materials Used in SNAP-21 Design and Proposed System)
19
of life of 13.8 watts) ;, heat pipe diameter (1 inch), fuel capsule thick-
ness (%-inch) , pressure vessel thickness (1 inch for the cylindrical
walls and %-inch for the hemispheres) , heat loss through shield structural
supports and generator insulation (47 watts), and the hot end operating
temperature of the generator (1100°F).
Since the SNAP-21 design is an operating system and the materials
used in the proposed design are identical with SNAP-21 specifications,
this parametric analysis should give results comparable to the building
of an operational system.
C. DESIGN VARIABLES
The parameters varied were the outer radii of the fuel, biological
shield, and insulation (also forcing the length of the fuel pellet to
vary)
.
Three mechanisms of the proposed RTG design (figure 3) are func-
tions of the variable parameters. The changing of any one of the radii
affects the safe level of the nuclear radiation at the outside of the
pressure vessel (discussed in the Nuclear Radiation Analysis). Both the
generator cold frame and insulation package heat transfer equations are
basically functions of radial variations. Thus the thermoelement cold
end operation temperature and the total system heat loss are also func-
tions of the variable radii (these effects are clarified in section III).
20
III. ANALYSIS OF PROPOSED RTG DESIGN
The heat transfer was analyzed using steady state, constant property,
radial heat conduction. The nuclear radiation was treated according to
equations given in Etherington's Nuclear Engineering Handbook , SNAP-21
specifications, and the principle of superposition of dose rates.
A digital computer program was written to analyze this system.
It takes into account these three effects as the outside radii of the
biological shield, fuel pellet, and insulation are varied. Within the
acceptable limits of the dose at the outside of the pressure vessel due
to nuclear radiation (200 MR/hr + 25 MR/hr) , the weight of the system
(excluding insulation and power conditioning unit) and the overall ef-
ficiency (at beginning of life) were calculated and plotted.
A. NUCLEAR RADIATION ANALYSIS
The analytical solution for the dose rate at a given distance from
a finite length cylinder of radioactive material is given in Etherington's
Nuclear Engineering Handbook , Chapter 7 [6], This solution (figure 4)
assumes a uniformly distributed source emitting radiation at only one
energy and shielded by only one type of shielding material in the form
of a slab. The RTG system as proposed in this design has four compli-
cating variations.
1) The gamma radiation from the fuel has a continuous energyspectrum with an E of 2.18 ev.
max
2) There is a series of shielding materials present -- fuelcapsule, biological shield, pressure vessel.
3) The fuel is an annular cylinder.
4) The shield is an annulus circumscribing the fuel pellet.
21
FUEL
SHIELD
D = 6.95xl0 -5^r^ EB<J> = KB(f)TO.
whe
P = source strength for volume source
/a = attenuation coefficient of shield
y^c = attenuation coefficient of source
tc= self absorption distance
t = shield thickness
Mo.t5— = mass absorption coefficient of airTO.
E = energy of nuclear radiation
B = bu i 1 dup factor
Figure k(Model employed to calculate dose rate due to nuclear
radiation)
22
The first difference was handled by breaking the energy range up
into ten equal intervals and considering each interval as one distinct
group at the mean energy of that group. The dose rate was then calcu-
lated for each interval and summed over the ten energy intervals to get
the total dose rate. The values of /u. (attenuation coefficients) for
Sr-90 fuel and the various shielding materials as a function of energy
are presented in appendix A. Values of V (& /ut-pu c-tA P Mc^-z. are plotted
in reference [11].
The second difficulty was removed by replacing Mt by ^ /><.."£• >
where i refers to the different shields, and then proceeding as usual.
Experiments made by the 3-M Company in their first quarterly report
SNAP 21-B Program [13 J indicated that this analytical model was approxi-
mately 307o conservative.
The third problem was overcome by assuming that the dose rate due to
different sources can be superimposed. Using the following sketch, the dose
rate due to A equals the dose rate due to B minus the dose rate due to C.
AnnulusA
Dose Rate
Due to A
CylinderB
Dose Rate
Due to B
Dose RateDue to C
23
The fourth variation was analyzed through geometrical considera-
tions. Using the following sketch, the annular shield presents more
shielding material to the nuclear radiation than the slab shield pro-
posed by Etherington's model. Thus the solution using a slab should be
conservative.Slab Shield
-^*-
Annular
Shield
Since A ^ B 9 more shielding was present than that
assumed and the proposed model was conservative.
Etherington's equation was programed on a digital computer (IBM
360) to handle the specific case of this design. Interpolations for F
( © . A*.t -f-yu^i. c ) and AJ^"tc were done assuming linear relation-
ships. The computer program's estimated accuracy is + 25 MR/hr (arrived
at by checking computerized answers with hand calculated values). A
numerical solution to Etherington's equation (as modified) is given in
appendix A, as well as the computerized solution.
B. HEAT LOSS THROUGH INSULATION
The proposed RTG design has a series of finite length concentric
annular cylinders restricting the heat transfer from the fuel pellet to
24
the surrounding water. In order to analyze the heat loss to the water
it was assumed that the concentric annular cylinders were of infinite
length. A cross section of the proposed RTG design is indicated in
figure 5. The annular fuel pellet requires the solution of an internal
heat generation, radial heat conduction equation. The remaining annular
cylinders were cases of pure radial heat conduction. The analytical
solutions for these two cases are derived in appendix B. The equations
for the particular case of the proposed RTG were combined to find the
heat transfer rate out, per unit length, / ^j-} , when the inside and
outside temperatures (T- and T-) are specified. This particular case1 o
is done analytically in Appendix B.
The adaption of this solution concerning an infinite length cylinder
(or finite length cylinder with insulated ends) to that of a finite length
cylinder necessitates a basic assumption. In order to make the assump-
tion reasonable, an analysis of the ratio between the end surface area
and the lateral surface area was made. Letting R * cylinder radius and
L cylinder length, the ratio of the areas becomes:
- 2ttR* _ Ra~
,2.TTRU L
lateral
Basing the total heat transfer of the finite length cylinder on an area
basis, the actual heat transfer (since / —- ) is calculated according\ I /out
to the equation given in Appendix B) is:
n e v\ c\ '^ \ j
25
PRESSURE VESSEL
INSULATION
SHIELDING
FUEL CAPSULE
FUEL
HEAT PIPE
T's represent temperatures at interfaces
kf = thermal conductivity of the fuel
kc = thermal conductivity of the fuel capsule
ks = thermal conductivity of the shielding material
kj = thermal conductivity of the insulation
Figure 5
(Cross section of proposed design)
26
Q , lies between 5 and 11 watts, thus making the initial assump-actual
tion of insulated ends (infinite length) close to correct. For values
of R such that R <A^ L, the lateral surface area is much larger than
the end surface areas. For these cases the heat transfer rate out the
end areas would be negligible.
C. GENERATOR COLD FRAME HEAT TRANSFER
Tellurium Copper was the material used for the cold frame due to
its high thermal conductivity of 209 BTU/hr-f t-°F. The basic design
considers the heat transfer from the cold end of the thermoelements to
the outside water as radial heat conduction with constant properties.
The heat conduction equation for an annulus is given below [2]:
transferred out =* 2ttW\_ V \~~ Q)—^~
where RO = outer radiusRl inner radiusTl = temperature at radius Rl
TO temperature at radius ROL length of annulusk = thermal conductivity
For the assumed model shown in figure 7;
Tl cold end temperature of thermoelementsRl = 1.3 inches = radius of thermoelements
cold endTO = 505 °R outside temperature of annulusL = 1 inch
The temperature variation in the radial direction was approximately from
70°F at a radius of 1.3 inches , to 45 °F at the outer radius RO; over such
a small range of temperatures the constant properties assumption is a valid
one.
The shape of the generator cold frame can be seen in figure 6. Since
both the upper and lower surfaces are insulated, the heat transfer is
27
i
5.7
v
K\\\W\V\V^
\
\ \
\ \
\ \
\
\
. ^* COD
THERMOELEMENT
LOWER
SPRING
HEAT PIPE
GENERATORCOLD FRAME
\\\\\\\\ \\\\\\\\\\\\\\\\\N
Figure 6
(Cross section of generator cold frame)
I•otWWWWWWWM
RO13H
k\\\\\\\\\\\WJ
Figure 7
(Geometry assumed for heat transfer throughgenerator cold frame)
28
"°li Oi ONIQNOdSBHbOO A3N3I3HJ3 %
o00
oCO
oJ-
oCM
i. . ^*_ ~x_
1 jE 41^N{ r
. .. _ :.*£ zL
l_1T
tf* fc[* IS
. _ _S ,. . l_*r *
- - - tr 4< ' ... _, r j.
ii, i^ j[i
fl> r^ r-i * Bit ,-'
T V T b" 1* .1
_ L L_Lrft\-' -~—^ '
—
__l l l —1
—
ljjl J*h'l
vr>—"i!"
