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AECRESEARCHANDDEVELOPMENT REPORT

PmJiMQ_~-R ~.$.2---

ByJQu@Jk~&@j81 qf

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ASS IFIED, DATE:

w’%~::...’ ~~~,;,--- --,- ,– -:,, .“.’. . .,.

LIGHTWEIGHT NUCLEAR ROCKET

(Title Unclassified)

.,:

.

REACTORS

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LAMs-2404

NUCLEAR ROCKET

ENGINES

(M-3679,24thEd.)

AND RAM-JET

Pa

- “d

Thisdocumentconsistsof 56 pages

(countingpreliminarypages)

LOS ALAMOS SCIENTIFIC LABORATORY

OF THE UNIVERSITYOF CALIFORNIA LOS ALAMOS NEW MEXICO

REPORT WRITTEN December1959

SERIESA DISTRIBUTED: May 6,1960

SERIESB DISTRIBUTED:July29,1960

LIGHTWEIGHT NUCLEAR ROCKET REACTORS

(TitleUnclassified)

by

RalphS.Cooper

AppendixB

by

WilliamKirk

-.

L

—c

All L AMS reports sre mfo

e within the Laboratory ratherthanfor

sarilyreflect the opinions of the L08

UNCLASSIFIED

~ory or the find opinion of the authors on the euhject.

This document centsfns res;ric.ted data as defined in the Atomic Energy Act of 1954.

Its tramsmittsl or the disclosure of its contents in sny msnner to sn unsnthorized persen is prohibited.

C-- ---P 1

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NUCLEAR ROCKET AND RAM-JET ENGINES

(M-3679,24thEd.)

IAhLS-2404

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ABsTRAcr

Up to the present$ the advantage of high specific impulse offered

by nuclear heat exchanger rocket engines utilizing hydrogen as a

propellant has been partially offset by the reactor weight} since a

large system is required for full effectiveness. The presently con.

templated minimum weight I?35-graphite (Kiwi) reactor will weigh

approximately 8000 pounds and deliver ‘jO}OOOpounds of thrust (1000 Mw

power).

It is our

utilizing F’35

belief tha~ applying the concept of fast reactors

carbide (U235C-ZrC solid solutions) or cermet (@3502-W)

fuel elements,one is capable of producing reactors weighing 1.200to

3000 pounds for the 1000 Mw power level (depending upon the fuel element

material) and of reducing the minimum weight of nuclear engines to

900 to 2000 pounds for a 200 I& (10$000 pounds thrust) level, including

.

pressure shell plus 100 pounds of miscellaneous extras.

Secondly} we show that the use of F33 in place of &’35 Cm reduce

the weights of the above systems by a factor of 2 in the 1000 Mw range

and a factor of 2.5 at the 200 Mw level. This includes halving the

minimum weight of graphite reactors. Alternat.ively9 one can ultimately

use the superior neutronic properties of #33to incres,sethe exit

gas temperature (and thus specific impulse) in carbide reactors by using

carbide solid solutions containing smaller percentages of UC. . Problems

associated with the use of fast reactors and $33 ‘eO~r~SSlF

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The fast reactor concept is currently being intensively studied

at Ios Alamos with regard to criticality, materials, heat transfer}

control, and other phases of reactor design.

IJNCLASSIFIED

● ☛☛ ● ● 9* ● O* ● * 9** ● m

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6* ● **

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CONTENTS

I. Introduction

II. Fast Reactors

A. General Considerations

B. 0y02-W Reactors

c. Carbide Reactors

D. Problems of Fast Reactors

III. U233 Reactors

A. Introduction

B. 23 02-W Reactors

C . #33 Carbide Reactors

D. U233 in Graphite Reactors

E. Problems Associated with U233

Iv. Discussion

A. The Function of Lightweight Reactors

B. The Development of Lightweight Reactors

v. summary

VI. Appendices

A. Criticality and Weight

B. Methods Used in Performance Analysis

Page

1

1

1

3

7

11

14

14

15

16

20

20

24

24

28

32

36

45

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10 mODU~ION

This report describes work done at Los Alsmos from

camber, 1959, concerning lightweight nuclear propulsion

June to Dereactors. The

conclusions

of numerous

and reactor

end opinions recorded here are the results of the efforts

people working in the fields of reactor physics, materials,

design.

With fast reactors utilizing Oy or #33 in the form of U02-W cermets

or UC-ZrC solid solutions$ it appears technically feasible to develop

power densities of the order of 1 Mw per pound in the range of 200 to

2000 Mw. This could open a new area of application for upper stage

nuclear rockets.

II. FAST REACTORS

A. General Considerations

As is shown in Appendti

tion in a critical assembly}

A, as one decreases the amount of moderathe total mass genersl.lydecreases, and

systems with little or no moderation may have low weights. Bare critical

spheres of #35 and @33 weigh 52 and 16 kg, respectively, and reflection

with Be reduces these weights even further. Thus criticality is not a

necessarily limiting factor in minimizing reactor weights, and the real

problems are seen to be (1) finding materials capable of withstanding

the high temperatures and H2 environment of propulsion reactors and

(2) designing a reactor that has structural integrity and yet has heat

transfer capable of removing the large quantities

for appreciable thrust. Fortunately, the neutron

1

of energy required

absorption cross

●

lJhfCLASSIFIEO

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UVCUSSIFIED

sections for most elements are uniformly

of fast reactors, allowing a free choice

low for the energy spectra

of materials. For exsmple,

W, Ta, and Hf, which have large resonance and thermal absorption cross

sections, can be used in bulk when desired for their refractory properties The similarity of high energy neutron cross sections for most

elements adds confidence to the numerical results reported herej and

insures that the weights need not be increased by large smounts because

of engineering details required for a working reactor. Furthermore,

since neutron mean free paths are of the order of several centimeters

for all materials at high energies, details of core construction such

as the exact disposition of structural materisl and fuel elements will

not affect criticality greatly, making it possible to predict reactor

weights knowing only gross quantities of materisls and void percentage.

The criticality calculations presented (in detail in Appendix A) were

done using multigroup transport (SNG) techniques which are based on a

wide variety of appropriate experimental critical assemblies. Some care

has been taken to approximate the effects of changing from one-dimensional

spherical.assemblies to right circular cylinders (of appropriate height

to diameter ratios) with sides and one end reflected. Heat transfer

calculationswere made by engineers familiar with nuclear propulsion

reactors, and their analyses are presented in some detail in Appendix B.

Under the turbulent flow conditions involved, the heat transferred to

the gas is in the range of 1000 to 2000 Mw per square foot of crosssectional.flow

for structural

area. Specific designs were considered with due regard

zindmetallurgical limitations based on the current best

2

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information on

therefore feel

L/h“,

gU[J n

w/~/f-&

the physical properties of the materials involved.

that the reactor weights and powers presented are

realistic, though definitely not final, and that the technology is

feasible to the extent discussed for each reactor type. These results

appear to offer a sufficient advance over present capability that there

is considerable leeway (factors of 2 or more) in both weight and power

before the concept becomes unattractive. A number of special problems

associated with fast reactors are considered.

BD 0y02-W Reactors*

As we have seen, the primary problem in propulsion reactor development is finding suitable materials. For the Dumbo program, cermets of

U02 dispersed in Mo andW were extensively studied. The thinness of

the foils (x.00j inches) limited loading to about 20 vol. ~ U02 in

the cermet. Early calculations (1,2) indicated Be-reflected fast

reactors would be interesting at about ~ loading, and it is now felt

that this is feasible in thicknesses of the order of .04 to .08 inches.

