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RESEARCHANDDEVE

LOS ALAMOS SCIENTIFIC

OF THE UNIVERSITYOF CALIFORNIAo LOS

.OPMENTREPORT

LABORATORY

ALAMOS NEW MEXICO

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STUDY OF THE

DISPOSAL OF A ROVER REACTOR

WITH HIGH EXPLOSIVES

(Title Unclassified)

UNCLASSIFIED

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LEGAL NOTICE

This report was prepared as an account of Government sponsored work. Neither the United States, nor the

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LAMS-2688

C-91 NUCLEAR REACTORS

FOR ROCKET PROPULSION

M-3679 (26th Ed.)

This document consists of 97 pages

.“.””-- —

135 copies, Series A

LOS ALAMOS SCIENTIFIC LABORATORY

OFTHEUNIVERSITYOFCALIFORNIA LOSALAMOS NEWMEXICO

VERIFIED

REPORT WIUTTEN March 1962

REPORT DISTRIBUTED: July 3, 1962

UNCLASSIFIED

A FEASIBILITY STUDY OF THE

DISPOSAL OF A ROVER REACTOR

WITH HIGH EXPLOSIVES

(Title Unclassified)

by

Jerry Wackerle

with AppendixB by

J. N. Fritz

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This study examines

ABSTRACT

the feasibility of utilizing a high

explosive charge projected into a NERVA engine core to reduce

it to small fragments for safety purposes. The technique described involves explosively reducing a number of scale-model

configurations, varying in certain properties from shot to shot.

The influence of these properties on obtained or expected fragment

sizes is compared through the use of empirical distribution expressions. Certain conclusions are presented regarding the

effects of scaling, explosive type and weight, graphite physical

properties, geometrical configurations, and metal parts. Some

rough estimates of fragment distributions anticipated in actual

devices are given. Data related to the dispersal of engine parts

in firing pad accidents, and some basic theoretical consideration

of the expected form of the fragment-size distribution are given in

Appendixes A and B.

.

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UNCLARIFIED

UNCLASSIFIED

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CONTENTS

Abstract

I.

II.

III .

IV.

v.

VI.

Introduction

Basic Approach of the Study

Experiments and Analysis

Comparison of Certain Factors

A. Effect of Varying Explosive-to-Graphite

Weight Ratios

B. Effect of Explosive Type

C. Effect of Change of Scale

D. Effect of Physical and Mechanical

Properties

E. Effect of Geometrical Configurations

F. Effect of Metal Parts

Estimates of the High-Explosive Fragmentation

of Kiwi Configurations

Some Conclusions and Suggestions Regarding

Future Work

Appendix A. Dispersal of One-Third-Scale Models

Appendix B. A Simple Fragmentation Distribution

I. Introduction

II. The Linear Problem

111. The 3-Dimensional Problem

Iv. Comparison with Experimental Results

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32

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57

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92

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1. INTRODUCTION

Among the various safety aspects associated with the flight

of nuclear rocket engines are problems which arise from combining

the potentially supercritical and radioactive features of the reactor

core with the possibility of failure to achieve a desired orbit in a

flight mission. Two primary problems which could result from the

uncontrolled return of a nuclear-powered vehicle to earth are as

f Ollows:

1. In the event that before a run the reflector-controlled

reactor should be suddenly immersed in water, it could become

supercritical and explode in the manner of a small nuclear device.

Estimatesl of the “maximum credible accident” possible from such

an event correspond to the detonation of a few tons of TNT. It is

supposed that the explosion could be prevented by separation of the

reactor core into about ten pieces prior to immersion.

1. LA-2409, “Nuclear Safety Aspects of the Rover Program, “

Appendix III (March, 1960) (SECRET).

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2. The high density of fission products in the reactor core

after a run makes even small pieces of it potentially hazardous to

the general population. Thus the possibility of a mission failure

in which the vehicle fails to achieve orbit after a run requires a

tolerable method for return of the core pieces to earth. The ideal

solution would be some mechanism which would so finely divide the

graphite material that it would remain suspended in the upper

atmosphere. or burn up on reentry. If this could not be accomplished,

it would at least be desirable to disperse the core in fragments

sufficiently small to be an acceptable hazard.

Just what size fragments could be permitted is a complicated

question involving their residual radioactivity, decay and other

factors; at present no criteria have been specified. Estimates of

acceptable size have ranged as low as submillimeter. The investigation described in this report is not concerned with the size of

fragments that could be permitted, but rather considers what sizes

can be achieved with a certain mechanism. Obviously, a fragmentation method which would solve the second problem listed

above should be quite adequate for the first. Consequently, this

study has been directed toward the disposal of the reactor at high

altitudes.

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In the summer of 1961 a program was initiated to determine

the feasibility of employing high explosives to dispose of a nuclear

rocket engine. The concept of the particular manner in which

explosives would be employed has been limited to a single mechanism. This mechanism is based on the idea of carrying in the

NERVA vehicle a device which in a destruct situation would project

a high-explosive shell into the engine. Such an arrangement

resulted from the expected difficulties in having high explosive

adjacent to the reactor during the run. Without an elaborate

shielding and cooling system, the high neutron and gamma-ray

flux would certainly alter the properties

could result in its undesired initiation.

The basic approach of the study,

of the explosive, and

which is detailed in

Section II, has been constructed around the fragmentation of

scaled cylindrical graphite configurations (representing to greater

or lesser extent actual Kiwi designs) with axially located, cylindrical. explosive charges. The design of the models was to a large

extent dictated by the type and shape of graphite materials which

were quickly and economically available. The experimental

discussed in Section III proceeded in two phases. The first

program

employed a so-called dispersal-recovery technique, to obtain

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information on the size of fragments produced in a given configuration

and the manner in which they were scattered by the explosion. The

dispersal information, which could prove of use to those concerned

with firing-pad accidents, such as a nuclear incident or the explosion

of a chemical booster, is presented in Appendix A. The recovery data

of this phase, while not as helpful as that obtained

were sufficient to give an approximate idea of the

with later techniques,

fragmentation which

could be accomplished with a reasonable amount of high explosive.

Fragments recovered were small enough (tens of grams maximum

to prove, when coupled with other factors, sufficiently promising2

size)

to

lead to the second phase of the program. In that part, less re~istic

models were fired to see how various parameters, e. g. , scaling or

explosive /graphite weight ratios, might affect and optimize fragment

size. The deductions, given in Section IV, were made on a strictly

empirical comparison basis.

Section V contains a rough estimate of the degree of fragmentation which would occur in an actual reactor destroyed by 100 lb. of

high explosive. Some conclusions and suggestions for further investigation are presented in Section VI.

2. Certainly graphite pieces of the order of tens of grams would be

sufficiently radioactive to be a serious hazard; however present feeling

is that fragments of such dimensions would be vaporized on reentry.

Plasma jet experiments are underway to help determine how large a

fragment may be permitted.

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11. BASIC APPROACH OF THE STUDY

A purely hydrodynamic computation of fragmentation of an

object by detonation of a centrally located explosive charge is a

problem of virtually insolvable complexity. The complexity is

magnified in this study by the fact that it deals with a material of

ill-defined shock wave properties in a complicated geometrical

configuration. Therefore, the approach in this program has been

an empirical parameter study.

Since it is not known when and where a piece breaks in the

explosion process, it is simply admitted that the process produces

a collection of fragments of varying sizes. It is assumed that the

performing of identical experiments dealing with a large number

of fragments will lead to the recovery of identical distributions.

These distributions may then be fit to mathematical expressions

which incorporate certain parameters, and the variations of the

parameters can be observed as certain aspects of the experiment

are changed. If enough experiments are performed, and the

APPROVED FOR PUBLIC RELEASE

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parameters of the fragment distribution function are found to vary

in a consistent fashion, predictions should be possi’ole for the

destruction of an object not available for an experimental test, a

class of objects which

in this

The important

program were:

presently includes a full-scale Rover reactor.

aspects of the experiments which were varied

1. Explosive-to-graphite mass ratio

2. Explosive type

3. Scale

4. Physical and mechanical properties of the graphite

5. Geometrical configurations

6. Presence of metal parts

The study of the parameters was made by the direct comparison of

groups of shots in which (usually) only one of the above conditions

was varied.

conclus ions

The

A detailed discussion of the comparisons, and the

drawn from them, appears in Section IV.

expression employed to fit the fragment data is known

3

as Rosin’s Law. If we define the incremental mass fraction of

fragments having dimensions between R and R + dR as (dF/dR)dR,

then Rosin’s Law may be written:

3. R. J. Finkelstein and G. Gamow; “Theory of the Detonation

Process, “ NAVORD Report 90-46 April, 1947) (CONFIDENTIAL).

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(dF/dR) dR = ( BRB-l/R~ ) exp - (R/Ro)B dR ,

where R. and B are constants for a given experiment, and the

parameters for varied experiments. The equation is readily

integrable, yielding for the fraction, F(R),

dimension greater than R, the expression:

F(R) = exp

[ 1

-(R/Ro)B .

of fragments of

(1)

(2)

The principal virtue of Eq. (2) is that, in most instances, it

provides a reasonable fit to the data. The formulation has some

vague theoretical justification for B = 1 in the one-dimensional

case. A particular disadvantage of the expression is that the

“constants” (especially B, which is primarily a “fudge” factor)

may not be in any simple way related to the physical situation, so

that their variation with changing experimental configurations may

not be reasonably predicted.