5 '
• 1 \ \ 'l\\ i 1
4t - -tcf -, U *V1 \ l> * 'L\ \ «l ••
r\ <T\ /^ '^ '? i™5' *< i 1 *? ~" ~*
1 \ s-* \
I Y c3-c^ -S 5\ V\ \ VV \ \ i
T \ \[3\ Jn \ti\f '< '^\ i ^
i \ \' 3 i_
, k k
r \ t*
A i \^
u 5 ^
V \ \,i\ y^ ' \«^
^L^l ± *$ -itp?" t+ ^ 44 _. Li Lk- V^ JX 4^X m M h\ s \ _i n rt 1\ \ !
!
1
'
\r > 5\ ^ cJ S V
L V J\ l/V ^i^ Kk_ fci-\'S V' w
oCN
ir\ if\
</>
cIV
E0)i]^
4)
OE1.
r^ 0>
i-H
<M1
ClO /"^ <O cc zin t/>
rH s^u-
X Oh-
9)LU 00 t-
cc 3O Z> (U 4-»
O 1- k. (0
N*> < 3 urH CC 60 a>
UJ •— aO. u. E2 IV
UJ 4-»
1-O •DO CrH z 0)
1-4 LU4-»
t- OO JZX
•
l/l
O >O01 1/)
0)
c0)
uO •«•
O M-1^ «*-
"U «**li 01 9NIQN0dS3cJ<J00 A3N3 I Idd3 %
29
assumed to take place in the configuration shown in figure 7. The
thermal gradients in the axial direction in the figure 7 model are
small and the proposed model assumes them negligible.
The efficiency ( V) ) of a thermoelectric generator can be divided •
into the Carnot efficiency ( h ) and the material efficiency (Y) ) as
indicated in figure 8 [1]. Figure 8 shows that Y) increases with in-
creasing temperature difference (AT ) between the hot and cold ends of
the thermoelements,, The model used is one where Vj was constant and
was thus conservative with respect to increasing AT • With V>
constant, the efficiency ( V) ) is then a function of V"l only, and
with the same hot end temperature ( T(-| ), V) is a function of £\~X
only (or more exactly, Tl)
.
The heat conduction equation shows that the temperature Tl and the
heat to be transferred out are linearly related. Since the efficiency
( V) ) is a function of Tl and Q _ , - the solution is itera-f transferred out
tive (i.e., pick Q - , ', this specifies Tl, which then speci-transferred out 8
fies a new Y\ , which then specifies a new () - , _).^ transferred out
D. DERIVATION OF COMPUTER PROGRAM
The subroutine HEAT was derived from the analytical model assumed
for the heat loss through the insulations, and determines the total system
heat loss (since all other losses were assumed constant) . The subroutine
QGEN determines the amount of fuel needed to supply 13.8 watts of power
at beginning of life,, and was derived from the analytical model assumed
for the generator cold frame. The subroutine DOSE determines the dose
rate in MR/hr at the surface of the pressure vessel for a given set of
variables (developed from the Nuclear Radiation Analysis)
.
30
The flow chart in figure 9 shows that a given set of radii were
picked and a total system heat loss (FUELS) was assumed. The subroutine
QGEN then calculated the required amount of fuel needed to fulfill the
design output (FUELG) . The total required amount of fuel was then given
by:
FUELT = FUELS + FUELG
Since the actual total system heat loss was obtained from an iterative
process, a new value for the total system heat loss (QOT) was calculated.
QOT was then compared to the assumed value (FUELS). With a positive
answer to the IF statement the dose rate was then calculated by the sub-
routine DOSE, and the printable output limited to the range:
175 MR/hr < dose rate ^ 225 MR/hr
31
FUELS
DO 400, L - 1,RF -
DO U00, LL= 1,
RS =
DO U00, LLL=1,Rl *
CALL QGEN (RI,FUELG)
FUELT » FUELS + FUELG
LF = FUELT/(tt(RF 2 -.75 2 ))
CALL HEAT (RF,RS, R»,QOT)
L FUELS = QOT
YES
CALL DOSE (RF,RS,RI,LF,DOSET)
NO
PRINT RF,RS,RI,LF,DOSET,FUELT
STOP
END
Figure 9
(Computer program flow chart)
32
IV. RESULTS AND DISCUSSION
Limiting conditions were imposed on the proposed RTG design due to
AEC regulations specifying a safe maximum external dose rate of 200 MR/hr.
For a given set of dimensions, the dose rate at the outer radius of the
pressure vessel was calculated (using the computer program) with an
assumed accuracy of + 25 MR/hr. Any information regarding total weight
or overall efficiency of the RTG was likewise limited to a range of dose
rate (175 MR/hr to 225 MR/hr). Most graphs have these corresponding
ranges in dose rate plotted. Note that in the following discussion,
weight refers to weight of major components, which is equal to total
weight minus weight of insulation and power conditioning units.
Figures 10 through 15 show values of weight versus fuel radius for
constant values of insulation thickness. The information contained in
these graphs indicates that there is a fuel radius where a minimum
weight is reached for each value of insulation thickness. Knowing that
the weight of various components are functions of the fuel radius and
length (i.e., the fuel surface area), a minimum is expected. In the
case of a solid cylinder, with a fixed volume, there is a set of dimen-
sions where the surface area is a minimum (i.e., diameter = length).
When values of weight versus insulation thickness at constant values
of fuel radius are plotted (figure 16), the radius of the fuel where
minimum weight is reached is seen to always lie between 1.3 and 1.5
inches. When values of the fuel radius at which minimum weight is reached
versus insulation thickness is plotted (figure 17), the general curve
suggests using a slightly smaller fuel radius with increasing insulation
thickness for minimum weight in the design.
33
Figure 18 plots overall efficiency at beginning of life versus fuel
radius at constant insulation thickness and shows two aspects of the
design:
1. Overall efficiency increases non-linearly with increasinginsulation thickness.
2„ Maximum efficiency is reached somewhere between a fuelradius of 1.55 and 1.70 inches. The maximum efficiencyis never located where the minimum weight occurs.
Thus it was never possible to combine minimum weight with the maximum ef-
ficiency for a specific value of insulation thickness.
A plot of efficiency versus insulation thickness (figure 19) shows
a non-linear increase in efficiency with insulation thickness. There-
fore the greatest gain in efficiency resulted from the initial addition
of .02 inches of insulation.
In order to get some comprehensive results it was necessary to plot
minimum weight and the efficiency at minimum weight versus insulation
thickness. Figure 20 shows that neither the minimum weight nor the ef-
ficiency are linear functions of insulation thickness until an insula-
tion thickness of 1.6 inches is reached. This is recognized when the
percentage increase in both minimum weight and overall efficiency is
plotted versus insulation thickness as in figure 21. Thus using 1.6
inches of insulation results in the greatest gain in efficiency at the
lowest gain in weight.
The SNAP-21 design has a maximum fuel temperature of 1700°F. The
proposed RTG, through the use of the heat pipe, has lowered this tempera-
ture to a range of from 1385°F to 1410°F.
The SNAP-21 design operates at 5% overall efficiency at the beginning
of life, and has a total weight of 640 pounds. Allowing 60 pounds (as
done in SNAP-21) for the weight of the power conditioning units and the
34
insulation, the design with the maximum total weight contains 613 pounds
and has an overall efficiency at beginning of life of 5.415%. This is
also the design with the maximum overall efficiency. The minimum total
weight obtained for any of the proposed RTG's was 555 pounds and had an
overall efficiency at beginning of life of 5.377o. If the RTG was de-
signed with 1.6 inches of insulation, the overall efficiency at begin-
ning of life would be 5.4% with a minimum total weight of 570 pounds.
Thus the introduction of the heat pipe has two effects, increasing the
overall efficiency at beginning of life and decreasing the total weight.