The physical, mechanical, and chemical properties ofW metal are fairly

weld.known, and methods of fabrication are being investigated. A

tentative reactor design based on loaded plates which also serve as

structural metiers with a small additional amount of W metal structure

has beeu selected. Twelve cm of Be at 75% of full density is used as

reflector in all fast reactor studies presented here. This provides

k

Nomenclature: We use “25” to denote U235,

9

to denote a mixture of

93.5?$u235 + 6e511u*38, “23*’to represent @ 3, and U for uranium in a

general sense.

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fairly good reflection of the high energy neutrons, with some power

peaking at the core edge due to return of thermals. while this pe~ing

may be removed by differential loading of the outer fuel plates or

placing a thermal neutron poison at the interface, loading of the

reflector is now being considered for this and another reason: the

heat transfer from a hot wall.to a fluid becomes poor if the fluid is

at a very much lower temperature, and so one would like to get an

appreciable amount of heat into the gas before it reaches the hot core,

raising the gas a few hundred degrees above zero Rankine.

The melting point ofW is 3370°C,but its mechanical properties

deteriorate at somewhat lower temperatures. Creep under the stress of

the pressure drop through the reactor appears at present to be a limiting

factor for the current design. For a given engine, both the heat tmmafer coefficient and flow rate are roughl.yproportional to the operating

pressure, end so one can reduce power to obtain luwer pressure drop

stresses and thus raise the maximuM operating temperature as limited

by creep in the metal. The maximum exit gas temperature is thus dependent upon design details and probably lies in the area of Z?ZOO~ 300°C.

Bleedout of uranium will probably not be a problem at these temperature.

The results of calculations (3) for w U02-loaded W are shown

in Figure 1. There is a possibility of increasing loadings to 5@,

and the effects of such an increase are shown also. Table 1 gives

approximate weights and powers for several cases. The reactor weight

includes not only core and reflector but pressure shell (200-300 pounds)

and 100 pounds for miscellaneous items (e.g., control system motors).

4

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Table 1

OY02-W Reactors

vol. $ Core Diam. Core +

0Y02 (%) (in.) Refl.

(lbs)

Misc. + Reactor

Press. SheIl Total

(lbs) (lbs)

$ -220 20 2500 400 2900*

165 15 1765 300 2065

190 16 1700 350 2050*

% 140 14 1250 300 1550*

50 275 20 245o 400 2850

Power

(Mw)

1000

1000

200

2450

*

By interpolation.

5

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4000

3000

2000

1000

—

0 1000 2000

POWER (MW)

Fig. 1 Weight vs. power for Oy-W reactors. Reactor weigh-t = core -Ireflector + pressure shell + 100 lb miscellaneous.

6

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C. Carbide Reactors

The carbide reactors present

difficult to assess at this t:ne.

a more complicated picture which is

They appear to offer luwer weights

and higher performance than cermets, but their technology is virtually

unexplored. This class of substances includes the highest melting

point solids, which fortunately also appear capable of holding uranium

at these high temperatures}

temperatures which might be

reactors. A certain amount

thus representing the ultimately highest

obtained with solid nuclear heat exchanger

of experience has been gained with one

member of this class, ZrC (M.F’.=

on this material.

As a result of work done for

studies of the UC-ZrC system were

carbides, these form a continuous

melting points as shown in Figure

3525°C), and so our results are based

the plasma thermocouple experiment,

conducted. (4) As do most metal

series of solid solutions and have

2. Although a number of pieces of

50-50 and 30-70 vol. % UC-ZrC have been made (and even subjected to

neutron fluxes), their physical and mechanical properties exe imperfect

known, especially as they might be affected

scale production of the material.

The first complication which arises is

by the techniques of

the

positions should be considered for reactor use.

and related mechanical.quantities increase with

so does the reactor weight, and one must choose

possibilities. We have considered 50-50vol. $

composition which will give both low weight and

question of what

largecomWhile the melting poin

increasing ZrC content,

from a spectrum of

(M.P. = 2’i’’i’5°C) as a

good exit gas temperatu

‘7

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0

N

0

m

0

*

0

In

0

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0

ro

OY

o

(20)”d”UU

8

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and base most of our results cm this. A systematic study has been made

for various compositions. (5,6) Because of the lack of information

on the mechanical. properties Of this solid solution, a very tentative

conservative design was adopted based on (.04” x 2“ x 2“) flat fuel

element plates supported by a W structure which occupies 10$ by volume

of the core. (7) This introduces the complexity of compatibility of

theW structure with the fuel. AW-ZrC eutectic temperature of-,2800°C

seems to be the limiting factcm as well as creep in the W. Further

increase in temperature may require advancing the carbide technology

to the point where it can be used structurally as well. The existing

information indicates U retention is quite adequate for propulsion

reactor use. A materials development program is currently under way

at Los Alamos to investigate carbide properties. Reactor weights are

appreciably better than the cermet system, being -1300 pounds for 1000

Mw and 900 pounds for 200 Mw, including pressure shell and 100 pounds

extra. Figure 3 and Table 2 give a number of results.

Table 2

UC-ZrC!Reactors

Comp ● Core

(vol.%) (g) Diamo

(in.)

50-50 95 u.

50-50 145 15

50-50 260 20

Cc,re Core + Misc. + Reactor Power

(1.bs) Refl. Press.Shell Total (m)

(lbs) (lbs) (lbs)

- k)o 640 260 900 ‘ 200

6&) 1060 300 1360 1000

1520 2210 400 2610 2540

Let us consider the ultimately best possible perfomnance (in terms

9

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3000

2000

1000

I I 1 I I

I I 1 I I

I 1 I

I I I I I I I I I I I 1 I

Fig.

0 1000

POWER (MW)

3 Reactor weight vs. power. 50-50 vol. $

of core as W structure. Reactor weight

pressure shell + 100 lb miscellaneous.

OyC-ZrC fuel; 10 vol. $

= core + reflector +

10

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of exit gas temperature) obtainable from carbide systems, assuming

they can be made structur~ly self-supporting. Both Hf(!md TaC

melt at 3800°C, snd a solid solLutionof composition 4-1 TaC-HfC

melts

small

alter

at 3930°C,the highest known melting point. Presumably, relatively

percentages (N2@) of UC (M.P. = N24~00C) will not drastic~

the physical properties of these compounds, end hopefully the

ursnium retention will also be adequate. A general examination of highmelting carbides containing UC should be conducted. A greater increase

in weight would probably result from decreasing the UC concentration

rather than substituting HfC for ZrC. A method of avoiding this weight

increase by use of &’33isdisrussed . in Section III.C. Criticality

calculations are being made for HfC and TaC reactors. Criticsl

assemblies and replacement measurements are under way for UCn bare and

Be-reflected cylinders. Present reactor design emphasis is on obtaining

a workable, moderate temperature (2200°C exit gas)

the concept as soon as possible rather than to try

possible temperature immediately.

D. Problems of Fast Reactors

As with any untried scheme,

defined at the outset. llanyare

fast reactor to

for the highest

a number of the problem areas can

general in nature and applicability,

test

be

such as the control of a fast reactor, while others depend upon specific

designs and materhlso We will.mention those of the former kind

apply particularly to this class of reactors, rather than review

the problems of nuclear rockets here, and try to point out those

11

which

of the

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latter which appear

The design of power

megawatts per cubic

most significant, indicating avenues of solution.

plants operating in the range of hundreds of

foot is obviously no mean task sndwilJ. require

much excellent engineering work.

