NPS ARCHIVE 1969 EWERS, B. - COnnecting REpositorieshalf-life composition meltingpoint...

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.

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






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 lî —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_. . î.-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. î 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 •

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

 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 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

- 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

Ô 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

ONôomoO'-ÔNinlONcoONcor^r^vX)ô|

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!

(^"BCVTînfVrO

(31

)

(4')

(?L*= ns (T^T^ ^t r^5) (5')

Q-2) -.Oo5-oZ(T5 -Tî//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 ê 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— # » •» 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 rûn** • 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\jrûj_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_ ô»-«r*-l-KLl I |VLL + * *^# »•« >>V + COrnjKU-l-X XU UJLL«toi~l-wv vtu-xt^* -4-crro* «• -jcocc'^-ôiti w.» a- ro_iro«-- h-r-cjocjujuj • »Ln—i_J»-<r-<—'ôir\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-wflflSOVÎ-^D •«<<jjui ^Muw*ua .oâa.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 oôoa»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-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


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)


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


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

NPS ARCHIVE 1969 EWERS, B. - COnnecting REpositorieshalf-life composition meltingpoint...

Documents

Transcript of NPS ARCHIVE 1969 EWERS, B. - COnnecting REpositorieshalf-life composition meltingpoint...