35
Ill 111 Ml MINIM II 11 Ml II llllPlll1
1
1 1 L 4\ i_1 "VT" r
J. _Q_ _+T —^U T7
s4. __i^ —4l_ t HJ^ T
«= H > ^v__ _|-^ -|- \7 ™"*1
£ U -<=-__-l- —2 r—
~
H^"~— 1
.w
:__ _ v in i——— 1-r H u I
~: yj . 4 _./ \. J
h- t *7 1*£ ir\ c in i /\J 1
<* 1- C £L '%/" "1
r-i CV PJ 1| ^\___l-LU ^ —————"t7~ 1
~: w l _^^_ —
—
jo I1
~""\7~~~ i
Q J. _i"^ i-T -\J Tt_j_ Pl__ 1_r v.^ t
" -1-_ j._ /\._Uo t— — "V/ T
~f 2 ^ Pi 1 it -*- J .s O ' *-__.{-}_—T>-
. , ^X-«J.to 1"—W"-"T
1——/"W-—[Z—tr—pr
L— xQ.. L_ J.p-H^- r~"t
l-__PL.__|lr——\J—~^"T1 _ _^v___.JT \7"~~n_i_ «jia___^7 HJ-~""t
1__ _Cl. •
t £h T____/!\.___ J.T \r 1
|
'1 _1 _0 1
-f -<jr-
—
r4. *-U— _1-T 1r—
r
i. ./:x___ 1T \s 1
1 i*•> 11 HJ 1
1
,
_ja.f H£>-
—
T1 rti. 11 —tr
—
•f
!___ y^L.T ~\r
—
1
4,_ f*\ 1T~ —X? 1
i ^N _iT h<3—1-
_jr> , 1H IJr—r_'"3_ 1
r H- -J-— T,1̂3-
, __4^_^7^^_ ^
-t>" 1
L_ _J^H3—
H
U—— __-J?k_ »-<^-—
r
t. ___0__ •T «- r1 " ' ' " 1
I I M M1M M ^M M<KM M 1 tp±tt
o
in <"^t£>
l/im
(A
CJ*u•»
jC4-*O
co c1-1
•mm
4-*
TO^—3\A
LT\C
LT>
O (0
>—.
»
l/t
• CO 9l-l => 3T>
<o:
u.
inJ-
3«4-
• u.i-H
>
*->
cOJ"
•
c
aEO
Oin
•"1
i^>
o60
OOOin
ocola
o-a-m
oCMin
ooin
o00-a
(*sq i) SlN3N0dW03 cJOrVW JO 1H3I3M
36
li1 1 1 Q 1 1 ill 1 1 1 1 1 1 1 1 1 1 1 1
|
1 1 1 1
4 ^v- -4-f—--—W ~
-
4 /V 1--j ^^ r1_____P>___1^ - —t—
-- f f-~»4 _Cl. 4T— C^ T4 _a___J
---f_____^_—_^
-C|_ ./:*. j-
'—or
Ul»-<
r w ~t4. Cl_ J-r———
—
t^ i
_4. .lis 4
i
-
r -t^ t4 -Jp— —4i ""'m
1^ ~1k t <_> Ll'\ i_ _j__/v 1k^- i_) IM i tr ^r-Tf-i p J CM 4 p. Jr .
LUtoOQ
1 L 1--f
L 4± Jlr \7 '
L_ /v i
- - P~~" \T »
OCO
>-CO
4———.^___1T -*M—— f-
-l....Pu...4- -f— — —C^T
4 ^^ 4r ^^ T4 _o_ 4-| "w 1
^ T4 /v. _J| V/'-p-T
L_ 4 _ip___4-~t H^- 1"|
L_ 4 _ru-——
4
-I "tr"—-t
~l_____i^___Jrt- —H« 1^
- 4____/*L. 41
i v,r +1
I -. ,v J-f—-HJ---
|
4 _j^ _J-f H^ t-
4 _*V——— I-r ~v^~"—-I
l y\._l_iT \>1
- 4 __i"^_J1 HJ—
f
l._ _JP>_Jn ^1- I—-Wl—__l^—%/ —_r ^~
1 _/:\ |
-
r——*/-- -I
4 ^^ i:f--(,> 1
- L___a__J.1
ij T4, /"* J.-1- — ^>.—
f
U •£*_ -LH €r +L___(=>___i-r—-cr--r
__ _ei_. _i" ^;JT— "»
L_ _i"> JJT --HJ' -ft!___ _Cl_ __lp-->— c> "1
_L _(!!_ 1.r ^H 1
1l|l
1 1Ul 1 1
III 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11
or*»
•
r-t
*^V)
V)
oin cCO .*
• u
oCO
inin
oLA
10
3
c
<M
MTO
3C —— HTD
CO=>
Q<
0)
3 0)
W> 3
>
oJ-
in
C<D
CoaEOu
E
x:bC
4)
O
o00in
otoin
oJ-in
oCMin
( *sqi) SlN3N0dW03 bOPVW
oo
dO 1H3I3M
o00
37
or^
•
i-t
^"»
IA
</>
in 0)to C
• J*i-H o
c
o<
LU
CD
CMrH </>
3
3 (0
66 U
0)
3
>
in*->
c0)
coaEOu
E
O•M
0)
(*sq i) SINBNOdWOD bOPVW dO
38
H rrreii
I I
ill
_t"l_ __.i
LU
<
LU C
co :
o
-joCO
\r—
1;h i
,Q jigr i
i_ -^^. _-r
—
\7 "r -N t. •\ c iik-
L__..— 0_._.._ j- i r ^ C -Ci-r
—
hj"—"—Tc * H a* -CL-
_..__C_. I1 —-f ~T gI ^X.___l e-—V7 1
*> -
._ — On i— ~~^ i-
i_. — £-> jr \i( — —1 i
1y 1;a *--
1 —
h
£*.——_ j^WP—3
t- —
1
cr
—
1
_1 ,Q__ i
-i
—
1^™ i
-± _. n i<> 'iCOn I—XT —1
A. — .- ^V |T —W 1
4.—.- -.2 J.T ^3 1 T-L_.- — /! \ J.T \ / T\.-— — — n J.T".—— - J T4. f\ 4_f
" \/ T_l. Hh__ J.T ' J^ T
I—— — /\1 VJ 1
l___ 1n i1 ^J 1
-1——__ Pi ii~" w 1
1 f\ j.T — \J ii._— /^ iT \J 1
- 1 t V. i_r ~v T f
4 /-\i
1 U —1~*~
1 j /I\l V7 ~\
l__ n i~j_ T J-" 1
J-—
—
_^rsr
—
~~<J- l_
_ j / \ ir— "V/ 1
/ v,_ _j- V T 1
_i_ / \_ jT— ""A T— n-.
-T_l 4, i %_ IT ~"^ .7~ ~TL o -'
IT -^ T_1|L n
I
r""""~ J4. _ _-^T *"— "*a
——-—£t- |_tr r
.____-"-<.2—
n
-4^--— -1^J —T1 1 1 1 1 1 1 1 -L|»LUALJJJi]
o
in
inir> 01LO c
• .*«-i u
•^JC4J
coo
to 4-*•
(T3
t-H p_3in
c•—
—IT> COin •
(D
inc 3•— »—o v-^
H-» *oun iH 10
• CO l_!-H 3 0)— W. !—
Q 3 <u< W 3cc
u.M-
_l •LT» LU inJ- 3 >
• LL.
i—
1
in
c0)
coaO F-* O
• u«-l
o•—
»
ro
FmK> u-
o 2
ooom
oto
CD-a-
OCMin
oom
C3ooJ-
Csqi) SINBNOdWOO bOTVW dO 1H9I3M
39
1 1 1 1 1 1 1 1 1 1 1 ill 1 1 1 Q 1 1 ill 1 1 1 1 1 1 1 1 1 1 i i ii i
|| | | | | | || | | | !
-L 4\ J.T "\7 "t
4.____^L____I-+ £h r- _i _/\ j_ 1
t "t?— "~r
|_ *?l_ 11 1> r
1____S V___ _l ,„ ._ . LlJ
: it" *> Z* tl^1~"— ~" ^ *j ^ *~ "in C>— -taV"
. .!... . .* Of C _i_ a _-.
• mi ct -t. -i<» er- <•*
. 1 ... ._ -w
III ft^ l_
L ,__y\ J l/i yi—r \/ — 1 ji?