Concept-, fast reactors differ from Kiwi systems in that the

average neutron energy is high} the prompt neutron lifetime is smallerJ

end they require considerably less non-fissile material. Minimum weight

graphite systems have intermediate neutron spectra, about the same

amount of fissile material, and relatively few thermal neutrons. Thus,

the differences are quantitative rather than qualitative, though one

should by no means minimize them. This difference comes in controlling

the reactor, especially with regard to prompt criticality.

In all normal operation of reactors, the time dependence is determined not by the prompt neutrons (with lifetimes .001 sec or less)

but by the delayed neutrons which have an average lifetime of 14 sec

and an abundance of

lifetime of 0.1 sec.

periods for reactors

is the same for both

at prompt critical.

.0075,giving all neutrons en effective aver%e

It is the latter number which determines reactor

operating below prompt critical, and this number

fast and thermal reactors. The difference comes

The prompt-neutron lifetime for Kiwi B is estimated

to be 5 x 10-5 see, within a factor of 2, which hardly makes the reactor

controllable at prompt critical. The fast reactor prompt-neutron lifetime is much smaller, perhaps of the order of 10-7 sec. While prompt

critical reactor excursions exe difficult

time and lack of a large mass of material

to predict, the shorter lifeto absorb the energy release

E!

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make the fast reactor excursion more likely to result in fusion and/or

vaporization of a portion of the reactor. Thus, control is an essentis3

problem area for fast reactors.

The hydrogen reactivity and startup problems are similar to those

of Kiwi B. The introduction of’a mass of liquid hydrogen into the core

can cause a large increase in reactivity. While the worth of hydrogen

per unit mass is higher for fast reactors, the total void is less because

of the smsll size of fast reactors, and the maximum reactivity rise

is about the same for both systems. The worth of the hydrogen apparently

varies with position in the core and with reactor type, the tungsten

reactors being less sensitive than carbide systems. This problem will

have to be solved for any nuclear rocket, though it may be more severe

for fast reactors.

We will now mention a number of technical design problems. First,

there are few elements which are good neutron poisons at high energies,

and the reactor core is at a very high temperature, making control by

means of absorbing rods run into the core appear impractic~. Several

schemes have been considered, including removal of fuel rods, poisoning

the side reflector, and moving the inlet end reflector. The last seems

the best, being mechanically possible and apparently providing adequate

control. There is virtually no temperature coefficient of reactivity

other than that due to thexmml expansion of the reflector.

It is desirable to have the radial power distribution flat or

adjust the gas flow such that t:he@tit gas temperature is uniformly high.

A truncated cosine power distribution holds over most of the core, with

1:3

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a rise at the edge due to slowed-down neutrons returning from the reflector. Variable loading, a thermal neutron shield, or fuel element

spacing can cope with the radial distribution. A more serious problem

of this type appears at the inlet end} where peeking occurs and the

heat transfer mechanism is insufficied. to transport dl the energy to

the cold gas. Loadhg the reflector with fissile material is being

considered to solve both problems simultaneously. The decrease in power

density at the unreflected end is what is desired to obtain the maximum

exit gas temperature, and this presents no problem.

One must maintain the structural integrity of the core against the

accelerations and vibrations attendant to flight end yet have sufficient

void and smald.nessof hydraulic diameters for good heat transfer. The

Be reflector must be thermally insulated from the hot core. The carbides

appear somewhat brittle at low temperatures, while their high temperature

ProPefiies @re sti~ largely ~-. -sten is limitedby creep at

high temperatures. These and other engineering difficulties must be

overcome before fast reactors are a reality.

-f--~. u=%EAcro Rs

A. Introduction

The neutronic properties of &’33 are much superior to those of Oy,

as can be seen from comparison of the bare sphere critical masses of

16 and 52 kg, respectively. Thus, fast reactors can be scaled down in

weight by factors of 2 to 3 when the Oy is replaced by 23, as has been

14

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confirmed by

sections for

energies of

weight with

temperature

calculations using the best available multigroup cross

#33 ● ‘Thissuperiority extends tothe intermediate

minimum weight graphite

23, as has been pointed

carbide reactors may be

The major disadvantage of *33

reactors, which can be halved in

out. (8,9) Lighter weight, high

~de best with &330

is the activity of a contaminant

(&’32) associated with its manufacture, which results in greater difficulty and expense in its production and use.

There are ways to reduce this contaminant or to handle the material

while its activity is low, as will be discussed in Section 111.E.

However, since its chemical, physical, and mechanical properties are

identical to those of 25 and 28, these materials can be used to develop

most of the technology required. me #33 reactors will.follow as a

direct extension of the Oy reactor experience. It is important to

recognize now the capabilities that nuclear reactors can have later.

The fast reactor and #33 deve].opments should extend the possible

domain of nuclear heat exchangers into areas where they have not been

given much consideration because of the assumed large minimum reactor

weight o

B. 23 02-W Reactors

Using the same design principles as in Oy-W reactors, $33 on-w

reactors can be made at one-holf to one-third the

power. Otherwise, statements concerning the cermet

equally well here. The weight reductions should be

15

c

weight at the same

reactors hold

independent of the

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
particular design. Results for two cases of M losding are given

in Table 3 and Figure 4, together with estbates for the 5@I loading.

The W loading gives a weight-power relation close to that for OyC

reactors. Typical values are lh pounds total for lCOO Mw and 83o

pounds total for 200 Mw.

Table 3

#330 .T#Reactors

2

Vol 0$

2502 (:;) Co;y:.

●

40 86 16

40 4411

50 -75*

50 -3P

Core + Misc. + Reactor

Refl. Press. Shell Total

(lbs) (lbs) (lbs)

1070 330 1400

610 220 830

960’

620*

Power

(Mw)

1000

200

1000

*

Estimate based on Oy ~ VS. 5@ loadings.

.. &33@rbide Reac.ors

nzz

One may use &“ in carbide reactors either to further reduce

their weight or to obtain higher melting point fuel elements.

Consider weight reduction first. The results indicate it is

possible to make reactors (5C-50 23C-ZrC, 10% W) weighing only 950

pounds for the 1000 Mw (50,000 pounds thrust) level and to make 200 Mw

reactors weighing only 500 pounds

pounds for miscellaneous extras).

16

(including pressure shell and 100

These weights are so low as to

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3000

2000

.

—.

,1 r’

/

/

/

/

/

/

/

/

/

o

4 Reactor weight vs.

core + reflector +

1000 2000

[>OWER (Mw)

power for U233 0 -bl reactors. Reactor weight =

pressure shell +2100 lb miscellaneous.

:L~

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effectively eliminate reactor weight as a serious limitation on the

use of nuclear rockets. Even the weight of shields, if such are

required, is reduced considerably, owing to the small reactor size.

The OyC reactors are already so light in weight at 1000 Mw that,

rather than save only a few hundred pounds by using 23, one can use it

to raise the melting point several hundred degrees and thus greatly

improve specific impulse, assuming the structural problems of all.

carbide cores or the W compatibility problems have been solved. A

calculation for the 1000 Mw sized reactor has shown-that the 50-50

OyC-ZrC fuel (M.P. = 2775°C) is neutronically equivalent to an equal

volume of 22 vol. ~ I?33C-78~ Zrc (M.p. = -~go”c), which melts 315°C

higher. This mixture weighs only 81% of the equivalent Oy fuel.