J. N. Fritz of LASL Group GMX-6 has performed a theoretical investigation to determine a better based fragment distribution

function. 4

In his work it was assumed only that the probability of

occurrence of a separation plane was the same throughout the

4. J. Fritz, Appendix B, this report.

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object to be broken. The expression he obtained bears some resemblance to Eq. (2) but, since Dr. Fritz did not permit himself

the luxury of a second parameter, it does not provide a very good

fit to the data of this work. From a comparison of his formulation with that of Rosin’s Law, it is observed that an exp( -R/Ro)

should be the dominant factor in any reasonably based distribution

function, and that the parameter R. should resemble, or be

proportional to, the expected distance between breaks.

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III . EXPERIMENTS AND ANALYSIS

The data discussed in this report are taken from 45 recovery

shots fired on various graphite configurations. Eight of these shots

were on approximately 1/3-scale models, and the remainder on

5

systems ranging from 1/9 to 1/10 of full size.

Four of the shots on larger-scale models were of a

“dispersal-recovery” type. For these, the shots were fired in the

middle of an open area, and the fragments were recovered on a

sampling basis on large tarpaulins spread out over distances up to

500 ft. The shots were additionally instrumented with a Fastax

camera and fiberboard screens at varying distances, upon which

the amount of perforation was observed. A discussion of the

dispersal is presented in Appendix A. The recovery information

was regarded as rather untrustworthy for these experiments, as

5. For this investigation the reactor core, including the graphite

outer cylinder, was taken as being— a right circular cylinder 54

inches long by 40 inches diameter, and-having a grap-hite weight

of 1700 kg.

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it was virtually impossible to obtain a “fair share” of the smaller

pieces. The dispersal-recovery series included an experiment

which represented the closest model to an actual Rover reactor.

This arrangement, which incorporated actual B-1 elements and

modules, is shown schematically in Fig. 1 and pictured in various

stages of assembly in Fig. 2.

All of the other shots were performed with

steel-walled recovery pit. The 1/3-scsle models

a4ftx4ftx4ft

were fired

suspended above the pit, as shown in Fig. 3, so that a certain

segment of the cylindrical assembly was recovered. The smsllerscale models, such as are shown in Figs. 4 and 5, were fired

inside the pit, approximately a foot from the bottom.

Two experimental problems were attendant to the recovery

shots . The first was secondary breakage of the fragments upon

striking the recovery chamber walls. This could have led to a

determination of fragment size distribution which was too low, and

probably selectively too low, since the larger pieces suffered less

deceleration from air resistance, and reached the walls with higher

velocity. Enough shots were fired to demonstrate that serious

secondary breakage resulted if the pit walls were not lined with some

soft material, and that a 1/4 in. neoprene rubber lining served as a

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Fig. 2 Stages in the assembly of the modular model for dispersalrecovery shot RFS-6.

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The shot shown is

RFS - 10, employing the same type of modular assembly as

RFS - 6, without the surrounding metal parts. The support

mechanism was successful in reducing the amount of extraneous

debris, such as wood splinters mixed with graphite, in the pit.

The height chosen was scaled so the shot-pit floor distance was

just 3 times the wall distance of the l/9-scale shots, and resulted in an expected recovery of 1/4 the original mass of the

graphite.

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practical means of reducing the effect to an acceptable level.

The second problem was in estimating the size distribution

of the fragments (approximately 157’0)which were not recovered as

expected. One could take the view that these pieces had the same

size distribution as those recovered, or, after observing motion

pictures of the great amount of smoke arising from a shot,

that the entire loss belonged in the smallest fragment-size

category. Computations were made on the

assumptions, with the eventual decision to

basis of both

choose the first

assume

one,

since it usually provided a better fit to Rosin’s Law and, if in

error, at least erred in the direction of pessimism.

After recovery, the fragments were separated into four to

seven size categories by passing them through graduated screens.

In addition to a pan to retain the smallest particles, sieves with

square holes of width 4.76, 2.00, 0.84, 0.50, 0.25 and O. 105 mm

were employed. The screening was done with a mechanical shaker,

and the time of the operation controlled so that the fragments from

each shot received the same treatment. Measurements of the

weights retained by various size screens provided the data for

fitting Eq. (2).

It is perhaps well to point out what is meant by the “diAPPROVED FOR PUBLIC RELEASE

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mension, “ R, employed in this discussion. In principle, a fragment

which will pass through a screen of size R s need have only a width

and depth to or less than that value, and could be substantially longer

than Rs. Fragments of length two to three times Rs have indeed

been observed in this work, but of course these always have dimensions in the other directions somewhat smaller than Rs. For

this study, it will be assumed that the largest fragment passing

a given size screen is a cube with edges of that particular size.

Consequently, the screen may be considered to divide the fragments

into categories of volume more than and less than R3. Sine e the

s

f ragrnents have a variety of shapes, the sharp division is not of

course the case. An examination of the fragments indicates that

to the extent the assumption employed is erroneous, it errs

conservatively, i. e. , toward the implication that the fragments

are larger than is actually the case.

The data were fit to Rosin’s distribution by least squares.

To accomplish this, Eq. (2) was reduced to the linear form:

Y(R) = A - BX, (3)

where

Y(R) = -ln [-In F(R)] ,

(4-a)

X = lnR, (4-b)

A= Bln R (4-c)

o’

● ☛☛ ●

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● : : ● 0:0 9*

● b : ● *

● 0 ● ** ● 00 ● *9 ;.* ● *

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
dii!lw~ .*● *m .** bme ..* . .

● * ● 00:: ● . ●:

●

●

:: :

: :

● 0 ●0: ● .G

:e

● ●:0 ●

and B is the same as previously defined. The actual arithmetic

was performed with an IBM-7090 computer.

I

When the data are presented graphically in this report, the I

result is usually in the form of Eq. (3). An examination of the I

expressions shows that Ro, corresponding to the value of R when

Y(R) = O, may be regarded as a “characteristic dimension”; in

fact, the distribution indicates that a fraction, 1/e, of the fragments have dimensions larger than Ro. One may equally well

define the values of R corresponding to other fixed fractions,

such as R. 01 and R. lo which are employed to indicate those

. .

dimensions dividing off, respectively, the largest l% and 10~0 of

the distribution.

Table I lists the graphite configurations for the 45 experiments and contains an explanation of the symbols employed in

tables and text. Table II lists the initial conditions for the 45

experiments, along with the values of B and R.. The standard I

deviation values listed for B and Ro, which are seen to vary from

2’70 to 10~0, reflect how well the measured distributions fit Rosin’s

Law, and do not represent any estimate of the

for the particular shot.

experiment al error

?..:.”. ● 0 ● 0 400 ● ● **

:: ●:

●

: ●:

::

●

● ,* :

9* 9.* ● . . . . . . . . . .

●

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
● 0 ● *e ● *

● 9* ●°0 : ●99 ●

-.----- ...6 ● =0

0

●

●

● 0 ●:0 ● 00 ●:0 :00 ● 0

● ● ● 0000: ● ::

● ** ● * ●:O ● *

● ● 00 : ●:O :00 ● 0

TABLE I. GRAPHITE CONFIGURATIONS AND OTHER

SHOT NOTATIONS

A. Graphite configurations

1.

2.

3.

4.

5.

6.

7.

8.

9.

Shots RFS-3, RFS-7, RFS-4, and RFS-5 were 12 in.

diam by 18 in. long solid cylinders, with a 2-1/8 in.

diam hole extending the entire length of the axis.

Shots RFS-8 and RFS-9 were “33-rod” assemblies

consisting of 30 rods 2 in. diam by 18 in. long plus (

6 half rods, arranged in a circtilar hexagonal. closepacked array.

Shots RFS-6 and RFS- 10 were fabricated of Kiwi B-1A

modules and elements as shown in Figs. 1 and 2. The

letter E refers to the fuel element portion of these

assemblies, and M to the module portion.

All R-series shots except R-7 and R-8 were “33-rod”

arrays as shown in Fig. 4.

Shot R-7 was a circular hexagonal-close-packed array

of 132 3/8 in. diam rods, and R-8 was an array of 297

1/4 in. rods.

Shot HR- 1 was a “33-rod” array of 7 in. long, hexagonal Kiwi B-4 fuel elements.

All S-series shots and shot G-1 were 4 in. diam by

7 in. long solid cylinders, with a 7/8 in. diam hole

extending the length of the center axis.

All T-series shots were 3-1/2 in. diam by 7 in. long

solid cylinders, with an axial 7/8 in. diam hole.

All W-series shots were 3-1/4 in. diam by 7 in. long

solid cylinders, with an axial 7 /8 in. diam hole. . .–

● ☛☛ ● ●°0 ●

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● ☛☛☛✎

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APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
● 0 ●

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:: 0:: ● - ●:

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B. Notations

1. Recovery type:

R refers to shots fired completely within the 4 ft x 4 ft x

4 ft steel recovery chamber open on the upper face; the

chamber itself was completely lined with 1/4 in. neoprene with an additional 1/8 in. layer of regions where

the bulk of fragments impacted.

R’ refers to shots fired just outside the mouth of the

recovery chamber lined with neoprene as above.

S refers to a shot fired within the unlined recovery

chamber in which the reactor mock-up was covered

with a one-inch layer of Styr~foam.

S‘ refers to shots fired just outside the mouth of the

recovery chamber in which the chamber was completely

lined with three to eight inches of Styrofoam. The

thicker layer was at the bottom of the chamber, opposite

the mouth.

W refers to a shot fired in the unlined recovery chamber

in which the reactor mock-up was covered with a fourinch layer of water.