*•
I I l^i —J q-f- —ly r- —| U_i /x — -I-j ^——
-i
j._ . _l_ _^_ __l_ _J1z i . ,
iH 3— -t: zf . - ,
J l. e, _t 2 '
M hir—"oH 1 ~_j__j
. .. I. ... - L _f5_ JL ^_ t
—'-^ — t- > h-i. — i
i/\i ii w r
1 .pL_ J| — ^r 1
J 4 ^v JT W T- -l ____i^s_ _4 . 4—-j h^——— "f
-l_ — J'X — — -ir \/ 1
l _jK Jr pj 1
1| _/"V.„__J
1 f_ t ^j.... __.|
__ fi Jr---p-k.r - i1 i/A Ir—pv 1
i___j *. _lir--r—'o^-
nl!_.._ —-i^- . —
1
r— -Hw~—
r
I ir> i
1 L> 1
-+- ~ l J5.ii-r- -ij~"T"l
L_. . ^i.-4-.-l- ,-tt v* L_
I A Zj1 "\7 ~t_n
I i^lr-"" "~l k-""
-[~ti
ll _SV.--i.l-4r~ ~~"""V7' 1
L. ^i 1 il1 ™m' 1
1 f\ 1 1r V/Tl "
i r\. J-J i
1
H cr-±H __ _ _1 _h
ii. <v ,T.i ! j 1
1
i
:
1 .... ~i 1 II i
ir "^' i
1 1
__ __d"^__._ _Jr 'J 1 \
1 Pl L L_._ . ___ .
1j (_> 1
u -_rv ir —L^ Ti y\ _j| „_ ^J -m
1 M II 11 1 1 M 1 1 1 Mil 1 1 Ifal II 1
1J11 II M 1 1 1 1 1 1 M 11 II 1 II 1 1
o
into
o10
(ft
(ft
4)
C
co
3(ft
C
inm
oin
in
uc
CO
o<
UJ3
OJ-
inrn
(ft
3
JfTJ
0)u •—
3 <D
60 3
(ft
>
(ft
*->
CVcoaEOo
uo•—
>
TO
E
2o
OOOin
oIDin
oJ-m
oCMin
ooin
o00
(•sqi) SINBNOdWOO bOPVW dO 1H9I3M
40
1 1 1 1 1
1
ill1 1 1 IPI 1
1
ill1 1 1 1 1 1 1 1 1
1
1 ' 1-1
1 1 1 1 1 1 1 1 1 1 1 1 1
1
1 14_____,a___j~t
-< - -— -i
_j j\ i_ _L-jr -<? h
i ^ l i
1 \7---rL-_.-^\_ J+ *?"--+
- UJ1 u.^i/V „_,,_, J 1— — i 1* " !t. < L. Jft JCI J.X1 /V Ji (V r 1* O («l^ ** h
. * -1=4 Bl_ -C*L_._. l____/\_ _i iii re
1 <* * £°?l____y^™ ™_. J o v-
*
n —1/ -1 '—
'
Q1 y\ l_j1 \7 ""»
4....A..J-f","~""\?~—"1
i_,*>
i _i 1—-C 1""-""!
i ^ . g it xit1
,\^— ~""r ™. . . - £
1 -(3—r ;>- 4
l rv- u_ i1 tr t
i _,fi ,»
f- C^ TL____a___....j.f-"—— ""
k-"———-
T
L-_—_"__— —JT — ——— M »-— — "T
. i _^ J_1 ^J^ 1
L ^n*_^_^lr -<^ i
L-.---/"t—i—-Jr~~~"!iiy - i
i— — —
—
Pi_.a_._j» -| W ^4—
1
L y\_*._jr '*
|
—
'
1 -j r\_L_J| — —— -H^-4——-f
L /\_ _J !
t w +. , _. ,., * ,
,*V 1 _. ._r— ""4~vJr-—
1
l._J _Tb_ _|r""""t^'_____ ___i\_ 1r 1 Iv,/— --IL _n
k____|F----,
b_,r----|
L-—— _/'V-.__it J **^T T ± it
!i l./\...... j 1
1 ^ i Ul___^^_ ,.,
i i f . ji ^ 1
L _,ni_ J-t -^>—-itL„_»ei. _i- -j- 1 ... ,r- 1^— r
ill f\ i-i- —w—
1
i- -.^v J !
i
1 T i5 1I
I
L_-.-__,p_- ji-*-— H = ^ -j- -+
L±a I . | _ Itff3 ' _I IT I
i ^|i
_ 1
-p— h __ _
j ,3:, .4 i itIT '^I h __ . 1±
1 M M 1 M M M il 1 j) 1 1 11 11 II i 1 II M 11 1 II 1 11 1 1 1 11
or>.
•
r-t
<»^
(ft
(A
m 0)
to c• J*
T-t u•—
£4-»
coo •—
to 4-*
• TOiH ^
3l/l
C•"•
in oin •
CM
<"% ID
c in.— 3v__- «—
o IAT3IT* </> ft ID
• => i_
^H — 0)
O l_ ^«
< 3 <U
on 60 3•— M-
_J u_UJ •
in 3 l/l
__• a. >•
i-i in
ca;
coQ.
o E-=r O
• oi-i
o
?m
b0
o
ooo
om
om
oCMin
ooin
o00
(•sqi) SlN3N0dW03 bOrVW dO 1H9I3M
41
oCM
00
TO
in
</>
0)
c
u
c j:
(0
_ 10COtoLUz
^t o
3CO
o o o00 CO j-in in in
oCMin
ooin
oooJ*
3 </>
</> 3CO C •—l-l ••" T3
TO
<u • l_
L. W3 > w—bfi <U.— «A 3u. M
c«+-
U U~C Ooa in
E 0)
O 3o
TO
l_ >o•—
1
•W
TO CE TO
<4- too c
o4J u-CW•—
a)
2(sqi) SlN3NOdWO0 cJOPVW JO 1H9I3M
42
•(/)
CNI >
0)
u
ool_
l-lV)
<-\
•(Ac 4-1 V)
•—-C Vs^bO C— -*
CO0) u
UD COr*. 5 —
• LU t-» jii-H z
oE -m3o
fc. E c^~ 3 — oX w c —MM — 4-»
z LL. E n-=f o -C 3
• ^~ U </>i-H h- — c< XL —3 *CO 4-1z
<C
(/>CNI 3
• >Mi-H
3
(•ui) 03H3V3bSI 1H9I3M WnWINIW 3b3HM SfllQVb 1303
43
or*-
• *"N
rH </>
I/)
0)
c.*u
in •—to £
• 4-1
rH
co••»
4->
to^»
O 3to (A
• C
in
0)
3in ^-in 10
•
rH •>
c *->
•— c<w (0
00 MCO fH (/»O 3 c
LT> — 0J c• Q L. u
rH < 3OC bfl+J
•— <0_1 u.UJ tf)
r> 3LL —
ITV oJ- (0
• ui-H
3
•
O inJ- >
•
rHoc0)
in
o
CM
in
ooJ-
•
in
oCO
in
o10
•
in
oJ-
•
in
u
cu
v.
>o
(%) ADN3l3ldd3 lIVbBAO
44
oc«0
U)
cou
oo
i-» (0
in
*"-S <u
• cc J^
. o *>s_^ — WJ
.c 3LO to 4J .—
• to CT> TJl—l UJ HCIBz O L.
^ o>—o l_ 4-1 •—
3 <T> 4)
X bO— 3»- — 3 «4-
J" z C M-• o — O
i-H —h- • </)
< (ft V-J > 3ID »—
to > (0
z o >
Csl
c
0)
>oin in in in in in
(%) AON3IOIdd3 llVbHAO
45
{%) 1H9I3M WnWINIW IV A3N3IOIdd3 11Vb3A0CMJ-
O oo CO J-rn
oooin
o oCO j-in m
oCMin
ooin
oooJ*
to
>»Uc0>
(sqi) SlN3NOdW03 UOPVW 30 1H9I3M WflWINIW
<u V)
«/)— 0»>- c<0-*
^^ »- u• a> —r >x:
O -M
TJ cCO c OCO o ro —LU CM 4-1
7" in <o
V 0) *j •—
r i l_ C 33 <D </>
X W) c c1— •« o —
u. a?" E •
o O in
o >1-<r i. *->
_
i
Ojc3 •—thOCO re-7* fer <u
Minimum
weight
of
minimum
w
46
oo
AONBIOIddB 1"IVa3A0 Nl 3SV3H0NI %
CO .* CNT»CID
CS (/)
• 4-1
«SI C0>
coaEOu
oo ^"N
• u </»
t-H O (/>
^-s —1 a>
. ID Cc E-*
o*w*
Ox:CO 4->
<X) to 4~»
• LU -c cf-l z bO O
SlN3NOdWO0bOPVW JO 1H0I3M wnwiNiw Nl 3SV3H0NI %
c > CM ft) 4-)
$ WX 0) r—
h- l_ fc 33 3 «/)
z WE Co •—
•
•— •—
Li- Ch- *— •
<r E w_j >3 cCO — >z O
Percentage
Increase
overal
1
efflclen
47
V. CONCLUSIONS
1) The use of a heat pipe in a RTG reduces the total weight
and increases the overall efficiency (as compared to SNAP-21) , while
maintaining reliability and long life.