Similar results may be expected with other refractory carbide solid

solutions. By comparing the weight-power relationships, we can see

that these low weight carbide reactors, including those using Oy, are

heat-transfer-limited and that

fraction decreases their power

in Table 4 and Figure 5.

m.

reducing their weight by any appreciable

correspondingly. The results are shown

#33C-ZrC Reactors

Vol.$ Core Core + Misc. +

(:;) :;j

Reactor Power

23c (lbs) Refl. Press. Shell Total (Mw)

(lbs) (lbs) (lbs)

50 k2 10” 195 320 180 500 200

50 15 420 690

E

260 1000

2P 500 250 ?% 200

22-E 64 870 300 1170 1000

*

Results estimated from 50-50 OyC reactors. The effect of increased exit

gas temperature upon power level is neglected. ld W structure is retained.

18

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2000

0

/

ESTIMATE FOR 22 VOL. ‘/o

23C FROM oyc

/

/

/

I I I I I I 1 I I

1000 2000

POWER (MW)

Fig. ~ Reactor weight vs. power. U233 C-ZrC fuel; 10 vol. $ of core

as W structure. Reactor weigh< . core + reflector + pressure

shell + 100 lb miscellaneous.

19

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.. #33in Graphite Reactors

Present designs for Kiwi B are based on having half the graphite

loaded with -b mg/cc of 0y02, while half is unloaded end used

structurally. This represents C/#35 ratios of 80 for the loaded portions and about 16o overall. As has been pointed out, (10) if one

could load all.the graphite, the reactor weight could be reduced to

75% of the present value, orto about 6000 pounds. It has been observed (8,9)that the weight of a given design can be hsl.vedby the

useof#33in place of Oyatthe same loading. Using the ratios

derived from Figure 6 for solid graphite spheres (these ratios are

expected to hold approximately for cases with void and reflection), we

can estimate minimum weights for various graphite reactors. The results

(Table 5) for pwer are nominal vslues scaled to a power range expected

for the Kiwi B weight.

Table 5

Graphite Reactors

Fuel $ Loaded Averege Approx. Power Range

Graphite c/u Weight (Mw)

(lbs)

25 50 160 1OOO-2OOO

25 100 m 6000 800-1600

23 50 160 4000 650-1300

23 100 80 3000 500-1000

E. Problems Associated with#33

#33 differs frm oralloy in

20

that it must be made artificially at

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IQOOO~1 I I I I I I I

m-J

.

m

(n

a

z

8

E

MT(c/lJ=80)

[

.74 FOR

MT(c/u=160)= .77 FoR

6

1

MT (23)

[

.46 FOR

MT(25) = .48 FOR

4

25

23

C/ U=160

C/U= 80

/--” /

2 –

,/

1,000

8

6

~

F

“~x.

4p-”~% \

●

●

●

2 –

\

●

100 I I I I I I I

MT(25)

MT(23)

MC(25)

MC (23)

10 30 80 100 160

c/u

Fig. 6 Total and fissile masses for

spheres using u235 and u233.

21

uranium-loaded

300

solid graphite

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the cost of one neutron per atom and that it is radioactive both

naturally and due to associated impurities. Details may be found in

reports on#33 (11.,12)butthemain featu.reswllLbe revieWed here.

pure F33 ~s a soft y component of about 15 kev giting a surface

dose (excluding the M x-ray component) of about 1.5 rep/hr, which can

be reduced to 0.1 rep/hr with gloves and a few roilscoating~ The 1.5

rep/hr value is comparable to 2.2

statices.

The real difficulty is a 2.6

rep/hr for Pu under similar circumMev y-ray from the decay products

of the #32 impu.rityformed with the t?33. Briefly, this decay chain

(4n series) is

228 a ~a224* :<? - BJ212 cY(34j4) *pb208 l?32 +-* ~ 1.9 y+

fast fast * ‘1W8 ?%

The Pb208

208 is formed from T1 only in its 2.6 Mev excited state and is

228

the source of the trouble. The 109 ~ hslf-life of Th centrols the

buildup of the activity for short times (<5 yr). The activity thus

builds up (linearly for about one year) from zero at the time of sepa232

ration (casting date) of the U from the Th ~d &28

. The amount of

l?32 impurity is strongly dependent upon the conditions of formation of

the t?33 and the methods of separation and ranges frcm 2 to 103 parts

per million. The major mode of fonnation of @32 is fr~ the reaction

~232 (n,2n)Th231 folJ_owedby ~ decay and neutron capture. The n,2n

reaction has a threshold of 6.35Mev, and so could be considerably

22

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reduced by separating

ator. Existing small

per million $32’ were

the breeding material from the fuel by a moder233 quantities of U containing 2 to 10 parts

233 (27 d~ half- probably made by separating Pa

life) and letting it decey to U

233● pa232

, the

a lo3 day half-life.

Thus, to minimize the activity of $33 and

one cen control its method of fcmnation and can

parent of I?32, has

its L?32 contaminant,

process it into fuel

228 elements quickly to avoid the buildup associated with Th formation.

Once the reactor has been run at power, the fission product activity

will dominate.

However$ while individual fuel elements

handled prior to a power run, the reactor as

will be capable of being

a whole will be somewhat

active, and It may be difficult to work in

Normally$ the reflector end self shielding

sity for heavy shields around the reactor.

contact with the core.

should eliminate the necesIn the event of a launch

pad accident for a cold reactor, #33 would be a much greater problem

than #35 because of the attendant activity. l“he~tent of this prOblem depends upon the likelihood.that the core material would be dispersed (e.g., by the chemical explosion or possibly even combustion of

the fuel elements themselves).

#33 and Pu have smaller fractions of delayed neutrons than #35,

the values being .30, .23, and .75per 100 fission neutrons> respectively.

The distribution of precursors results in average lifetimes for delayed

neutrons of 16.7,14.4, and 14.1 see, respectively, for #33, Pu, and

&’35which ) withthe abun&nce afdel~ed neutrons, gives averwe

23

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lifetimes of all neutrons of .05, .033, and .1o6 sec.

While this makes control more difficult for #33 .r p. fueled

reactors, it does not make it infeasible, as evidenced by the existing

Pu fast critical reactors and assemblies.

FinaSLy, &33 is not available in quantity, and several years and

considerable expense would be required for its production. Because of

these considerations, it appears that the

pulsion art will be advsnced to a working

usedO A second-stage engine might be the

state of the nuclear prolevel before $33 is actually

most likely candidate for its

initial test, especially since upper stsges are the

of smell reactors, and the light weight would allow

relatively small boosters (Thor or Atlas).

most useful domain

it to be put on

IVO DISCUSSION

A. The Function of Lightweight Reactors

The domain of lightweight reactors can be seen in perspective by

comparison (Figure 7) with the graphite system which leads to Condor,

a 10,000 Mw reactor weighing about 20,000 pounds. Condor is capable

of placing 25,000 pounds of psyload into orbit with a h,000 pound

single stage, a mission equivalent to that of the three-stage SaturnTitan-Centaur rocket. Kiwi B is, to a certain extent, a small-scale

model having one-fourth the power-to-weight ratio of Condor. Thus,

Kiwi B besxs the same relation to Condor as the 200 Mw fast reactors

do to the 2000 Mw class. The smaller models, while not opttium for their

24

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20

19

18

17

16

15

14

13

12

II

10

9

I I

“r

8

7

6

5

4

3

2

I

o

/

REACTORS

~ /

‘ESTIMATE

‘/ KIWI B;

/C/U= 160

/+

-/ ~KIWl B;

>0 C/U=80

u233_GRApH,TE

Y

FAST REACTORS

f

2 4

Fig. 7 A com-pari.son of the

graphite systems.