D refers to shots fired with the dispersal-recovery

technique described in Appendix A.

2. Graphite type: A refers to AUC graphite, CS to CS-312

graphite, G to Graph-i-tite G, UE to Los Alamos

unloaded fuel element material, LE to normal-loaded

(O. 4 gm depleted uranium per cm3) Los Alamos graphite,

and LEC to this material after a carbiding process.

Further description appears in Section IV-D.

3. Cased: X indicates that Duralumin mock-ups of the

pressure shell and reflector were used.

● 0 .243.:. ,9 909. ●

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::

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a“

● O* O**

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APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
40 Explosive type: B refers to Composition B, C to

Composition C and P to plastic bonded explosive,

all further described in Section IV-B.

5. Explosive cased: X denotes that the charge was surrounded by 1/32 in. wall copper tubing, and XP

denotes additional plastic filter between the explosive

and the copper tube.

6. Explosive full scale equivalent: Equivalent weight, in

pounds, in full-scale device having 1700 kg graphite.

7. Fraction original mass recovered: Values denoted by

an asterisk were fractions of computed recovery expected from geometry of recovery system.

9*9 ● ●.- : “;” :?” ;“:

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IV. COMPARISON OF CERTAIN FACTORS

A. Effect of Varying Explosive-to-Graphite Weight Ratios

This study has consistently shown that the parameter B is

relatively unaffected by the explosive-to-graphite weight ratio,

whereas increasing the relative amount of high explosive results

in a corresponding reduction of the value of R It in fact appears

o“

that, for a given type of graphite in a given geometry and dimension,

the product of R. and We (We is the ratio of the equivalent weight

of high explosive to 100 lb) is roughly constant above a certain

limit. The limits of the proportionslity seem to be from about

60 lb full-scale equivalent weight of explosive to 200 lb. The

products RoWe are listed in Table III for certain sets of shots

wherein other parameters were approximately the same.

As may be observed on certain small-scale shots (W-3,

T-7, and T-8), the values of R. are substantially larger than would

be predicted by the proportionality. All of these shots involved

21 gm Composition C charges packed in Lucite tubes, with the

.*: .0: .:20 ● .*.

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APPROVED FOR PUBLIC RELEASE
● ☛ ● *9**** ●

● ☛

✚✚

● ☛

90

● 0

●

●

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●

TABLE III. TESTS OF PROPORTIONALITY OF R_ AND EQUIVALENT

EXPLOSIVE WEIGHT u

(Both parameters are defined in text)

Shot

No.

RFS-3

RFS-7

RFS-8

RFS-9

w-1

w-2

W-6

W-4

W-7

w-5

w-3

T-5

T-6

T-7

T-8

R-1

R-12

R-6

R-3

R-9

R-4

R-10

f

.

Configuration

Solid CS cylinder

12” diam x 18”

33 AUC rods

2“ diam x 18”

Solid AUC cylinders

3-1/4” diam x 7“

Solid Graph-i-tite G

cylinders

3-1/4” diam x 7“

Solid AUC cylinders

3-1/2” diam x 7“

33 AUC rods

3/4” diam x 7“

33 loaded elements

3/4” diam x 7“

33 unloaded elements

3/4” diam x 7“

we

1.08

0.57

1.17

0.44

1.93

1.09

0.58

1.94

1.91

1.01

0.44

1.87

0.93

0.45

0.44

1.18

1.20

0.55

1.22

0.84

1.23

0.84

RoWe

(mm)

4.02

3.86

1.79

1.90

0.79

0.93

1.14

0.95

0.96

1.03

1.68

0.95

1.14

2.32

2.73

0.86

1.06

1.39

0.45

0.61

0. 8“6

0.92

4.12

3.20

1.89

1.45

0.99

0.95

0.94

1.18

1.19

1.03

1.28

1.17

1.12

1.81

2.08

0.91

1.12

1.13

0.48

0.58

0.92

0.87

4.09

3.45

1.84

1.62

0.91

0.94

1.02

1.09

1.09

1.03

1.42

1.10

1.13

1.99

2.31

0.89

1.10

1.23

0.47”

0.59

0.90

0.89

,.. . Sb:. :.. :.O ..:::OO

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APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
● ☛ ● .e b.

● ●*9 : ●“a ● 99

8* .*: ●✚✎9.8 ● *. ● .

● * ● *

● O*** ●:00

● be* ●

be : :*

● * ●0: ●:0 ● Q:. ●

explosive dimensions 3/8 in. diam by 7 in. long. The density

of packing was about the same as in other shots, and 3/8 in. is

several

obvious

times the failure diameter of Composition C. There is no

experimental reason for the failure of the proportionality

rule in these smsller-scale shots, and it remains vslid into the

region of 50 lb equivalent high explosive in the 1/3-scsle shot,

RFS-7.

General trends in the data indicate, at least in the smallerscale data, that R. is slightly more strongly dependent on We than

the straight inverse

R. * I/w:

proportion. Consequently, a form of the type: I

(5)

was computed for the various experiments, using k-values of

1.33 and 1.20. Examination of the two right-hand columns in

Table III indicates that the use of the 1.20 value provides the best

“rule of thumb” to fit the observations.

B. Effect of Explosive Type

Three

program:

types of high explosive were employed in this

1. Composition B

of RDX/TNT, in the form

density.

(Comp B), a mixture of 60/40 by weight

of machined castings of 1.72 gm /cm3

““ ““: “;32 : “;” :“. :: ●:

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● 00 ● m

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
WiiiiiB ● ..:0 :00 ●:0 ● m. . .

●

● **.

●

● *

9* ::

●:

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● ● ● : :: :0 : ● m. . . . ● *

2. Composition C (Comp C), a plastic explosive

primarily of RDX, hand-packed to a density between 1.3

gm/cm3.

3. 9404 Plastic Bonded

94% HMX explosive in a binder,

composed

and 1.4

Explosive (PBX), consisting of

with density of 1.825 gm/cm3.

In the one pair of shots (T-4 and T-5)

ative effects of Comp B and Comp C could be

in which the comparobserved, no

significant difference in fragmentation was noted. In three pairs

of shots in which the effect of PBX could be compared with that of

Comp B, it was found, after compens sting for equivalent explosive weight, that in one the use of PBX reduced R. by Ilyo, in

another the change was less than 1~0, and in the third the R. value

was 14% larger. Uncontrolled factors and lack of reproducibility

have a greater effect than does changing from one to another of

these rather similar explosives. In future computations, no

compensation will be made for whichever of these three types of

explosive is used.

The three explosives employed in this study are actually

quite similar in properties, composition, detonation pressure,

and products. An explosive of a somewhat different type shows

some possibilities for increased fragmentation of a reactor core.

.:. : 35* ● @m ●’b 8

● 00 ●

● 000 ● o

● ** :

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● 0bmam 9* ●e0*a09* ●9

9e 9e9 ●

● ☛

9*

::

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8’*

●

●

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● e

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
● ☛ ● ☛ ● 00 ● *

.*9e *mm ● 00

● ☛ ● *9 ● ** ● 9* ●:0 99

● m** ●

● aeao .:0- ● 00: b

● . : :*

● * bb: ● 09 ● ●:* ●

Oxygen-rich high explosive diluted with aluminum (frequently called

ALEX) has been recognized for some time as possessing some

virtue as a bursting charge in large-scale blasting operations,

6

and is presently favored for use in depth charges. Fickett has

computed that a mixture of 2 moles of aluminum with one of

ammonium nitrate has a total available energy about 55% greater

than RDX. However, the aluminized explosive releases its energy

substantially later in the detonation process than do explosives of

the type employed in this work. The work done by an explosive

depends upon the degree to which the product gases are allowed to

expand; and aluminized explosives require substantially more

expansion, or less confining pressure, to liberate their chemical

energy than do more conventional types. The question reduces to

this: at what confining pressure is the fragmentation of

concluded. The detonation pressure, and consequently

the graphite

the initial

stress introduced into the core configuration, is actually less for

the NH4N03-Al mixture than for RDX. According to Fickett’s

calculations, the aluminized material would not exceed the RDX

in energy release until the explosive had relieved to around 15 kb

6. Wildon Fickett, Private Communication. (March, 1962).

●S:

● 0

::

● *

●**

●

●

●

● O

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
● e ● ** ● e

● ** .=* : ●e* ●

● **

::

● *

● s

● ☛ ● ee ● 00 ● *D ● *O ● O

● ● ● 0

● :es o.. ::

● 0s ●:

::

8 :

● ●:8 : ● ** ● 00 ● 9

pressure. At 1 kb the aluminized material provides only about

1170more work than the RDX, at O. 1 kb about 19’7’omore, and

only 3l% more at atmospheric pressure. If one considers that

shock-induced fracture, the principal mechanism by which the

graphite is broken, requires pressures of the order of 100 atm,

the gain from the use of aluminized explosives does not appear

substantial. It is possible that the degree of fragmentation depends

entirely on the strength of the initial shock, in which case the

aluminized explosive would prove inferior. However, it is also

possible that some of the fragmentation is accomplished through

abrasion by

presence of

the core.

escaping detonation products, in which case the

aluminum could serve to enhance the reduction of

C. Effect of Change of Scsle

One pair of shots in the program provides a reasonable

comparison of the fragmentation of solid cylinders of substantially

different sizes. If the fragment distributions from shots RFS -3

( l/3-scale CS-312 graphite cylinder) and S-5 ( 1/9-scale cylinder

of the same material) are compared, it is seen that the values of

B do not differ substantially, and that the figures for R. differ by

roughly a factor of three. More precisely, the ratio of the cube

● ● *O ● 35:. :00 :00°: ● :

● ● ● *

● 0:0::. ::

●

● = ●:0 ● *8 ● *9 ● ** ● 0

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
● ✘ ● *O .:* ● ** “,* ● O

● 0 ● 0 ● eO:a ●: @ ●

root of the graphite volumes for the two

the values of RoWe 1.20

(which corrects

plosive equivalent weight) is 2.78. The

shots is 2.86, and that for

for difference in eximplied scsling rule is

that the fragment distribution should have a characteristic

dimension, Ro, directly proportional to the originsl dimensions

(as manifested by the cube root of the volume) of the assembly.