2) The design with minimum total weight has a different fuel
radius than the design with maximum overall efficiency (at a specified
value of insulation thickness).
3) The use of the heat pipe decreases the maximum temperature of
the fuel from 1700°F to approximately 1400°F.
4) In most cases , the biological shield accounts for 40% of the
total system weight.
48
VI. RECOMMENDATIONS
1) Perform experiments to verify the accuracy of the analytical
solution for the dose rate due to the nuclear radiation.
2) Parametrically analyze the system for variable operating
temperatures of the thermoelements.
3) Derive an analytical model for the heat transfer through the
insulation surrounding the biological shield that doesn't assume in-
finite length geometry.
4) Analyze the relationship between the higher cost but lower
amount of shielding required for an o( emitting fuel.
5) Consider different heat pipe geometries for a more efficient
heat transfer system.
49
APPENDIX A
NUCLEAR RADIATION ANALYSIS
Considering the model whose dimensions are shown in figure 22,
tables 3 and 4 contain all the information necessary to calculate the dose
rate due to the annular geometry fuel pellet. The final equation for the
dose rate is (from figure 4) [13];
where * '2(Z°f to l
F (e^McU + Lm^i)]
K - constant given in figure 4
B = buildup factor
The computer program for this specific case calculates a dose rate of
118 MR/hr. The hand calculated dose rate is 134 MR/hr.
HEAT PIPE/PRESSURE VESSEL
SHIELDFUEL
FUEL CAPSULEINSULATION
Figure 22
(Dimensions of example used in sample dose rate calculations)
50
o
(X)
<H
m CM m r>- OvO vO CM
CMvOo oo
T—
1
CMt>» m <T <T CO CO CO CO CO
:> in CM vO m CM CO1—
t
CM00 m
-V • • e 6 • • « • a
soON
CO 00r-t
1—
t
1-tCO r- vO vO m m
*
Xco
i—loon
COon
ONCOvO
inONm
om
inCOm Om
=s
5:
^
3
*
=N
^
>10£U<U
cw
CMo
<-• <r oo
CO CO CO
mCM
00
CM CM CM
vO
CM
COCO
o CM vOCM
vO CM
r—
1
On i—
1
I—
1
CM CO 00O ON vO m« • • •
CM O
CO m •<t i-t
m 00 ON mt-i CO CM CM
I—I <f-
00
min
ONON
CO m
00
v£>
CM
r-> vo o voSO CO r-t 00<t ^- <f CO
r-4 m CM <ro 00 1^ oCM 1—4 j—
1
<-*
r--
oo
00
CM
o o <t o vO <r CMi i r^ vO m m <t <r <fi I o o o o o o o
m 00 ON vO r^. t^. o m mm 00 CO vO CM a^ CM vO <f CO00 m <f CO CO CM CM CM CM CM
• • * « « « e • •
i—i
00 in <i- o CM oo CO r-~
r~. r~- \0 i—i 00 o >* CM I—I oo <f CO CO CM CM CM CM CM CM6
CO On i—i ^O00 O v£> CMON ON 00 00
ON
CO
v£>
ONo
(D
^
+N
N
o
co
co•HU«01—1
i—i 3CO o CJ
CO 1—1 i—
1
• • CO
CJ
00c'ri
u-N vO r-l
• • 0Jr-4 i—l •H1—! i—l X.
co
uCO
01
1-1
.—
1
i-H CO ur- r-~ 3
• • m 5Soo CO i-3
pa U< OH
CO•—
i
r-t 4-1
i-~ r^ CO• • Q
CO co1—
(
i—i i-i
CO
o•H
Em 3o 00 S5• •
<t CO T3CCO
o•H
o co 4J• • 01m \0
1i—i T-t
01
O
ON
pa o
CO CO< <
51
o rf
d
1IaJ
+
^
I-V r^ CM m CO CO <J- m vO
<J CM i—l ON ON ON ON ON ON
^ i-H
•
i—
1
* * 8 * °
r
cw
co cm in oocm vo r-. onO co <fr coo o o o
00 vO CMI-*, cm inCM <—
I
Oo o o
*- <n *o ^S (s.
'o »o "o "o 'oi
ONcoCO O
^O CM
m
CO
CM mco
*" +
wHas
wenoQ(J
HOH(v. v« m vn
8 'o 'o 'o 'o 'o 'o 'o!I r-l i-« i-t i—I rH sH
X X y XCM O CM O
• • e e
cm r» cm m
X X Xo m m
6 6 o
!-< y-l CM
mco 00 00 00
o00
CM«
00
oCM
00
mm r-.
ONON
co m
CM
00
00
vr> CM ON CM •vt- .—1 r-^• • c © «
CO o 00 CO r-- r-^ vO
mCO
•
CO
1—1
CO
i—l
CO
Oo
CO
CM
CO
CM
CO
CO
CO
COo 00
mMD
CO vOm mmCMin
CMm
m O 00 O 00 m <tr^ r-^ <© V© m m m
ONoCM
r-» oON ONO OO t-t
o o
oCO00
o00
ooCMCOCOoo
O ON
I—I i—l
O vO
* * * Vi Vi >S s'o 'o 'o b 'o 'o 'o
ONCO00
1^.
oin 1^
CM m vO
vO CM CO
+
I
wH
wtnoo
oH
j«_ >a tn i/i ^ -'o >o 'o 'o 'o 'O
m
o
mm
x v x
m o co• • e
CO 00 CO
om
co
oXm
m co <t oo<r -d- <t *tf
ONm
ONON
min
CMm
CO-cl-
in
om
co
Oi—l r-t
x x
• •
i-l CM
OCMOOOCMCOCO• «••«•••0000000000000000
ON^oomoO'-^ONinlONcoONcor^r^vX)^o|
NsfNNfM<tlT|lfl
00 vOvo <f \o co co m m mlCO CO CM CM CM CM CM CMI
om ml
ONoCM
CO
prf
0)
(0
o
co•H4JCO
•H'OCO
erf
uCO
<u1—1
o3S3
u-i
o
0}
ao1-1
4JCOt-H
3O
CO
o<U1-1
a
C/>
fl 3SVD d asvo
52
From the superposition of dose ratess
the dose rate due to A equals
the dose rate due to B minus that due to C. Thus the dose rate in Rad/hr
is .1714-. 06119 .102. This is then converted into Rem/hr for the dose
rate to be given in MR/hr (134 MR/hr) . Note that 1.31 Rem equals 1 Rad.
APPENDIX B
HEAT LOSS DERIVATION
The solution to the heat transfer equation for the annular cylinder
both with and without internal heat generation is given on the following
page [2]. Using these solutions when considering the geometry shown in
figure 5, there can be derived six equations with six unknowns. The
solution of these six equations results in the calculation of f-^= 1
The six equations are;
/out*
(1)
(2)
'9\ = QW-c'z-rrk< a)
9] -P-n-l, Ch -TO
'Q\ - ?Trk OV-TQ
(4)
(5)
(6)
The known values of k and r are then substituted to simplify the six
equations.
54
Annulus with no Internal Heat Generation
k - thermal conductivity
T3 -T2t * To +M"s/o
UL(r/r£)
Annulus with Internal Heat Generation
Q - internal heat/ watts \
^ cm3 J
k - thermal conductivity
Q r2
5i~r - -2. tt k /- •
^k
where C#' T3 - T2 + ^T ( ^ - ^)^k
Q*~3
Q- = T3 + -££- -C'A.54k
2), - Q C.O\Z2 5) -20.1C,' (2«)
Qtf/W
- QTTr32 -ZOA C!