6 8 10 12 14

POWER (103MW)

weight--powerdomains of fast reactors and

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type, nevertheless can perform useful functions.

We see that for graphite reactors, the weight cannot be appreciably reduced below that for the 1000 Mw reactor, and this vslue is

then a rough lower limit for the useful power range, other things being

equal. This ssme state is reached for the fast reactors at about

200 Mw. We have done very few mission studies thus far and cannot

comment at length upon the possibilities of such a power level, but

a general study (13) of missions starting from earth orbit has indicated that thrust-to-mass ratios of 0.1 are quite adequate under many

circumstances. Thus, a 200 Mw reactor (10,000 pounds thrust) could be

used to propel a 100,000 pound stage which has been placed in a low

earth orbit. The thrust level is high enough for soft landings of

smaller vehicles or sfter a large portion of the propellant has been

used as opposed to that of ion or plasma rockets, which have very low

thrusts. Fast reactors appear at present to be quicker to develop than

electrical systems. One thing can be gsined by reducing the power,

which is higher exit gas temperature and consequently higher specific

impulse. The 1000-2000 Mw level appears best for fast reactors, their

having a thrust of 50 times their weight. It is difficult to say what

the upper power limit is for such reactors. One may be limited by

structural considerations to a maximum void fraction of about 0.6,

which limits the size for a given core composition.

We have investigated scxneapplications (14, 15, 16) for fast

reactors in the 1000-~ Mw level and find that an increase in payload

of about 5CW0 pounds over Kiwi powered rockets is possible at the same

26

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exit gas temperature simply d~e to the lighter weight, with further

increases if better performance can be obtained from fast systems.

One application for which Kiwi powered rockets seem marginal$ i.e.$

as second stages on Atlas-class boosters, seems ideal for fast reactors

in the power range of 600-1300 MW. Such a ccnnbination(Atlas + fast

reactor stage) might equal the 1)000}000 pound Saturn three-stage

chemicsl rocket performance, at much lower cost.

For small vehicles, radiation at the payload may be an important

factor. This depends strongly upon the vehicle geometry and duration

of the run, so it is difficult to make quantitative statements without

a particular situation in mind. However> some general statements csn

be made based on estimates for a 1000 14w}300 sec run and some genersl

considerations. Radiation effects in an unmanned rocket will be negligible except possibly to semiconductors and} of course, radiation

detectors. The propellant acts as a shadow shield, and the total dose

at the payload is very sensiti(e to the amount left in the tank at

reactor shutdown time. In a manned vehicle the biological dose for

this case is of the order of 103 rads} and some form of shielding would

be necessary even for a larger rocket. Manned rockets would probably

have a storable chemical final stage, and its propellant could be

utilized as a biological shield. Because of their higher density and

luwer weight} fast reactors have much smaller diameters than Kiwi B

and would thus require much less shield weight should shielding be

necessary.

27

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B. The Development of Lightweight Reactors

A comparison of the various types

8) gives only part of the picture. We

~ense necessary to develop each type

in terms of performance.

of lightweight reactors (Figure

must also consider the time and

and its ultimate possibilities

The Oy-W systems appear at present (December$ 1959) to be easiest

and

the

quickest to develop because of the experience in fabrication and

knowledge of the mechanical properties of the material. They have

I

an absolute upper limit of 3370°C (M.P. of W) for the exit gas temperature, and a practical limit 300-1000°C less than that owing to

structural limitations.

The UC

information

tions, even

reactors, though lighter in weight, suffer from lack of

concerning the physical properties of carbide solid soluof the UC-ZrC system. As presently conceived, they require

W structural support members, which limits their achievable temperature.

Development of carbide technology to the point where the carbide is

self-supporting and the use of HfC-TaC-UC solid solutions promise the

ultimate performance for solid nuclear heat exchanger rocket engines,

having an absolute upper limit of 3930°C(M.P. of 1 HfC-1 ‘TaC).

The value of high exit gas temperature can be seen as follows.

Almost any practical nuclear rocket engine”will operate at 2000°C,

giving a specific impulse of about 750 sec compared to 375 for very good

chemical rockets. For a simple gas, the specific impulse is approximately proportional.to the square root of the temperate, and so increasing T to 3000°C will.raise the impulse to ne~ 900 sec. At this

28

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400C

3000

+ -r I

‘23-GRAPHITE ; C/U= 160

I I 1 I I I

/

/

/

7’

I I I I I I I I I I I I I

1000 2000

POWER (MW)

A comparison of weights for the various reactor types. Weights

include pressure shell + 100 lb miscellaneous.

29

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point, hydrogen dissociation begins to enter the picture, and by

3500°C, with appropriate pressures, the specific impulse might be

raised to 1050 sec or more. This is the motivation for seeking the

ultimate in exit gas temperature.

On a short-term scsle$ we seek to demonstrate

fast reactors as quickly as possible. In 1960,we

the feasibility of

hope to evaluate

carbides and cermets and decide which offers the best opportunity for

an early feasibility demonstration. While studies will continue on

both types of materials} the main light-reactor program will aim tow~ds

construction of a 1000 Mw fast reactor which will be first tested at

the 100 Mw level. This plan represents a considerable extrapolation

and is quite subject to change.

It is relatively easier to evaluate the situation with regard

the use of U233 in propulsion reactors. It is clear that, where a

cept employing Oy works> the corresponding reactor using 1333 will

to

conalso

be feasible snd offer considerable weight and/or performance advances.

It is equally clear that complications arise owing to the activity and

availability of the material. The activity of #33 and its contaminant

I?32 necessitates additional cost and effort in fabrication, makes subsequent manipulations in the core more difficult} and adds the problem

of contamination from accidents prior to full power operation.

Thus, it would be much easier to use F33 in a proven reactor type

than to develop a new concept with it as an added complication. Nevertheless, these problems are by no means insurmountable. The Kiwi

system is sn important case in point. Much of the technology has

30

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already been developed and to some extent, the Kiwi A test proved

feasibility. A continuing series of Oy-fueled test reactors leading

to a breadboard engine will further advance the technology, and it

is hoped will.lead to an early flight demonstration of a graphite

reactor. An &)OO pound 1OOO-2CIOOMw reactor is only marginally useful as a single-stage,

snAtlas or Titan. At

would weigh, one might

ground-l,aunchedrocket or as a second stsge on

MOO pounds, which is what a fi33-fueled reactor

expect a considerable improvement in the capability of a nuclear rocket, especially as a second stage on Titan or a

lsrger booster. This capability should be explored and evaluated in

the light of the added problems associated with the use of $33 and

the possibility of the smaller Oy-fueled fast reactors beccxning operational in time to compete with graphite systems. On one hand, we have

at least a two-year lead time required before large quantities (4100 kg)

of l?33 could be produced, while on the other, the fact that fast

reactors are as yet completely untried. One should keep the possibility

of e, #33-graphite reactor under continuous scrutiny, for while it does

not appear optimum in the long run, it may represent a useful rocket

reactor over an intermediate period, especially if lighter systems are

late in materializing. It may be worth pointing out here that Pu, while

neutronicaJdy slightly superior to t?33 and much more readily available,

does not have as favorable physical and chemical properties as uranium

(e.g., melting points of oxides and carbides) and would require development of a new technology (e.g., loading of Pu oxide in graphite) with

active material.