Two available comparisons of 1/3- and 1/9-scale AUC rod

configurations do not quite bear out the above rule. The ratio of

original dimensions for these comparisons is 2.63, whereas the

ratios of ItoWe 1“20 are 2.07 (RFS-8 vs R-1) and 1.32 (RFS-9 VS R-6).

Though these

form, in this

RoWe

comparisons do not especially well demonstrate the

work the rule

1/3

s (Original graphite volume) (6)

will be employed for configurations of identical geometry and

material, with the usual consideration that the error is conservative.

Such a scaling rule is equivalent to a detailed application

of the similarity principle. This principle, as expounded by

Cole,

7

asserts that the pressure and other properties of a shock

7. Robert H. Cole, Chap. IV Underwater Explosions, Princeton

University Press ( 1948).

.o: ●0: ●:f3f5 ● ● 00

9*

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● . ●: ●

:: ...: .

● . ● 00 ● *9 980 ● O* ● *

.**

●

● ● ● :: ● ● ee* 0: ●m..*

● O.

9** . .

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9* ● *#

● 00 .“. ~ :“: .:.

● aOO*

.* ● m. ● ** ● ** .*. . .

● ● ee

● :*9*9. ::

●

● **m be

: ● 0

● 9:0 : ●:8 :00 ● *

process remain unchanged if the scales of time and length by

which they are measured are altered by the same factor as are

the dimensions of the explosive charge. To extend the principle

to this problem, one may argue that a “break” occurs at a given

point in a graphite assembly when a certain limiting strain is

reached at that point, and that the fragment size distribution is

dictated by the spacing of these breaking points. Thus, if the

size of an assembly is tripled, the explosion results in exactly

the same values for the shock-wave parameters in a space and

time scaled by a factor of three, with the breaking points occurring three times as far apart and the recovered pieces being

three times as large as those from the smaller experiment.

The principle of similarity argued above always requires

that the process be nondissipative, i. e. , that the medium in “

which it occurs be hydrodynamically ideal. Graphite, far

from having this feature, displays an anomalous compressibility

at lower pressures, so that normal steep shock fronts are not

developed. It appears that this property could explain the fact

that the rod assemblies fail to “scale” in the manner of the

solid cylinders.

The scaling rule stated above, and this study, are in

-

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APPROVED FOR PUBLIC RELEASE
● ☛ *mm

● ●** : ●*. ● ●°:

● ✎ ● 00 ● e* ● om ..0 ● “

● a ● 00: : .: : .“

9*** ●

9* :0

ma ●9: .:* ● ●:n ●

contradiction to an approach attempted earlier in the program.

In the previous concept, it was proposed that in a given geometrical configuration, regardless of scale, the efficiency of

the explosive energy in producing surface area would remain

constant. The energy required to produce unit surface area

was assumed to be that required to vaporize one layer of atoms

from it. Thus, regardless of scsle, the surface generated per

unit volume would be the same, and with any reasonable description of the fragment-size distribution (i. e. , one not employing

the second parameter, B), the size of the pieces recovered

would prove independent of the size of the original assembly.

As well as being inconsistent with the scaling observations,

this approach allows for little sensitivity in fragment size as a

function of mechanical yield strength of the material. It will be

shown in Section D that mechanical yield values do sometimes

influence the. fragment ation of the graphite.

D. Effect of Physical and Mechanical Properties

After the early dispersal-recovery shot on the modular

B-1A mock-up (RFS-6), the fragments were separated with a

high density liquid into two classes. One class included those

fragments originating from the Graph-i-tit e G modules, and

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APPROVED FOR PUBLIC RELEASE
● m ● *9 ● 9

● ** ●°0 : ●’* ●

● Oe*b ●

● ☛ ● ✎ ✎ ● *e .*e .*. .9

● ● ** ● 9

● :*9 ***.*

● eea ● O ●: ● ● 0

● ●:0 : ●:0 ● O* ● m

the other those originally part of the normal-loaded (i. e. ,

containing O. 4 gm /cm3 depleted uranium) elements. The

fragment distribution for the loaded material was found to tend

toward smaller sizes than the one for Graph-i-tite G. This

implied that either the physical properties or the geometry,

both, of the originsl materisls strongly influenced the fragmentation of the graphite.

or

To eliminate the effect of the geometry, two identical

configurations were fired at 1/9-scsle, one of which (R-3)

employed normal-loaded graphite

“unloaded elements. “ These last

as the loaded elements, produced

elements, and the other (R-4)

were rods of the same shape

by a similar method from

similar carbon material. As seen in Fig. 6, the loaded material

produced substantially smaller fragments.

In shot R-5, an assembly of 3/4 in. diam AUC rods

combined with normal-loaded fuel elements (see

fired. The distributions obtained are compared

corresponding “pure” AUC rod and fuel element

Fig. 4) was

in Fig. 7 with

shots in similar

configuration. As is seen, mixing the two materials appears to

increase the differences in their fragmentation; i. e. , the more

finely. shattering fuel elements became still more finely divided

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in the mixed shot, and the coarser AUC portion became more

coarse.

Experiments R-3 and R-4 clearly demonstrated that some

property arising from the presence of uranium in the graphite increased the degree of fragmentation. One interesting, if Uflikely,

explanation of the effect is that some manner of inertial separation

of the uranium and graphite under shock leads to the enhanced fragmentation of the loaded material. In work at Lawrence Radiation

Laboratory, plastic

served under shock

loaded with finely divided lead has been ob -

with framing cameras and flash x-ray, simultaneously. A definite separation of the lead

lighter plastic was seen.

Neglecting the above suggestion, the

component from the

property of uraniumloaded graphite most likely to

reduced mechanical strength.

cause the smsll.er pieces is its greatly

Studies in LASL’s N- Division8 have

shown that most mechanical strength properties of the loaded

material are reduced by a factor of two to four below those of its

unloaded counterpart. The effect is especially pronounced when the

loaded material (so-called “shelf-type”) is aged in a normal

8. P. N. Wagner, and A. M. Gage, Private Corn.rnunication.

.O: .O: ●:042 g . ..

● ● .m.

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●

●“e :

● 9

● ● ●

::..:

● O**

●*... ● O.

● 00 9*

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. . . . . . . . .

● 0 9** ● 00 ● 00 ● *O .*

● ● *

● : :0 ● 0 ::

● 0 ●:

:000

●

9* ●:0 : ●:0 :0s ● 0

)

atmosp kre, in which case the observed weakening is associated

with thk conversion of 20 to 30% of the uranium carbide component

to uranium oxide. To check the effect of this strength alteration,

one assembly of fuel elements was “re-carbided” by heating in a

furnace and kept in an inert atmosphere until fired. The fragment

distribution from this assembly is compared in Fig. 8 with that of

shelf-type loaded elements and unloaded elements. It is seen that

the distribution for the carbided elements lies intermediate between those for the other two tests,

in fragment size

the atmosphere,

after the process.

the NERVA engine

indic sting a definite increase

Since, in being run outside

would also subject the fuel

elements to this carbiding procedure, it seems that some degree

of carbiding should be considered in an estimate for an actual.

destruct situation.

To further study the effect of physical properties on the

fragmentation of graphite, the results from the shots on the three

types of graphite (AUC, CS-312 and Graph-i-tit e G) employed in

solid cylinder configurations were compared. The information

discussed in the previous sections was employed to correct for

differences in explosive weight and scsle.

If one applies the rules for scaling and equivalent explosive

●

● ●

9 ●

a:: ..*.**:* ● ● e

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0

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7

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weight stated in previous sections, a “normalized characteristic

dimension, “ Rn , may be written:

Rn = 100 RoWel” 20V -1/3

g“

(7)

We and R. have been previously defined, Vg is the volume of

graphite in cm3, and the fact or of 100 arises from considering

the graphite volume of the full-scale engine to be 106 cm3. If

the choice of allowance

variations in Rn should

for scale and explosive weight is correct,

be primarily due to differences in physical

properties of the graphite and in the geometric configurations in

which it is employed.

Table IV shows values of Rn for the shots on solid cylinders,

excluding both those in which metsl parts were employed and the

21 gm Comp C shots mentioned in Section IV-A. It is now seen

that the average vslues obtained have hardly a significant, and

certainly not a substantial, difference.

Data on the mechanical properties of graphite are scarce,

and subject to wide variation among “identical” samples. A

handbook valueg for the tensile strength of CS-grade graphite is

9. Industrial Graphite Engineering Handbook, National Carbide Co. ,

New York (1959).