(^"BCVT^infVrO
(31
)
(4')
(?L*= ns (T^T^ ^t r^5) (5')
Q-2) -.Oo5-oZ(T5 -T^i//l(r?/r4)JL/ovd
<6»)
The resulting six equations are then solved simultaneously. First set
the two equations for ( -^ ) , equal to one another.
Then put in the value of C1
and solve for T. in terms of T_ and T1
.
T, -C^T3 t \55T, ± C;
5"5 + C 2
(7')
u;V>e ^e C^ = ZO.I JUl (.75"/^)
C, = Qc2
12.
8
(^*-nl)-.o»z2 5-
]
56
/Q \
Next solve for T, in terms of 7T 1 and T, by using equations3 \ ^ /out 6
4', 5*, and 6'.
T3= "^ t C, (f
)
(8')
where f = ^ ^^ + Uif*/u) U (^/r5)1 &Z.8 \\Q\ ,oo5oa
From equations 3J and 7° solve for T in terms of — 1 and T-
.
3 V i >ut 1
T =T - 0" + cOL(ffLi-Cr-<u] -C X C3
where C4 = Q TT Tj Z
C 5 - (V-n-)4S-
Then T_ can be eliminated between equations 8" and 9' to find / S±t )3
\ q/out
in terms of T , T,, r , r , r,„ r.j r_, and r,.
J^/out " I5-5-C/C2. -V\5*5" + C2
57
APPENDIX C
CRITICAL DIMENSIONS AND VOLUME DERIVATIONS
Knowing the fixed outside diameter of the heat pipe (1 inch) and
the required hot plate area of the generator (A-as specified in the
SNAP-21 design) the length of the heat pipe needed next to the genera-
tor to fulfill the required hot plate area is easily calculated. There
is an additional specification of 1/16 of an inch gap between the heat
pipe and the hot plate for heat transfer by conduction and radiation
(at a temperature drop of 200°F). Figure 23 shows the geometry and the
required hot plate length.
From the figures 24, 25, 26 and 27 the respective volumes of the
generator cold frame, pressure vessel, shield, and fuel capsule can be
easily verified„ Note that in each case these volumes are functions of
the variable radii (RF-radius of the fuel, RS-radius of the shield,
Rl-radius of the insulation).
58
total hot plate area = A = 6.6 in 2
A » IL D2 L D « l| |n
.'. L = 6.7 in
Figure 23(Length dimension of annular generator)
59
GENERATOR __
COLD FRAME
HEAT PIPE
VOLUME = TT [((3.57) 2 -(.57) 2) 5.7
+((RI+.5) 2 -(.57) 2)]
Figure 2k(Volume derivation of annular generator)
PRESSURE VESSEL
VOLUME = TT [((RI-H.5) 2 -(RI+75) 2 )(LF+3.5 + 2(RS-A))
U/3)((RI+1.) 3-(RI+. 5)3)1
Figure 25(Volume derivation of pressure vessel)
60
SHIE
VOLUME = Tr[RS2(LF+.5*2(RS-A))-.86A(RS-A) 2
-.25(RS-A)-A 2 (LF+.5)]
where TTRS 2( LF* . 5*2(RS-A) ) = volume of solid
cyl Inder
TT(RS-A)(l/2) 2 = volume cut out forpassage of heat pipe
TTA*(LF+.5) = volume cut out for fuel andfuel capsule
TT.86A(RS-A) 2 volume cut out for therounded corners (I.e. see below)
area = (1-fT/U) (RS-A) 2
RS-A
volume 2TT (2A)(area)(l*-TT)TTA(RS-A) 2
= ,86A(RS-A) 2
Figure 26(Volume derivation of shield)
61
VOLUME = 1T[.5(A 2 -(.5) 2 )*(A 2 -RF2)LF
+((.75) 2 -(.5)2)Lf]
Figure 27(Volume derivation of fuel capsule)
b2
APPENDIX D
COMPUTER PROGRAM
u
o
l oo i_> U'oc c> t_'u <_:> <_> c>ououuu
au.Q.
V,
a-7
UJ
CO
UJa;
O 3t— toI— 00
00
a
•-« <tcIX. _J_)U< JDLUJ
3^xr
LLLLULLL'UOUto 00COX33_>H-.- 1 »-< >-f (J
nr or a_j11 11 11 II
UL»_ny>U_aacr_j
l/;
1-3<G(XQCIjUXir»-LU
ucY--
<r<rUJUiXX
5 2.
CDCLULUXXH-KII II
_J_JLULUJDU LL
a:Q-
LL
C
UJOK"
a.acoac_i3cxt-UOOLL.
3 oIr-Z
+ <!-.C -JJH>UJIU3-vLL 2 OII LJI-_iofuj It)
U_i-«Q
3: UJ
K- toCOU'
a. ujLU >3O to<r uua»-h e*r<r
_jC3cj>_JtOUUH/'J
•—• UJ Uj
Dior 3I— toa ti-
ll ILL LLLL3000LJ
LU(J—
<T_JO-
c2:
3D
Q<or >-
O o>-I— 2TO<r u. <c
a >— 'jj
zui»->oUiXLL •—
Oa li uIJJU.
U LL 1 Li
DOJ<l_i
UJ LULUXXtoootic^cr1
LJ (_ !(_;•—( •—
1
QOQUJUIII II II .»_*t~.-if\J II II
UJLUUICOCLto C" to t—'—«
CJl_H_'UJUJ
XXXcootr»—« •—1 »—
1
ujuku
li II 11
OO LL
LULUUJ
u_'aK 1X1
<t >
II II
LLLLLLLLIliUJ
CO
LL
li-
on.
o<T
wLL
tn
O
—. tr,
UJ
O
CD *<TC0C
CLLO<t<3.
— <LL<J«U.r-<i:< •• -
<JOCLL OO'
aJSCOUlO'UMl
OCTOCT"if st-
ir;?
ctctu. u.
O
in * **
HO II OII ••-1 •.-. + .-.+
o> oO rvio V'O »o •
%$-« <j-r\j
II II
OLLOt^c_a C-iu
oo
oosr
LL —
•
r\j<—
1
• or
-1 I
+ </)
tOQC
II
•— LLQC •—
1
II II
e>co
LLIUJ
1
a-j
U-LUII 3OIL
ill
3LL
I U r-<
<M« U-O—*• _JO—<LL »J •
Qt«-H «.I
~-orcr—— »-.l l-
O « i>o (_;-JvOiXOOC?uj—« ••>3-
1
3-4-LL to
+ •*» «UJtorn 03_Jw.|_^LL»-
3-JUJI— 00C?sfLL LUXCJOD II
II 3 C?<t0l_i—ILL I-
—^——II
—
ULI II I UJ3U <LLLL3UU__JL_'»—•—1U.O
a-
LLQr-
-IvCLU^-<
3<rU_r-I
+ •
uoro•— _i—l_JUJ"vC?3_lII LLU)to II 3—J-JU.UJLU II
33UL
St
CUO r-t
Nt-m in
UtOUUUUOUUUUUUUUUUUUb
63
<r cm • "v v. xcu
</) * # lTi_J • V.Oa if «— •!? o mow • c\j coco a. ••* I * u_a .—»com cm— # »<i » mux-<n — —• - o ll • »ro^• •«• < r- H a'- v»m
I in I tr\ u_ » cou- n -^ •
im r-co • llo - </> •» my^* •a' — IL II C«W »U-* >——' I LU(— _J II IDCO~ * •*• cvj X -J mu..< it • * _ie> »uj i— coa •»(!