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The most likely Pu

dispersed in W, similar

reactor might be one with PU02 (MoP. 22~0C)

to U02-W cermets. We have exsmined the

criticslity of such PU02 cermets with 35, 25, and 20 vol. ~ loadings

(17) md find them good possibilities, even up to 10,000 MW or more

if the PuO. can be retained in the fuel element in a molten condition.

z

The cost of the Pu for

(-$8,000,000) compared

booster which could do

the latter case (10,000 Mw, 500 kg Pu) is small

to the fabrication cost of a large chemical.

an equivalent job, and also small compared to

other costs

material is

In the

for a nuclear missile. Thus actual cost for fissionable

not prohibitive.

long view, I?33 appears as a natural choice as the fuel

for lightweight reactors as a natural consequence of experience with

Oy fast reactors. Hopefully, the thorium breeding program will

eventually result in extensive experience with #33 and production

of the large quantities required for economic consumption of the

world’s supply of fertile material.

v. SJJMMARY

1. The fast reactor concept leads to

reactors for power levels of 200-2000 Mw.

lightweight nuclear rocket

Power densities of the order

of 1 Mw per pound open a new area for upper stage use of nuclear rockets.

2. Because of the uniformity of high energy cross sections, fast

reactors may employ almost any element in bulk, allowing the use of

the

and

most refractory materials and leeding to high exit gas temperature

specific impulse.

32

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I

3 ● WO types of fuel materiels are being

U02-W cermets and UC-ZrC solid solutions. The

ceived more study to date and seems capable of

The carbide materials offer much lower weights

but suffer from a lack of information on their

properties.

offering the

rockebs.

~+. The

fast reactor

exsmined for such use:

cermet fuel has requicker development.

and higher temperatures

physical and mechanical I

Carbides include the highest melting solids known,

ultimate performance for solid nuclear

main problem area for fast reactors is

neutron kinetics are the same as those

heat exchanger

in control. While

for thermal reactors

while operating below prompt critical} excursions above prmnpt critical

are more likely to lead to fusio~ or vaporization due to the shorter

period snd the smaUer amount of material present to absorb the energy

released.

~. The use of #33 in place of Oy can reduce reactor weights by

factors of 2 to 3 for intermediate and fast reactors or, alternatively,

can be used to increase the exit gas temperatures for lightweight carbide reactors.

6. Because of radioactivity associated with &’33 and its contaminant #32, it is somewhat more difficult and more costly to use,

especially in development work. Thus, #33 is likely to be used in

fast reactors only after

the

cell

ful

fissile material.

70 The use of #33

they have been made operational.with #35 as

as a fuel in small (1000 Mw) graphite reactors

reduce their weight to 3000-4000 pounds, making them much more useas motors for second stage vehicles. One must consider the lead

33

APPROVED FOR PUBLIC RELEASE

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time required for production of the necesssry &33 if such reactors

are to be constructed in a useful time period.

REFERENCES

1.

20

3.

4.

5*

6.

79

8.

9.

10 ●

U.

12 ●

13 ●

Cooper, R., T-1106, “Fast Reactors for Nuclear Propulsion,” April 2,

1959 (internal document).

Cooper, R., T-1.117

!

“Further Fast Reactor

(internal document .

Kirk, W. N-3-639, “W-U02 Fast Reactors,”

document!.

Witteman, W., Leitnsker, J., and Bomnn ~ M.$ LA-2159j ‘The

1959

(internal

Solid

Volubility of Uranium Monoc&rbide and Zirconium Carbide,” October 15,

1957.

Kirk, W., N-3-615, “Fast Reactor Parameter Study,” September 8,

1959 (internal document).

Kirk, W., N-3-619, “Fast Reactor Performance,” September 23, 1959

(internal document).

Newman, Ho, Blevins, D., and Kirk, W., N-3-624, “Fast Reactor

Conceptual Design Study,” September m, 1959 (internal document).

Hsnsen, G., N-2-1185, page 22, February, 1959 (internal document).

Cooper, R., T--ll44,“ReducedWeight Kiwi Reactors Using 933, I,

November 20, 1959 (internal docmnent).

MacMillan, D., and Orndoff, J., Private Communication.

Hsll.,J., in TID-7521 (Pt. 2), “Papers for Thorium-U233 I@omtion

Meeting Held at Wilmington, August 3, 19’53,“ issued February, 1957.

Devaney, J., LA-1892 “Radiation Intensity From Spheres of $33

Contaminated with U2~2,” Februm?y, 1955.

Brueckner, K., in “Topics on Thrust and Orbit Optimization,” September}

1959.

34

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140 Cooper, R., T-1.161

~

“Nuclear Rocket Missions I,” February 2, 1960

(internal document .

15. Cooper$ R.} T-ll&, ‘:FastReactor Powered Second Stages)” February 15,

1960 (internal document).

16. Cooper, R., T-1169, “Missions forEarlyR over Reactors (1000-~00 Mw),”

March 1, 1960 (internal document).

17. Cooper, R., T-1170

J

‘@u02Propulsion Reactors,’’March 2, 1960

(internal document .

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APPROVED FOR PUBLIC RELEASE
APPENDIX A

CRITICALITY AND WEIGHT

Figure Al is a plot of mass (both total snd fissile material) vs.

diameter for bare solid spheres of graphite uniformly loaded with

#35 > (A1.)with thexnoderation (C/Uratio) asapa,rameter. This

behavior is representative of all light element moderators (with the

exception of hydrogen). Starting with a sphere of solid uranium, the

critical mass (fissile material) increases with the addition of C,

as the moderation lowers the neutron energies from the fast region

(neutronicall.yfavorable) toward the intermediate energy resonance

region, where the average capture to fission ratio is higher. Other

effects such as moderator scattering and dilution of the fissile

material (which affect the leakage probability) also play a role in

this region. The high energy capture in the light moderator is ususUy

very small, but heavy elements will be significant in this respect.

The critical mass goes through a maximum as the scattering reduces

leslcsgeand the moderation lowers the average neutron energy toward

regions of lower capture to fission ratios. A minimum is reached where

the neutrons are slmost completely thermslized and the critical mass

rises again, owing to absorption by the very large amount of moderator

present and in the fissile material itself. The important point is

that the total mass increases monotonically with moderation.

36

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10,000

3,000

1,000

m-J

100

30

10

I I I I I I I I I II I I I I I I I I II I I I I

I04

3000

i

91000

300 m

/

8100

/

TOTAL MASS (U+C)

“/

30

i 10

/

./.3<

10 ●100

\ ●300

I

FISSILE MASS (U235)

●0

.1000

I3000

\

/

K? ~ ’05

I I 1 I I I I I I II I 1 I I I I I I I II 1 I I I

o 2 4 6810 2 4 6 8100 2 4

DIAMETER ( IN.)

Fig. Al Bare solid spheres of U

235 in graphite; C/U as parameter.

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
There sre several items in a reactor which affect the total mass

relationship quantitatively, but not qualitatively, such as void,

reflection and non-uniform loading. Addition of void for gas

passages increases the total and critical masses inversely as the

square of the averege density for bare reactors. Reflection decreases

the critical mass and is most effective for small reactors, where the

total mass maybe appreciably decreased, especial.lywith a low density

reflector (such as Be) on a dense core. Non-uniform loading can affect

masses in either direction, though in propulsion reactors where one

tries to flatten the power distribution this results in increased

critical masses.