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
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TABLE IV. NORMALIZED CHARACTERISTIC DIMENSION ON

SOLID CYLINDERS

Shot No. Cylinder

Diam (in. )

AUC Graphite

T-1

T-2

T-4

T-5

T-6

w-1

w-2

W-6

T-3

T-10

S-5

3-1/2

3-1/2

3-1/2

3-1/2

3-1/2

3-1/4

3-1/4

3-1/4

CS-312 Graphite

3-1/2

3-1/2

4

RFS-3 12

RFS-7 12

Graph-i-tite G

W-4 3-1/4

w-5 3-1/4

W-7 3-1/4

G-1 4

we

1.88

1.95

1.88

1.87

0.93

1.93

1.09

0.58

1.82

1.92

1.37

1.08

0.57

1.94

1.01

1.91

1.26

Rn

(mm)

13.3

11.9

11.4

10.7

11.2

9.5

9.9

10.7

14.6

15.0

13.3

12.9

10.9

11.4

10.8

11.4

12.5

Rn (avg. )

(mm)

11. 1+0.8

1303 *0.9

11.5 +0.4

.c: co: ●:4(5 ● ● .. .

:!:*

● ::..: ● ● *O*

● . . . . .*: ..:

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
● 9 ● a* ● O

b*O ●°0 : ●“e ●

● *e9em0 ● m

00

9*

. .

. . ● .9 ● m. ●:. :** ● *

bae ● a

.*:* ● ***

● :0 ● b ●: ● ● ● O

● 0:0 ● ●:* ● 9* ● 9

about 1400 psi. Morton Smith of LASL Group CMF - 13 has made

measurements on the other two materials employed as solid

10 cylinders in the work. He found room temperature tensile

strengths ranging from 2400 to 4000 psi for Graph-i-tite G. The

few samples of AUC graphite tested broke at the specimen thread,

rather than the “neck, ‘‘ implying some type of notch sensitivity y.

The strength vslues obtained ranged from 2500 to 3000 psi. Thus,

available figures yield the rather strange indication that the

weakest graphite provides the distribution of largest fragments.

Barring such an unreasonable suggestion, other properties

of the graphite must explain the differences and perhaps compensate for the anomalous correlation with tensile strengths. Two

possible “other properties” are brittleness and grain size. A more

brittle nature, as manifested by the notch sensitivity of the AUC

material, could lead to enhanced fragmentation. The maximum

9, 10

grain sizes reported for CS, AUC and Graph-i-tite G

materials are, respectively, O. 030, 0.008 and O. 003 in., with

the larger grained material correlattig to that producing the larger

fragments.

10. Morton Smith, Private Communication.

.;. ; 4?:s :.* :.O .*:

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6..**:* ::

● ● * .0 9* ● 08 *** ●:* ● ** ● *

mmmeb:: ...”.”... .0

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
In conclusion,

\

bear some relation to

● ☛

● ●“0 $ .*. ●0: .O:

● ✍ ● 9* 8*9 ● om .*O ● m

● O ● e ● 00: : .:. .

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the fragmentation distribution, Rn, must

the physical and mechanical properties of

the material; however, except for

the differences are smsll. There

the shelf-type loaded material,

appears to be no simple method

of correlation. The subs equent approach in this report will be to

employ conservatively estimated values of Rn, based on the

experiments available, as empirically characteristic of the

material. As will be shown, Rn does not appear very sensitive

to geometry.

E. Effect of Geometrical Configurations

It is unfortunate e that while the geometricsJ configuration

of the elements of a reactor engine could be the most dominant

influence on its fragment at ion with high explosive, obtaining

acceptable data on this aspect was the most difficult part of the

program. The difficulty arose from the unavailability of 1/3-

or 1/9-scale pieces which could adequately detail the geometry

of the actual engines. Thus, while some general rules may be

derived to correlate to the small-scsle shots on aggregates of

rods and elements, the question as to whether they will apply at

full scale remains.

One empirical observation, from examination of Table II,

90

::

● *

● .

● *

●**

●

●

●

● O

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
O*e- ● ** ::.

● ***O* ●

00

● 8 ● *

● ☛ ● ☛☛ 9** .9* ● ** ● m

—

● ● *e

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● 9O ● : : ::

● ●:O : ●:O ● 00 ● *

is that the geometric configuration slone has a strong influence on

the parameter B. Neglecting the disperssl-recovery data, it can

be observed that fits to data obtained from assemblies involving

aggregates of rods result in a set of B-values clustered around

a figure of about 2/3,

solid cylinders group

while those obtained for experiments on

around unity. The scatter in the values

obtained is quite large, and the statement above may not be

extended to a more detailed correlation to the particular type of

geometric configuration, i. e., specific values for mod~ar

assemblies with elements, solid rod, aggregates, etc. However,

the observation is consistent enough to give a vadue of B = 2/3

as a crude “rule of thumb” for rod configurations.

The values computed for Rn for 1/9-scale rod assemblies

are shown in Table V. It may be noted that the values for AUC

graphite average about 18!f0lower than those for the solid cylinders.

While, with the accuracy of the experiments, this figure is

considered hardly significant, it is assumed that the smaller

values result from the geometry effect. It is further believed

that, had it been possible to obtain unloaded element materials

in rod form, the fragmentation from such assemblies would have

produced an Rn value similar to that of AUC graphite. Thus the

● ☛☛ ● ● 9O ● 9* 9* ●°0 :

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APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
TABLE V.

. . ● ☛☛ ● ☛☛ ● ✎ ✎ ✎✎✘ ● ☛

●

::0: : ●: :0 ● *,, ●

● * : :0

● 0 ●0: ●:0 ● .:0 ●

COMPUTED PARAMETERS FOR RODS OF ELEMENT

AGGREGATE SHOTS

Shot No. B

Solid AUC Rods

R-1 0.57

R-12 0.64

R-2 0.76

R-6 0.55

R-7 0.66

R-8 0.68

Normal-loaded B-1A Elements

R-3 0.85

R-9 0.68

R-n 0.75

Unloaded B-1A Element Shape

R-4 0.70

R-10 0.75

Normal-loaded B-4 Elements

HR- 1 0.61

Rn

(mm)

7.4

9.1

8.7

10.2

10.9

9.1

3.9

4.8

5.8

7.5

7.4

5.2

““ ●“: y) : ●;. :.O .0

● * ●00:0 ●: ●

● 0 :

.* ..: .:O ..: . . . ● .

●

—

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APPROVED FOR PUBLIC RELEASE
● ☛ ● 9O ●°0 :

● *

● *O .9* ●

● *

..

● e ● . . 9.. ● 9* 8*m . .

● ● em ● e

● :.*9.*99

● 9- ●: : ::

● ●:0 : ●:a ● ,* ● *

20% lower value observed for the element shapes is considered

primarily due to the seven holes in these assemblies. The

further reduced values of Rn for the loaded elements resulted

from the presence of uranium,

In the single experiment done,

discussed in the previous section.

there was no significant difference

between the hexagonal nineteen-hole B-4 elements and the B-1A

elements. In the comparison of shots R-1 and R-12 on 3/4 in.

AUC rods with R-7 on 3/8 in. rods and R-8 on 1/4 in. rods, it was

hoped to obtain some feeling for the effect of reduced rod diameter.

The shots were made with roughly the same volume of material,

the same type of graphite, and the same fraction of voids in the

hexagonal close-packed assemblies. The values of Rn were found

to be slightly larger for the smsller rods, but sfter comparing

the “identicsl” R-1 and R-12 it is difficult to attach much signif -

icance to the rather small clifference.

To further allow for the effect of geometry, the form of

the distribution law employed was modified to admit no fragments

over a specified maximum dimension, R The differential max”

form of Rosin’s Law, Eq. ( 1), was considered correct as R

ranged from O to Rmax, and it was assumed that (dF /dR) vanished

for larger values of R. Thus, for the normalization involved for

● ☛ ● **a** ● *

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
● ☛ ● *O

. ●99 : bee ● ●°:

Eq. (2), the integration

rather than to infinity.

[

exp - (R/R’ )B’

F(R) =

o 1- ‘Xp l.-(Rmax’R~)B’.l

1- exp

[

- (R max/R’)B

o 1

● ✎ ● ☛☛ 9*O ● *9 .00 ● *

● O ● m

..O{ : ●: ●

● a ● :

● * : :0

● m ●0: b:b ● ●:O ●

of Eq. (1) was performed only to Rma

The modified form thus obtained is:

. . .

(8)

The parameters R: and B f are now slightly cliff erent from the

similar quantities in the nontruncated expression, and R: does

not, like R represent the dimension dividing off a fraction, o’

1/e, of the larger fragments.

Actual fitting of the data to Eq. (8) was accomplished on

the computers by an iterative process. The least squares fit

was made to the data initially in the nontruncated form; then new,

+j+l) fictional data points i were defined:

[

(j)

1

#+1) . +J) + e~p - (Rmax/R(~) )B (1 - l?!))

i i o 1

[

= exp -

~R,R, (j))B’(j)

o

1

(9)

and the least squares process repeated. In general, five iterations

were

alter

R

ma

(j) (“) employed, and in no case did the values of B’ and R’ ~

o

as much as 170between the last two iterations.

Whfle it will be seen in the next section that the choice of

can strongly influence the estimates of particle size

K

‘“ ““; “g2 : “:” f. :: 9* ● ●:.* ::

● O ..: .:. ..: .:. . .

●

●°0

●

● ● ● 900 ● :: ● 0: .*.

● @e*. ● 9* 9*

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
● ☛ ● 99

::

:*.