I -JCN) * JhXD <tt/)<t- CMCO + + ~ <LUCOU_ LUOCX II UJct u.in in cxj*^. x_i co«-» «J • • IK- f\)U_ - DIO« * m + > •• »C M-_JH Q<? — + —
«
k i— oxer x<iujo i
* fNju. ex uj <-< • mu-h- rnujt-.^—<
— nO *_J — CO UU •>>. *X MIUJUIcm cc •« w w OS Xf\j- e: m co_jcouj • u_* + o m»n»-i»-f-ato 1 a:— r- •. u. vo- uj <t> »jg
-~n — 1 rv • M w mu j? ULncxujM—to — CM* —'ITi ILi UJ • «.UJ- »UMDhLU * <3. •* * —••«- CO 3. CO- CO •> - (-"V.U.UJcom 1 #<—ro— o * u. 11 cox 11 «aro- coah- co <in#cM Q o •• luco— a: • -0O • QC —' •* # UL * t-i - 0>"^f\JQrUJCOXQ
l w + +•—*• —<-i uj 11 _j cm •uzu.ro-OU_ -M- in«-«m—
»
UJUJ_iJI UJUJ •Ok— UJ »V.• or • •cr »r- 3Ctou' u.«-«cxcMJ-<tej5- -oxO * ro cm -tfw+ir. +UDO. U-X— u. -ex 11 »ro-u. - + «— 1
<-• • eou.H aicoco — ujQ oov.u 1 00 10 (Mrgct~- •— - -uj t/>- ll2Kcou.ro-J 00 • # •«• «— 1 uju to js oruLUJii uj 3 - ••*-h >t>t- + * # 1 c\j — 2r_j_i » OOtt (-OKm» O'
»-cx » - u_ cc> —.ro* >P + -luocm 1— clcxX <C II U-cc * t\io _j r^un** • a.— :d«->u <k oeoai< --co -o •— • •*—. rOt-ictru-LUU- rexu-h- *~4f— XeXtO-COCXCMCM>f •&
I ^-»h- <T\Ui »-JKLU UJOO<TUJ 3 II
a. »uj r\j rvj+ »ia «4-jIuocj » •• Zm cx jkh- ll _j»-<
»inco-»— c; # «•»-«—< • * -kx_joor-1 tuijj*— uj < ujocm—u-r-omin-j * -~* ex +mviu —<tj »uj»-iu. ojexz-JUJ_j^J<ujro-»a •or\jr^uj_J i/)-.<i-hwjjo org.-<u.Z5UiUL • > otu<xi-UU-Qt«/> «roww
i r\j—iw'iLi ai/i—'Ct-uujJ «ujcxu-jeu.i * •> (~tC3»— • Z3- o—* •
r-< • «a.r> ^ •wwww>>uo— jc » •« •• xxlu o »u_ ^o»-«r*-l-KLl I |VLL + * *^# »•« >>V + COrnjKU-l-X XU UJLL«toi~l-wv vtu-xt^* -4-crro* «• -jcocc'^-^oiti w.» a- ro_iro«-- h-r-cjocjujuj • »Ln—i_J»-<r-<—'^oir\j>oc\iuj»-'cro(r oujww « «»w<wj- ww<<Ooocoroorvj »w • • • •vOro—iroX'Uj^ •J-^-^^ XKX H- <Ia ex ii (_)(_!•-<«-< •m-«- romfiro • • • •u.jc ^.y- h-roxmh-CJ^- — - t— t—
H-QO II II + l| CM 11 l| V II l| II II II II II KHht-wflflSOV^I-^D •«<<jjui ^Muw*ua .o^aa.ou.i-zzzzi-rxN'-Mr* xwnrsa_l_|uO U-LLCX—J* —Jw^-J"-"-!mmmmwwmm 2: tX CX • UJ «CX •-CXZ' ^CXCXOO«iuu.u uu ii o<cC'«-'Cru!U]utuiuju.icX(Xac:aroc)Ocj>ji:craxO'--aooi-zuuCmhujuj«i> i >> + >SJtjtj;3;iCLaaauu.u.u.- u_u_r<>u-- u_a.u.couj
CM rH «—tr-t^H i—t —Ii-h
cmco oloo r- to o^ooa»o o o> oo
64
UUUCUL'O-J<
5
ououuuoouuuu
o
U'U3ujLLC
I
ar i
«~ •
I
2T I
uj I
O I
U I
I
UJ I
Z I
»- I
t- I
-J I
Cj I
a: l
cc I
3 I
«/; I
I
I
a3
-ja:r-Luor
ClH-
MQliiGQZ35! UJ_jqc:oUUJZIOM«».-,-H
azu t~000«-i LUl-O-J<2UU—iUJU3 2wuaZ_JUJ«OIOH-
2T U.
<•-
3ai»-•— Qf <*
com<h-xCc<a.—
1
CXILK1LlJCLt-
3>JJt-uk
11
11 11
UJ
cct-u..
inOin•f
ou
mr-
1
I
Uj
u
o*
NO
— LU
• *
# —• rH f\l
CMh- ••
—4I —I
«•»' • •
«-o ^— in —*tH—»r-4 •• •
^CJ I
(_h-—'LUar 1 »3— • OIL
•OOm—in •>tOvO ,-'t/i <*>
•cj-4-_im l cci ^.+h^«a^o<OHUOaOf U> II w^._w I) \~^ II 3II II UJ II ^ UJ II UUH-OOODh II IL IX DOODUIZu.*-U_H-Q*-«»-~iLLH-C>U.a.UJ
m >4 CM
3Ucar
u.
_Ji/(2«a—<>—
1
QCf-
ctu.•>LU
U.Ou- I
cc 1— I
\- I
<t 1
UJ 1
I I
UJ I
2 I
»-> I
I
2a
_j_j3LU-Ji/li-«UI
2X3-«</) LL.
LLU u000l/)t/>«/>
CJOCJ<<.<!cca.cc
11 II 11
•-K/3LLt-HSilL.
a
-13UJOODZa <-"
UJUJxx
LUK-h-CC3U-X
1 3ooocorCO
_IUJUJCC_JujQ-jrx
U UIQ. <H- VILLI
IL O00ICUJ'-C
Q-LL_l_l1mm <Ii-auHi-O LU«5C_)^HQ-UJI—UJ<OOX_JU II
X II II
II \~II V~t- K-
IL 033U.HQUU-jj-qcjo
OOOoO^'O
3U I
CC I
CD I
3 I
I
I
I
I
IUUUUUUUUUUOU
infM
LL(X
COcc
o
oo•
I
nj
CO
ego
• cco *-o "-'
• u.-<ooo u_r- «o
mm 11 11 <MNt_J>-h-wII It <03 II
--IVCUJOO.-Ihl-aOO(j
LL
—.r-l
CC •• ro
ininv.tMOhN*o «o*
— Ltincsj— actsi—>
L0O-h)LLauou.*v_J »cc
O •CJCJOOQO< II II II
65
ouuuuuouo
mcj*<\l
+ —
cj •
• *in •
inrvj
ou.I-U.
I CX
t-u_— U_
IA—o*I-*
CJPJwOin* +r\j— •r\jr\jin
r-Hoino + -*• • +* innjt—mo<_>—«*
c?~ cj"•«—*CO II •
i_>*-mit Omco-
rn
+
+
CJ
II <LI— (XI-D3I-0CJUI2TOatai
cou
oCOJ2U-O»—
<
CX*-«COU.»LUQCQU- I— I
I
<t(X
UJ I
Z I
-" I
I- I
-J I
a i
ex I
en i
3 I
co |
I
I
I
I
CO «"»
CO h-UJ •» «»
> O in
UJ ^ •
a » *3 r- ^*
to w _iuj *: «—UJ X<X 9* z>a 0*1
o h-UJ «-• O"X cc •
uUJ
z oCJ <I<-> _JU_i— ujor
-IJU-LO_JZ>LU
LL«-iC1»—
h
U-U.U-U I—oaoa<COCOCOXUJZ3Z)r>»-tO•—* n-4 ^.i conC-3CJUZC!<<i<UJCX(XCX_I II
II II II II UJCO
a-a.cx.jcju-i—cou-a
x3
r
3
XO
Oi3 *
a:z»—o2-_l
oiuCJCi
Ofa,
I
r-
+in—•au_
ex*
o— tn•* •
il in—Ul «*vconjMC II II
X+
ai
in<NJ
•
I xQC X *a * ml— mo
eta. o •
coll • I— * | rn
* ^^H COrH lflr-«—«u .
•» » • •> •
in
mI
+inr\i
o
*XI
aoO
m
O•
fnjo
*xI
rsj
— *
X*rvj
O•
I
CM
*<\J
in•i—
»
•0 +f-OivJ
_J* *
CJtn_Jo •—>rr\io
il r>oi— it
LDJ
*X<\J*m in
—oo— I
o
• •© »iO«o i i-iin——
<
l in i +ZOD2inO
LL II OLL II O
in —f- • o-inv. • • «i—i ro
r»--~ cr>"v >v^»— —*in **» •» »Z3 *
•—» co • o • •—i* mvO • ro t-»ro rOr^nj *->
-t — I I I o— I oinjso—jcoj»— «o—• jso •—-o •—O—' i + O •
^- *, ^i ro «^ _imw ^t »^ f\j rri rvj >j-
I + I + I + -• » rvj |
^rvOJC>4-OJJf\JU(MX »CJX—C0K«— r- »—-»vO*- >0——«l—
—
• • • • ||
u ii on n an. ii a ii ul3"ou.
r-» njrf) vi-ui >or- Qua OOh (M
CvOO CJ CJ l_> CJO CJ
66
ma
(Nl
CM
X ~ OI X *-• I
—CM • —
.