We see, then, from Figure Al that to have a lightweight reactor

we would like as high a ratio of fissile to moderating material as

possible within the constraints of material, structural, and heat

transfer considerations. The optimum regime of graphite propulsion

reactors is in relatively large systems (of the order of 10,000 Mw

and 20,000 pounds), but many conditions caused the Laboratory to begin

with a graphite reactor as small es practicable. It was found possible

to make fuel elements with loadings representing C/U ratios of about

80, and the need for unloaded graphite structure in the present design

(Kiwi B) incre=ed the average C/U ratio to about 16o. Note that this

causes Kiwi to be sn intermediate rather than thermal reactor, requiring

a relatively large criticsl.mass (“lb kg Oy in practice). This design

is limited by the maximum loading of graphite, and to go to the lighter

weights theoretically possible requires a new fuel material, e.g.}

38

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
a carbide solid solution. Ideallyj pure solid fissile material would

give the lowest weight, but materials} gas void} and heat transfer

area force a compromise at higher C/U ratios. This must be examined

individually for each material; e.g.} Zr has a low absorption cross

section in the resonance end fission energy regions} while Hf has

appreciable absorption, and large HfC/UC ratios may not be practical.

Basis of Calculations

Most of the calculations were made using a one dimensional Sk

transport code employing 20 to k space points and 13 energy groups.

The cross sections employed were checked against a wide variety

of experimental criticsl assemblies (A2) and replacement measurements

in fast spectra. (A3) These included Oy spheres, bare snd reflected

withl?%, Be, W,etc., andmixtures of Oyand C. Uranium and Zr

cross sections were transcribed from Hansen’s work, (Ah) and various

theoretical and empirical correlations were used where data was insufficient.

The cloudy crystal bti model.(A5) was used to obtain high energy

transport cross sections and the statistical model for inelastically

scattered neutron distributions. (A6) The energy groups covered

energies down to thermal, and they are listed in Table Al, along with

the spectra and fission rates for a typical fast reactor. By comparison with an Oy sphere reflected with 2 inches of Be, we see that

the propulsion reactors are truly fast.

39

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
0

=1-

lQ

ii

l-l

40

APPROVED FOR PUBLIC RELEASE
The one dimensional transport code was used for straightforward

calculations such as variation of core composition, reflector thickness

and density, fission distributions, reactivity worth of H , etc. To

2

check a few of the more critical points, i.e., the control worth of

a movable inlet end reflector and the extra core material required in

the absence of the exit end reflector (snd to

from spheres to cylinders) we ran a series of

port calculations. (A7) In order to conserve

check the conversion

two dimensional Sk transmachine time, we collapsed the 13 group cross sections to 4 groups, based on the neutron

spectra obtained from the one dimensional calculations. The 4 group

constants gave satisfactory results for the reactivity (k = 1.006

compared to 1~000 for 13 groups) for the one dimensional check caseO

The two dimensional cases (Figure A2) showed that our buckling conversion from sphere to cylinder was conservative, that our estimate for

reflector savings was adequate, and that enough reactivity change could

be induced by movement of the inlet end reflector for its consideration

as a means of control. Power distributions for final designs can also

be evaluated with this code.

Some representative calculations for spheres

Table A2 to give the data before corrections were

are presented in

made for non-sphericity,

removal of the exit reflector, etc. Experiments are in progress to

check the validity of these cmrputations.

41

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
A. 1 dim.checkon

4 groupcrosssections

@

22.9

31.9

4 group,1 dim. k = 1.006

13 group,1 dim. k = 1.000

B. Completelyreflected

(9 cm Be) cylinder

~~64n

I

Q

i

YT

~23 36 54

L]

k = 1.038

D. Movement of

inletreflector

c. Exitreflectorremoved;

replacedby 12 cm of core

II

k = 1.033

9 cm

TT

48 57

11

Core compositionat./ccX 10-24

El

k = .971

Ak = .062

= .007/cm,-$1/cm

~295 .00588

U298 .00040

c .0139

Zr .0076

Mo .0064

FIGURE A2 TWO DIMENSIONAL CASES

42

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
Oyc

x

20

3

15

W2

15

35

35

$33C

20

w

8.3

$3302

20

32

m

67

50

20

TABLN

Representative

Core (Vol. %)

ZrC

m

20

25

E

25

w

22.5

32.5

35

ZrC

20

w

29*7

w

w

48

Mo or W

10 Mo

10 Mo

10 Mo

10 Mo

10 w

Lading (%)

40

40

50

w

10

10

10

Loading(*)

$

A2

Calculations

Reflector

(% FuU Density)

c(p=1067g/cc) ~SS Oy(kg)

% $

80 55

98

98

98

9:

75

75

75

75

E

75

75

100

100

100

R

core(m)

17.0

22.9

26.9

43.0

27.6

28.35

20.6

20.6

16.4

12.9

25.4

t

refl.(m)

8.5

9.2

11.o

0

9.2

12

12

12

13..6

9.1

15●2

21.4 u.6

14.8 SL05

8.16 7.0

909 7.1

15.2 10.0

43

wvQ/qsslFIED

+

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
LJ!’!CLASSIFIED

APPENDIXA REFERENCES

Al.

A2.

A3.

d+.

A5.

A6o

A7.

Mills, C. B., LAMS-2288 (Suppl. 1), “Physics of Intermediate

Reactors,” April, 1959.

psxton, H., LA-1%8, “Critical Masses of Fissionable Metals as

Basic Nuclear Safety Data,” June, 1%5.

Engle, L., Hansen, G., and Paxton, H., LA-l’i’@,“Materiel

Replacement Measurements in Topsy and Godiva Assemblies,” July$

1954.

Hansen, G., N-2-731.,%x Group Cross Section#(internal document).

Hansen, G., and Roach, W., N-2-E3, “Sixteen Group Cross Sections,”

(internal document).

Beyster, J. R., LA-2099,“Predictions of Fast Neutron Scattering

Data with a Diffuse Surface Potential Well,” December, 1956.

Weinberg, A., and Wigner, E., The Physical Theory of Neutron Chain

Reactors, Univ. of Chicago Press (1%6).

Carlson, B., Lee, C.~t

TDC Transport Codes,

and Worlton, J., LAMS-2346, “The DSN and

October, 1939.

44

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
● ☛

● ●☛☛ ✚ boo6**

● 8. ● 4’: :a: C99.

● OQS :0: 6*”

b ● 8 ● 41* ● ●*: 6 .

● 8

.,’ .,

● * ●*: ● OO 996 ● .* ,.

● D

‘.

:.,,/.:.

● *

::

: s:

... :

: ~a

. J

● W

o

:

s c .-.. >

● O ● ** .:,.

:

:0

● ●:0 *

‘;:;;;/&’iib

APPENDIX B* -.

METHODS USED IN PERFORMANCE ANALYSIS

The general problem of determining the relationship between

reactor size and performance characteristics is not one which can be

solved quickly with precision. However, if one is content to deal

with averages and a~roximations with the realization that the detailed

behavior and design problems of the reactor system may require con.

siderable modification of the re&iLts, very simple and straightforward

analyses are possible.

It is assumed that reactor power is limited by:

(1) Core exit Mach number

(2) ~el element internal temperature *OP

(3) Wel element surface temperature

(4) Reactor core pressure drop.

It is, of course, not alwqys possible to assign the correct meximum value to each of these quantities for a variety of reactor configurations, so it is

on a best guess as to

Mach Number

necessary to make rather arbitrary choices based

what constitute reasonable values.