● O ● 90 ● mm 9.* ● ** .0

● ● ● 0

● :00000 ::

● *O ●: : ::

● ●:e : ●:0 ● OO ● *

distributions for the f ragrnentation of full-scale reactors, the

selection did not seriously alter the fit over the range of screen

sizes and the geometric configurations

In general the vslue “selected for Rmax

employed in this work.

for aggregates of solid

rods was the rod diameter. Keeping in mind that in this study

the quantity R is identified with a volume R3, the invariable

observation on examining the larger fragments is that such a

choice is quite large enough. The fit to the data of shot R-8,

involved 1/4 in. AUC rods, shown in Fig. 9. Two means of

which

choosing Rmax

configurations.

were employed for experiments with fuel element

The first was to use the element diameter, and

the second, to use a distance approximately equal to the separation

of second-nearest neighbors in the hole array in the elements. The

examination of recovered element pieces favors the second choice.

In the great amount of fuel-element rubble accumulated in the

program, a piece with an included hole was seen only in the

exceptional case cited in Section VI. Figure 10 shows the fit

to the data from shot HR- 1, based on the two assumptions of Rmax.

The values of R: and B‘ are shown in Table VI for those

shots in which the application of a maximum fragment size made

a significant change. Comparison with Table II shows that the

●** “y : E?q”:“” :“e

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9sHmlm!! ,00 ● ** ●e* ●

● e ● ** ● ● ● O

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
—

q

tN

0.

m“

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g“

a ‘*

&>

/

/

c

(

11

0 0

(-J3601-)a601-.A y

—

—

—

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4

/

● . .“; “54 ; ●:” ::”

● *

● 0

● ombooa

N“”

_—.

<

!j

s

—’

o

1-

z

_. 0 —

O..

a

-iN“,—

0

(y

0.,

—.—

o

APPROVED FOR PUBLIC RELEASE
4

,—o

m“

o

—o

q

-1-+

—

—

—

—

r

(

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—

—

—

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—

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. I

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(-J %O1-)%O1-=A ~

—

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1

—

(

I

(

a)

APPROVED FOR PUBLIC RELEASE
● 0 ●.: ●:0 ● 00 ● ** *e

● 0 ● O

:: 000 ●:09

● b

● O : : :0

*O ●*: SO* ● ●:o ●

TABLE VI. COMPUTED PARAMETERS FOR TRUNCATED

DISTRIBUTION

Shot No. R B’

max

(mm)

AUC Rods

R-6 19.0 0.53

R-7 9.5 0.64

R-8 6.4 0.62

R-13 19.0 0.62

RFS-9 50.8 0.68

Element Configurations

R-10 19.0 0.75

R-10 11.0 0.75

R-4 11.0 0.69

R-9 11.0 0.69

R-n 11.0 0.75

HR-~ 7.0 0.60

R;

(mm)

3.37

1.21

1.41

2.00

4.38

1.11

1.12

0.71

0.74

0.87

0.54

R;

(mm)

13.6

12.0

11.9

20.0

5.0

7.5

7.6

7.6

4.9

5.8

5.4

9*““ ““: ?6 : “~” :“.

● * ● 0m:o ●: ●

● *** :0 ● e ● 00 ● .* ●.: .m. ● *

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
9* boo ● ● e

● .9 9bm ● ●em.

9* 9*. ● ** ● mm ● a* .0

● ● e*

● : ● * ●0::

● ● 0 :0 :

● 9

● c:. :

● 9 ●:0 :00 ● 0

invariable result of truncating the distribution was an increased

R. and decreased B. The standard deviations of these parameters

were altered little, and were worsened as often as improved.

However, as a general rule, the fit to the data was improved

for points corresponding to the larger mesh screens, which is

of course the area of primary interest in the study.

In summarizing the geometry, it may be pointed out that

there are two partially compensating hydrodynamic effects

obtained in going from solid configurations to those involving

aggregates of rods and holes.

assemblies are more subject

Certainly, the rod or element

to fragmentation from a given shock

strength, due to the many more sites for stress concentration

and interactions of rarefactions. On the other hand, the numerous

voids in the divided assemblies tend to attenuate the shock far more

than does the continuous medium. Apparently in the configurations

tested in this program, the first effect slightly dominates the

second.

F. Effect of Metal Parts

A few shots were fired with simple inertial mock-um

the beryllium reflector and the Duralumin pressure shell

surrounding the graphite core model. These arrangements,

of

I

~

● e Om* **e ● *

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
● 9 ●0: 99* ● O* 99* ● 0

9* ● *

● 000 : ●: ●

● *O :

9* : : :*

● * ●0: 9** ● ●:0 ●

depicted in Figs. 1, 2 and 4, substituted Duralumin for the beryllium

parts, since the two metals have approximately the same shock

impedance.

The effect of the

in Table VII in terms of

presence of the “cases” is considered

direct comparison of the values of R_.

11

It is seen that the case resulted in an increase in the vslue Rn

of 2l% to 42~o for systems with solid cylinders, and in a factor

of two increase in the one experiment with rod aggregates.

As with geometric variations, the presence of the metal

parts about the graphite could be considered to have partially

compensating hydrodynamic effects. The degree of breakup

would be aided by the case to the extent that it confines the

energy of the explosive and increases the time in which the

product gases act upon the core. Conversely, most of the explosive energy is employed to provide kinetic energy for the

surrounding material, and if more is required to accelerate metal

parts, there is less left

material representing a

to shatter the core. Also the presence of

fair impedance match about the graphite

must result in some reduction of critical strains at the periphery

of the core caused by the raref action waves and their interactions.

The indisputable evidence of the program is that the metal

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
9*998*** ● e

● ✎☛ ● e* ● 9*

9. . . . . .. . . . . . . . .

● ● O*

● :.* . . . ::

●

● *99 ● *

: ● @

● ●:0 : ●:0 :00 ● 0

TABLE VII . EFFECT OF METAL PARTS

Shots Compared Rn(cased) /Rn(not cased)

RFs-5/RFs-4 1.21

S-6/S-5 1.42

T-9/T-6 1.37

T-12/T-3 1.29

R-13/R-l 2.54

R-13/R-12 2.10

● e* ● gob b~ ● 0

.’. a*:m ● m

● ● ●

b : ● O ● O ::

● ● : ● 0

● * ●:8 ● ** ● 9* :00 ● 0

9Ep ● 0 ● ****8

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
-

● ☛ ●0: ●:0 ,00 ● 00 ● *

● * ● e

99*** .: ●

● **m* :0 ● . ● 99*

● 9 90: ●:a ● ● *9 ●

parts do somewhat reduce the degree of breakup of the graphite.

Whether in an actual engine the effect would be as pronounced as

in the one comparison made on a divided assembly is difficult to

estimate.

Only one direct observation was made of the effect of

surrounding the high explosive with a metal ‘Ishell-case. “ The

comparison of T-4 with T-1 indicates that a 1/32 in. wall copper

tube around the Comp B charge reduced R.

ence was not considered significant, and is

by 147’0. This cliffer -

simply taken to

indicate that the addition of a shell-case does not hinder the

objective of the program, and may slightly aid it. No consideration of, or compensation for, the existence or nonexistence

of a shell case has been made in the comparisons and computations of other factors in the investigation.

:“: “q ‘;” : “;” :“.

● 9.* +.0

● ***

● * ● ** . . . .*. .:. . .

●

● mme* ● O* ● *

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
● *0”” *”*9 ●-0 ●--

● * ●:. ... ... ● .. ● .

● ● m.

● **9 ● b ::

● ● O :: : ::

● ●:0 : ●:0 ● ,0 ● 0

V. ESTIMATES OF THE HIGH-EXPLOSIVE FRAGMENTATION

OF KIWI CONFIGURATIONS

If one assumes that the actual high-explosive reduction

of a NERVA engine results in a fragment distribution of the form

employed in this study, then reasonable estimates of the parameters

controlling this distribution may be made and order-of-magnitude

figures obtained for the degree of destruction of the core.

It seems sensible to apply the truncated distribution

expressed in Eq. (8) to describe the fragmentation of a full-scale

model. Indeed, if reasonable values for R. and B are chosen

and the distributic)n is not cut off at a maximum size, one observes

that about 10% of the original volume of a B-4 engine would be

left in a single piece, a rather unlikely circumstance for a

configuration originally composed of approximate ely two thousand

elements of equal size. The principal assumption which must

be made in using the cut-off form is that the rules regarding

explosive weight, scaling, etc. , derived for the nontruncated

distribution also apply to the parameters of the truncated one.

900 ● ●°0 “~” y :*.

b : :

● *** ● be ::

● ● 0

● O ●:0 :00 ●:0 :00 ● 0

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
● m ● O* ● *

● ●9* : ●°0

-–. – ,,. . ,. .,

uver me range 01

mental program,

question remains

divided geometry

geome~rles ana

this assumption

● 9* ● *9 ● O* ● *

●

: ●: :0

● 00

:0000

● .9 ● ● 9* ●

scales employed in the experiappears valid. However, the

as to its validity for the much more finely

of the actual engine configurations.

Before proceeding to the fu.11-scsle Kiwi configurations, it

is interesting to attempt the “prediction” of the distribution of

element fragments in the modular experiment, RFS - 10. In

the calculation, the rule-of -thumb value of 2/3 was employed for

B!e The value of R: may be predicted using Eq. (7) and the

average value of Rn and R~ from shots R-3

reducing the value obtained by 20% to allow

and R-9. After

for the tendency

discussed in Section IV-D for “ mixed” assemblies,

of R: of 1.37 mm was obtained. Finally, an R

max

to the second-nearest hole separation (11 mm) was

an estimate

corresponding

selected.