ID UJ— %} rr\ in r-*-«-» m o •
•J5-— o • ro
in .«• • # *-
o cm # —o O — <f —• O -4" 00 '-*
+ • CO • <NO + • v. .
f\J lf\ >v — '•v
O *- K «- sT •• O 3 — ao r*- ro
-~ • * cm in r-<-~mK- — m >*• cm •—»*I— ~
- wt ro • i ocnD I- O <-« • I hi- •
+ 3 • ~ "v I- Z + «~
r- + + o »- 2" <fvi*ro >$• r>- in h-a^^" »-•< «-— u_
M- • • • rsl •>«-' •«•-• + »0— * » # -»cr* —» + mm*• ^«-» on— —» **-»—• cmcm sO-^<~
CM t-H • i—« • • • •*•» »»CM i—«*V_JV. »CM •'(NJ CM CMOh- CM • •—»«—-» m»V ^"v "V —'CMh- CM— «-<MOX ^— r-4— — «V ZD * *# *I »X *X X -»-.— | —— —--~LU• m i r- i i _j^cm— cc— —•— _jton h • w • • 2L-—m^o. mi- h-^-'O— <f <0 C03LO »rnX CMh hinOCO—o-——o«—o— *:3fM «u_o ooj •* ++ •—O •"O— JL'V*
I ttO I IOI CM— t/IUJ
mcM»o + cMcu + cM + +xjh-mmi rn*-* -jcocm i so i cm m»— i-UL^rin <ca clcx—o^:.^•oxccoxr^-ouo* -<mo<xcxu-^ it <— ex
»-4h<— • !-«-• »h • II X II «- .1 UJhUJ— II UIK-3ii ii ii tr •— it •— — — —oocoi:i-ornu.roiLros'i-uza n oul ii o ii ii oooui?5 0«-2_0«-X OlDh<i>-U.C"-'U.OU.OQaU0Clii
CO yJUt *Gf-~ OLO LT O—I (MO O_4 t-tr-4 r-(l—4 r-4O «H CM CM CMO O
cm m vt
67
BIBLIOGRAPHY
1. Angrist, Stanley W., Direct Energy Conversion ,, Allyn and Bacon,Inc., Boston, 1965.
2. Carslaw, H. S„, and Jaeger^ J. C, Conduction of Heat in Solids ,
Oxford University Press , Great Britain, 1959.
3. Chapman, Alan J., Heat Transfer , Macmillan Company, New York,1967.
4. Cheung , Henry, A Critical Review of Heat Pipe Theory and Applica -
tions , Lawrence Radiation Laboratory, University of California,Livermore, UCRL-50453, 1968.
5. Corliss, William R. and Harvey, Douglas G., Radioisotopic PowerGeneration , Prentice -Hall, Inc., Englewood Cliffs, N. J.,1964.
6. Etherington, Harold, Editor, Nuclear Engineering Handbook ,
McGraw-Hill Book Company, Inc., New York, N. Y., 1958.
7. Feldman, K. Thomas, Jr., and whiting, Glen H. , "The Heat Pipe",Mechanical Engineering , February, 1967.
8. Feldman, K. Thomas, Jr., and Whiting, Glen H. , "Applications ofthe Heat Pipe", Mechanical Engineering , November, 1968.
9. Levy, E. K. , "Theoretical Investigation of Heat Pipes Operatingat Low Vapor Pressures," Transactions of the ASME , November,1968.
10. Martin Nuclear Division Report #MND°322°25, SNAP-21A Ten-WattDeep Sea Isotopic Power Supply, Summary Report Phase 1,
1965.
11. Rockwell, Theodore III, Ed., Reactor Shielding Design Manual ,
D. Van Nostrand Company, Inc., Princeton, New Jersey.
12. 3-M Company Report # MMM(3321) =19, SNAP 21-B Program, Deep SeaRadioisotope-fueled Thermoelectric Generator Power SupplySystem, Final Report, June 1966.
13. 3-M Company Report # MMM(3691) -49, SNAP-21 Program, Phase II ,
Final System Safety Analysis, June 1969.
14. Ward, James J. and Blair, Larry S., Parametric Analysis of
Radioisotope Fueled Thermionic Generators, Lewis ResearchCenter, Cleveland,, Ohio,
68
INITIAL DISTRIBUTION LIST
No. Copies
1. Defense Documentation Center 20
Cameron StationAlexandria, Virginia 22314
2. Library, Code 0212 2
Naval Postgraduate SchoolMonterey, California 93940
3. Naval Ship Systems Command Code 2052 1
Department of the NavyWashington, D. C. 20360
4. Mechanical Engineering Department 2
Naval Postgraduate SchoolMonterey, California 93940
5. Professor P, J, Marto 1
Mechanical Engineering DepartmentNaval Postgraduate SchoolMonterey, California 93940
6. Professor P. F, Pucci 1
Mechanical Engineering DepartmentNaval Postgraduate SchoolMonterey, California 93940
7. LTJG Benjamin Jo Ewers , Jr«, USN 2
1947 Blaine Ave,
,
Racine, Wisconsin 53405
8. Mr, Robert Pannemann 1
Defense Products DepartmentBldg 551
3-M CompanySt Paul, Minn, 55101
UnclassifiedSecurity Classification
DOCUMENT CONTROL DATA -R&D(Security classification of title, body of abstract and indexing annotation must be entered when the overall report is classified)
I ORIGINATING ACTIVITY (Corporate author)
Naval Postgraduate SchoolMonterey, California 93940
2«. REPORT SECURITY CLASSIFICATION
Unclassified2b. GROUP
3 REPORT TITLE
A Parametric Analysis of a Deep Sea Radioisotopic Thermoelectric Generator Employinga Heat Pipe
4. DESCRIPTIVE NOTES (Type of report and.inclusive dates)
Master's Thesis; June 19695 AUTHOR(S) (First name, middle initial, last name)
Benjamin James Ewers, Jr.
6 REPORT DATE
June 19697a. TOTAL NO. OF PAGES
6976. NO. OF REFS
148a. CONTRACT OR GRANT NO.
b. PROJEC T NO.
9a. ORIGINATOR'S REPORT NUMBER(S)
9b. OTHER REPORT NOIS) (Any other numbers that may be assignedthis report)
10. DISTRIBUTION STATEMENT
Distribution of this document is unlimited
I. SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY
Naval Postgraduate SchoolMonterey, California 93940
ABSTRACT
A parametric design analysis was performed using a heat pipe in an existingdeep sea Radioisotopic Thermoelectric Generator (SNAP-21). Heat is transferredfrom an annular fuel pellet to an annular thermoelectric generator through a con-necting heat pipe. The fuel pellet is fully shielded so that the thermoelectricgenerator is easily removable. Overall efficiency and the weight of major com-ponents were determined for varying fuel radii of from 1.3 to 1.7 inches and forvarying insulation thicknesses of from 1.0 inch to 2.0 inch.
The analysis indicates that there is a particular fuel radius (at constantinsulation thickness) at which minimum weight is reached, while the maximum over-all efficiency is obtained at a larger fuel radius. The median design has anoverall efficiency (at the beginning of life) of 5.4% and a total weight of 570lbs. These design results, when compared to the existing SNAP-21 design gives anincrease in overall efficiency of at least 7%, and a reduction in total weight of127..
DD FORM I47O1 NOV 6S I *T I Sj
S/N 0101 -807-681 1
(PAGE 1 )
Unclassified71 Security Classification
A-31408
UnclassifiedSecurity Classification
key wo RDSRO L E W T
Radioisotopic Thermoelectric Generator
Heat Pipe
SNAP- 21
DD ,rj473 (back
S/N Ot 01 -807-61 72Unclassified
Security Classification A- 3 I 409
thesE93
AuwT
met"C analysis of a deep sea radi
3 2768 001 89221 9DUDLEY KNOX LIBRARY