The core exit Mach number

M=+=

:Lsgiven by

i~ (R’dyg)l/20

“Symbols used here are defined at the end of the

●a.

●

●

● ☛

appendix.

~IVCL4SSlFlED

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
If exit gas temperature and Mach number

;= clA~e

and since power is proportional to flow

are now fixed, then

rate for

temperatures, the Mach number limited power of a

with known flow area is

Qn

In the analysis

taken as 0.261,

C$e ●

ftied inlet and outlet

particular reactor

of the various fast reactors, the exit Mach number waE

the exit gas temperature as ~OOR, and the weight

flow to power ratio as .07 lbs/Mw-sec. Various exit pressures were

used.

Fuel Element AT

It is assumed that the fuel elements are thin flat plates of

uniform thickness and spacing. The flat plate equation:

A, . Q&

f

taken for ~ * = Q/vf

may be rewritten to obtain

8kfvf AT

Qsm

~

(.HWLASSIFIED

●O: *OO

9

● ●: ●

● *

● ** ● 9*

●

:0

●

●

●C: ::

● *● ,

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
● ☛

9 ●** : .OO9**

● ● ●°: :0: ● ● **.

● *m@ :

00: ● e.

● ● 9 .,, . .

.*: ●.:

.O: ●Q: ●:0 ● 00 . . . .O

● * ,

:: ●:

●

:.

● m : :

.. ● *m ● .* : ::.

● ● . . ●

which for a given reactor with fuel conductivity bown or assumed

and a given minimum fuel thickness becomes

Q = Cim.

Thus, if one knows or is willing to guess an acceptable fi, the internal

temperature drop limited power can be ascertained. Values for these

quantities which were used in the fast reactor studies were: UC-ZrC

thermal.conductivity, 16

20 BTU/hr-ft-°F;minimum

to 500°Fwere studied.

BTU/hr-ft-°F;* W-U02 thermal conductivity,

pkte thickness} .040inch. Values of = UP

IkiL Element Surface Temperature

The accurate determination of the maximum fuel element surface

temperature requires a knowledge c)fradial and axial power profiles and

the coolant flow distribution, ancleven then usually requires extensive

calculation. Again, however, approxhmte results can be quickly obtained

using the following empirical expression (Ref. 6 of text) which i~ores

many variables which have a more cm less negligible effect.

*-

This value was based on conductivlties of pure UC and pure ZrC. Very

recent measurements indicate conductivity for solid solutions which are

much lower (half the above value), as is the case with disordered metal

alloys for which the resistivity (both electrical and thermal) displays

a parabolic variation (x - #) with composition (x). Since thermal

conductivity is frequently the property which limits the power for a

given design, and the power is a linear function of the conductivity

for a given plate thickness, the results presented in the body of this

report are quite sensitive to this parameter. Thus different designs,

thinner plates, variable loading or other techniques might be required

to achieve the heat transfer estimated in the body of this report for

UC-ZrC reactors. (The above footnote was written by Ralph S. Cooper.)

9:0 ● ** ● *

“::“y7:o ● ;e ; :

● 00: ● 0

● 8 ● ** ● 00 ● .* :.. ● . uNCiASS/FIE

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
UNCLASSIFIED

● *9 ●

● 0

● *

● O* .*9 ● :*: ●

.m.. *O ●

● OO:. :

● O*

● O. 9 ● ●e*

● * ● O* *

● *O ● ●

● 0 ● -O ● *O .:. :- ~. ● *:a *m. .*

9 ●● -::

.0

.:OC .*

9 ● ** ●

. . . . . . ● *

TV-T

% L

TV-T = ‘120D

%

Thus maximumwall

which core length

temperatures can be computed for each reactor for

and hydraulic diameter are known.

Core Pressure Drop

Since pressure drop depends on both flow rate and pressure level,

it is not convenient to obtain an independent formula linking power

level to pressure drop for each reactor. The alternate approach is to

calculate approximate pressure drops for power levels which are otherwise determined, i.e., Mach number or temperature limited power, using

reasonable values of pressure. The formula used for these calculations

was:

.002 TmG2

AP= ml? ln~+ “OO:LO

‘2

Pressure drops of 200 to 300 psi were considered tolerable with average

pressures near 1200 psi.

~

To illustrate the use of these

with core composition 20 v/o UC, 20

formulas, we consider a UC-ZrC reactor

V/O ZrC, 10 V,O W, and ~ V/O void.

Nuclear calculations establish the core dimensions as 20.1 cm radius

and 54.4 an length or 15.8 inches diameter by 21.4 inches long. The

cross-sectional flow area is then 98.3 im2.

● ☛ 9** ●:0 ● ● ** ●

.*m

● e ● y : :.” ●00:0 ● * ● O

● * 90:●:0●0: ● 00 ● e

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
● ●☛✎ ✚ .OO ● *O

*

● ●

● ●°: :0: ●8*.

● 00. :

:0 ● *,

“* &!gl@t .*:9 ●

.-== ‘“

-—.-—

● ---

/ : ● ● .-

●

‘e. .*:@e ●

UNCLASSIFIED The Mach number li%l%~ ~%r ‘a~”16& psi exit pressure is found

to be 1~ Mw. The ~ limited power is @+ Mw for ~ u ~% and

1640 Mw for ~ = 500%. The maximum wall temperature is calculated

to

we

of

be 47&)OR.

If we assume that the fuel material oan withstand a = of 500%,

see that the maximum power for this reactor is 1400 Mw, the smaller

the Mach number and ~ limited values. At this power

pressure drop is calculated to be 305 psi for em ave~e

level the core

pressure of

1.150psi.

sunmm?L

It is quite clear that the many assumptions and

which are c!ont&inedin the methods of analysis leave

appreximaticms

considerable room

for doubt in the results. However, as is pointed out in the body of

this report, there is considerable margin for error in the calculations

before these aoncepts cease to be of interest. lhxrthermore,a number

of considerably more rigorous techniques which have been employed to

evaluate the reactors of immedh~te interest, the 1000 Mw -ss, indicate

that the approximate methods described here yield reasonably valid

results in this power range.

● 00 ● ●*. ... ... .. WX.ASSIFIED

:4$ ; L :;

9* ● mb... .:.:..● *

,A .&we;+

●. ... . . . ● m

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
Af Cross-sectional flew area, ft2

c, c,, cm Censtants

D

G

g

‘f

L

M

m

Pe$ P

&se

Q

Q!t ,

R

T, AT

Tm

Hydmmlic diameter, ft

Mass velocity, lbs/ft2-sec

Conversion factor, 32.2 @sec2

~el thermal conductivity, BTU/hr-ft-°F

Core length, ft

&ch number

Moleoular weight

Core exit pressure, core average pressure, psi

Core pressure drop, psi

Reactor power,

Power density,

Gas constant

Mw odBTU/hr

BTU/hr-f%3

Temperature, temperature difference, OR

Mean gas temperature in core, OR

T,T Gas entrance and exit temperatures, %

% %!

Tw

t

v

‘f

G

P

7

MaSmum fuel surface temperature, %

Fuel plate thickness, ft

Gas velocity, ft/sec

Fuel volume, ft3

Mass flow rate, lbs/sec

Gas density, lbs/ft3

Ratio of specific heats

● m 9** . . . ● 99* 9

●-9- “*- ; ● 9*O ● *

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APPROVED FOR PUBLIC RELEASE