The computed distribution, which was obtained before the actual

data were analyzed, is compared with the experimental points

and analysis in Fig. 11. As may be seen, the estimate suggests

somewhat larger pieces than those obtained, arising largely out

of the choice of R’o, which was only O. 78 mm in the experimental

fit. The overestimation of R: quite probably arose from the

failure of the linear scaling rule, as was noted in the case of

● O ● ** ● ** ● ● ** ::62::::”0 8 *9.* ● **O

90000

● * ● ** ● *e ● 00 ●:o ● 0

●

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
m“

o

.0.

al

.0

—“

/ /

ml

0.

I

/

/

—

—

—

—

—

f

/

—

—

—

—

—

—

/

/

—

o*-

mJ

oolN - .—

—.

0

—

g-

● 9O ● ●°0 ● “;” fyr :“.

● * :

9 *.* ●*::

● *O : ● 0

● e ● O9 ● 09 ● 00 :00 ● O

9* 9um5 9** ● ● b ●—9 APPROVED FOR PUBLIC RELEASE
● 9 ● 9O

● ●** : ●°0 ● ●°:

9. 9** ● O* ● *9 ● 00 ● *

9** ● 0

9*** : ●:00

● 00 ●

● 0 : :.:*

● 0 ●0: ● O* ● ● 99 ●

the l/3-scale, 2 in. diam rod assemblies.

Computations were executed for two full-scale Kiwi

configurations, the B- 1A type

The former is an array of 3/4

arrangement and the B-4 type.

in. diam, seven-hole fuel elements

arranged seven to a Graph-i-tite G Module. The core of the B-4

assembly is composed, except for the central rod of each sevenunit hexagonal array, entirely of 3/4 in. diam, nineteen-hole,

hexagonaJ fuel elements. The entire original volume of each

configuration was taken as 106 cm3, with the weight of the loaded

graphite, the only part of concern, taken>as 7 x 105 gm in the

B-1A engine and 106 gm in the B-4 assembly. All computations

were based on disposal with 100 lb of high explosive. A value

of 2/3 was again employed for B’. The definition of R: was such

that no corrections for scaling and explosive weight were required.

Allowing that the “heat treatment” of a run would produce

of R: more like that of the carbided or unloaded elements

a value

than that

observed for the normal elements fired, a value of 7.5 mm was

chosen for the parameter. This figure then multiplied by a

factor of two for the presence of the case, and, for the B-1A

!

system, reduced by 20% for the mixed nature of the assembly.

In the computations, an example using R: = 9 rnm was added

:“; w “:” : “:” .“*

● ● O ● 00:0 ●:.*

● m

● * ●.: .:. ..: .:. . .

●

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
4-hliib ● .● 0. ● ** ●:0 :.0 :*0

● ●

● :**...*.

● *9 ● :00 ●

: :: :0 ● ** . .

to those for R: = 12 ;d”~~ “mm, which were argued above. The

values of Rmax were chosen on two bases:

1. That the entire diameter of the elements would survive,

corresponding to Rmax = 19 mm;

4

2. That fragments would be no larger than the secondnearest neighbor distances in the webs of the elements,

providing values of 11 mm for the B-1A elements and 7 mm

for the B-4 assembly.

The computed results for the nine combinations which

arise from the three values each of R: and R are shown

max

graphically in Fig. 12. The four most likely combinations

(R: =. 12 mm, R = 11 mm or 19 mm for the B-1A assembly; max

R: = 15 mm, R = 9 mm or 19 mm for the B-4 configuration) msx

are shown in Table VIII. For convenience, the tabulation is in

terms of weights rather than fractions and dimensions. The

figures mentioned above provided the original weights, and the

relation discussed earlier (R3 = V) connected the fragment sizes

with the dimension quantities.

● *O b ●:e ●(35. . ●** ● ● 9 ● .

● ● *a

● : ● 0 ● m ::

● ** : 9*

● * ● 9* ● 00 ● . . :.. . .

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
—

-+----

—“

.0

al

0.

0“

o

N“

—

—

—

—

—

—

—

—

—

—-

0. AL

—

—

—

—

—

g 

“x

E=

0

IX “x

E

m

0..

_. 0 —

o“

u-)

o..

I

tN - .—

0

y

0..

0

—.

:“; 68 “;” : “~”:“.

●: ● ●{:0

:: ●

● 0 ●0: ●:0 ● 00 ● 00 ● 0

APPROVED FOR PUBLIC RELEASE
**e *.*.* :*W ●

-

● . ● .. ,** (?. . ● . . .“

● ● *.*

-ma. ●r::

●

so :

:0 ● 0

:

* ● O* : ● ● a

:0 **9 ● *

TABLE VIII . ESTIMATES OF FRAGMENTATION OF FULL-SCALE

KIWI CONFIGURATIONS WITH 100 LB OF HIGH

EXPLOSIVE.

The maximum fragment weights are determined by Rmax

with the assumption V = R3 .

In the computations, the

fragment densities we%ea&summe&to be 2.15 gm/cm3 when the

pieces were smaller than the second nearest neighbor with sizes.

When larger pieces were considered, such that holes were included,

“effective” densities of 1.63 gm/cm3 and 1.47 gm/cm3 were used

for the B-1A and B-4 models, respectively.

Kiwi Model B-1A

Assumed Original Mass of Fuel

Element Material (kg)

Assumed R: (mm)

Assumed Rmax (mm)

Weight (kg) of material

having fragment weights

greater than:

10 gm

5

2

1

0.5

0.2

0.1

0.05

0.02

0.01

700

12

11

none

none

31

91

160

230

280

340

390

430

Maximum Fragment Weight (gin) 2.9

19

28

81

150

200

250

320

340

400

450

480

11.2

B-4

1, 000

15

7 19

none

none

none

none

55

200

290

380

480

550

0.7

2

80

190

270

380

480

540

590

660

700

10.1

● O* ● ●:0 ~~ ● . ●*9 ● ● *

● :00

● : :* ● O ::

● : ● *

● 0 ●:6 ● me 9** :*9 ● O

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
VI. SOME CONCLUSIONS AND SUGGESTIONS

REGARDING FUTURE WORK

The factors discussed in Section IV may generally be

separated into two groups: those important to the degree of

fragmentation accomplished in a graphite assembly with centrally

located explosive; and those not important. In the former

category are scaling, amount of explosive, and the initial

geometry of the configuration. Less sensitive factors include

the effects of metal parts and variations in the physical properties

of the graphite. The type of explosive employed was found, as

expected, to have very little effect.

In examining the more important variables, it was observed

that a linear scaling rule proved sufficient for prediction of fullscale arrangements. Over a modest range around the 100 lb

equivalent explosive weight which has been suggested, it was

found that the degree of fragmentation was roughly inversely

proportional to the amount of explosive employed. More on the

basis of direct observation than of trends in the distribution

00000 ●*DO

● O 9

● 0 ●.: ●:0 ●0: ●:0 ● 0

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
-

● ☛ 9** ● *O ● 00 ● *9 ● O

● ● **

● : ● 0 ●0::

● * ● :

:000

● .:* :

9* ●:0 :Oe ● 0

parameters, it was concluded that the initial geometry of the

system tended to place an upper limit on the size of fragments

obtained.

The arguments regarding geometry provided somewhat

more optimistic estimates of the fragmentation of the full-scale

devices than those which had been accepted earlier. The conclusion was that disposal with 100 lb of explosive would leave

virtually no element material in pieces larger than 10 gm, and

would reduce

of less than 2

the major portion of the reactor core to fragments

W“ This estimate was predicated on very consistent

observations of maximum fuel element fragment sizes in 1/3- and

l/9-scale shots. No real guarantee can be provided that these

observations would prove true in a full-scale experiment;

however, common sense suggests that they would.

If the estimates in the previous section, coupled with

information about “acceptable” piece sizes (both what could be

allowed to reach the earth, and what would burn up on reentering

the atmosphere), should indicate the true feasibility of the method;

then the most desirable future experiment would be the destruction

of a full-scale, detailed device. The design of such an experiment

should prove quite simple. Firing the arrangement on a tower in

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
M● 0 ● 00 9:* ● 00 9** ● 0

●●b ● 0

**; *a ●: ●

● 0 :

● 0 :0 :0

● * ●0: ● e* ● ●:. ●

a large, barren, flat area, with a subsequent sweeping operation,

should serve very well. Acquisition of the model would no doubt

prove far more difficult, and considerable further work should be

done before such an expensive step can really be warranted.

The geometry effect is probably the most uncertain area

of the investigation , and that in greatest need of further attention.

Kreyenhagen has suggested the possibility of experiments in which

11

only a small sector of the assembly is recovered. These have

the immediate advantage that considerable care could be taken in

the recovery of the sector, using a sufficiently elaborate means

that secondary breakup need be of no concern. With such an

arrangement, a full-scsle experiment to determine if the complicated

element shapes do, indeed, break at the hole sites could be conducted

in a fashion which would be relatively economical in critical parts.

In such an experiment only the segment to be recovered would need

to be composed of element shapes, and stock graphite material,

such as 3/4” rods, should serve as an adequate inertial mock-up

for the remainder of the system.

The invariable observation from the shots listed in Table II

was that the maximum size of element piece recovered was

11. K. N. Kreyenhagen, Private Communication.

70 :“; ““: ‘;” : “;’ :“.

● *.:. ●; ● ●

● a ●

“o ..: ●:0 ● 00 ●:0 ● 0

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
WwiiiB ● m ● . . ● m9 ● 00 ● 09 .*

● O**** ●

● *9, ● 000

●

● 9 :

: :

● ●:* :

:: ●:0 ● ** ● 0

determined by the web size. This raises the question of how far

the equivalent explosive weight could be reduced without alteration

of this fact. Since substantial reduction of the dispossl system

weight could be effected if a projectile weight reduction could be

allowed, further experiments of the type done in this program on

the fuel elements are strongly indicated. A recently fired shot,

not analyzed with the other data, has demonstrated that a limit

of explosive weight exists below which the elements no longer

break at every web. A 1/9-scsle mixed element (B-1A shapes

both loaded and unloaded, and loaded B-4 elements) assembly,

similar to those shown in Fig. 4, was fired with the equivalent

of 31 lb of explosive. While no intact rod portions were recovered, numerous pieces of all types were found to have included

holes. The largest unloaded B-1A piece weighed 17 gm,

corresponding to a volume of a cube 22 mm on an edge. The

largest fragments of loaded elements in the B-1A and B-4 shapes,

respectively, were 12 gm, equivalent to a 19.4 mlm cube, and 6

gm representing a cube of dimension 16 mm.

Present disposal schemes include the use of a self-induced

after-heat process to reduce the radioactivity of the core before

exploding it. This suggests the advisability of an experiment in

● *O ● ●** ● ● “:0 :“” :“. 71

● ☛☛☛☛

● ☛✎☛ ● 0 ::

● ** : ● *

● * ● *O ● *9 ● ** :00 ● m

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
-

● 0 ● 09 ● ee boo ● 00 9*

99* ● *

● @e* : ●: ●

9** :

● 0 : :.:*

● * ●*: ● @* ● ● *e ●

which a core model is destroyed while at a high temperature. Such

an experiment could prove a bit elaborate; however, present

technology would allow, without great difficulty, the design of a

simple “air-gun” projector to place the explosive charge in the

heated model.

The possibilities of increased fragmentation per pound of

explosive through the use of certain aluminized explosives was

discussed in Section IV-C. While the advantage accruing from

the use of the loaded explosive does not appear substantial, an

experimental check of the gain would require very little effort.

The present view is that, barring appreciable differences in

fragrnentation, selection of the type of explosive for an actual

11 It

system would be dictated by its resistivity to radiation.

could be advisable to include aluminized explosives with those

now being tested for nuclear radiation damage.

All the experiments discussed above involve charges

extending the entire length of a cylindrical assembly; this

requirement seems quite advisable in the design of an actusl

system. In some early experiments not covered in this report,

it was found that charges extending only part of the length of a

solid cylinder left an unshatt ered cone at the end not containing

72 :“: ““: “;” . : :“. ● 900

● 00: ●:00

9* ●

● 0 ●0: ●:0 ●0: ●:0 ● 0

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
m● ● *e

● : ● 0 ● 9 ::

●

● 0 :0 ● e

: ● O

● ●:. : ●:0 :00 ● 0

11

explosives. It has been reported that disposal mechanisms

involving the implanting of s evera3 charges in the core are

under consideration. Both the scaling rule and an experimental

observation in this program (that most of the larger fragments

originate from the periphery of the assembly) indicate that

such an arrangement would provide greater fragmentation per

pound of explosive. A few scaled experiments would be useful

to assay the extent of the gain that could be obtained.

Finally, there is considerable area for improvement in

the theoretical and computational aspects of the study. The

difficulties in the purely empirical use of an unjustified distribution

became quite apparent when the question of geometry entered the

computations for the full-scale devices. While the principle that

enough empirical information could allow reas enable predictions

may still be valid, there certainly was not enough data on the

geometry effect for this program. Perhaps a better justification of -

Rosin’s Law than the author has observed (which is reputed to

11

exist ) would either justify the computational method used, or

point the way to a correct one. Also, the original view held in

this program, that hydrodynamic calculations of the problem would

prove fruitless, should probably be moderated to the attitude that

8** ● ●✎☛ “:” :“” :“; 73

● : :* 9*** :0 ● ** : be

● 0 ● 00 ● 00 9*9 :0* ● 0

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
such an approach

which the results

90 ● m ●: : ●:00

::00

● e : : :@

● . ●0: ●:0 ● . .. ●

might prove helpful. There are now data against

of such a study could be compared.

74 .“: “.: ● ●O* .Q ● .00 . ..

●

●

*

*O* ● m

: ●: ● 99** :0 ● * ● . . ● *. ..: ● .* ..

— ---

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
● 0 ● ** ● -e 9m* ● -* . .

● ● 00

● :00 . . . ::

● ● *,.*. :

● ●:0 : ● ● 0

:0 :.0 . .

DISPERSAL OF

Three shots in the

APPENDIX A

ONE-THIRD-SCALE MODELS

program were conducted to obtain

information on the manner in which the fragments and debris

were

were

dispersed by the explosive. Results from such shots

intended to give a guide to dispersal of engine parts in

a possible firing pad accident with NERVA. The purely

qualitative observations are presented below.

The recovery phase of these dispersal-recovery shots

was accomplished by a sampling technique with tarpaulins on

the ground at various distances. Two tarpaulins were located

at each of the following distances from the zero-point: 25, 50,

100, 150, 200, 250, 300, 400 and 500 ft. The center.of the

shot was elevated 3-1 /2 ft above the plane of the tarpaulins.

.

The size of each tarpaulin was graduated so as to have its

area numerically equal (in square feet) the distance from zeropoint in feet.

● 00 ● ● *8 9** ● * ●*. ● b ..75 ● : :0 ● : ● 0 ● m ::

● 00 : 9*

.8 ● . . ..* . . . :.. . .

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
● ☛ ●0: 9*9 ● 00 .** ● 0

● e ● *

● * : .:** ::0 ●

● * : :0 :0

. . ●.: ..0 ● ● *9 ●

The mass of fragments recovered at each distance is

listed in Table IX. Considering the graduation of the tarpaulin

sizes, and assuming angular symmetry, the amounts recovered

at each distance represent 2/m the amount deposited in a zeropoint centered, ring- shaped area with a width of 1 ft and radius

from zero equal

function derived

mass dispersed

to the distance listed. Integration of the

from such consideration to obtain the total

generally fell short of original mass by about

207’0. This probably indicated a real or virtual loss of finer

material, either as smoke, or due to improper construction of

the function at distances less than 25 ft.

The shots were slso instrumented with upright 4 ft x 8 ft

Celotex screens 25, 50, and 100 ft from zero point. The conditions

of these screens after the shots are shown in Figs. 13, 14 and 15,

.-

and some qualitative remarks are made in the figure captions.

A further qualitative observation may be made regarding the

tarpaulin recoveries. The zero values shown in Table IX at

distances of 400 and 500 ft do not indicate that no fragments

attained that distance; pieces, but very few of them, were found

at distances exceeding 500 ft. The tarpaulin data, as well as

those from the screens, indicated a decided distribution of

76 :“; ““; “:” . : +

● ● **

#*e*: ●:*.

● 9 ●

● 0 ●0: ●:0 ●0: ●:0 ● 0

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
● ☛ Uee ● *m ● *W moo ● o

● ● **

c’ :Os 000 ::

see ● :

● *

: ● 9

● ●:* : ●:s ● .* ● 0

TABLE IX.

The sizes of

text.

Shot Numb er

DISPERSAL DATA FROM DISPERSAL-RECOVERY SHOTS

samples taken at various distances are discussed in the

Graphite Mass (kg)

Graphite Configuration

Cased

High-Explosive Mass (kg)

Dispersal Data: Mass (gin) of

graphite recovered at distance

25 ft

50 ft

100 ft

150 ft

200 ft

250 ft

300 ft

400 ft

500 ft

r

RFS-4

60.8

Solid Cyl.

No

1.75

of:

21

78

57

48

43

24

16

3

0

RFS- 5 RFS-6

58.1 68.2

Solid Cyl. Modular

Yes Yes

1.69 1.70

101

70

77

32

31

11

10

0

0

68

151

110

67

18

5

9

0

0

● *O ● ● ** ● ** ● 0 ●’e ● ● 0 ..77 88 :00

● *** ● 0 ::

● : ● 9

● * ●:0 :00 ● 00 :00 ● O —, ----

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
m. ● ● *

$*O ● m

.

● O ● 9* 89* *99 ● 9* 60

9* ● ● m

-.*:O 4**

Fig. 13 Screen penetration from shot RFS-4. The setup, with

tarpaulins and screens, is shown in the upper left. The screens

shown in the other panels are labeled as to distance, in feet, from

the shot. As would be expected, the density of f ragrnents impact -

ing the screens is substantially reduced at greater distances, by

more than the factor of four expected for comparison of the 25 ft

and 100 ft distances. (Due to the cylindrical geometry, it is the

plane, and not the solid angle which should be considered. ) It may

be noted that at greater distances only the larger pieces

the single layer of 1/2” Celotex.

penetrate

78 :“; ““: “;” : :

● 99*

● 00:0 9* 9* ● :

● a ●0: ●:* ● ** ● m=

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● 9 ● m. ●** :

!!!----● ’.

shot RFS-5. This shot was Fig. 14 Screen penetration from

virtually identical to RFS-4, except that simulated metal parts

were employed around the solid graphite cylinders. Comparison

with Fig. 13 shows that the confining effect of the case mock-up

served to substantially reduce the number of graphite pieces

sticking to or penetrating the screens at all distances.

● *9 ●

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● *** ●:: ● *S : am

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‘m--’A –..

RFS-6 \

100ft ..

---- ..— .

,_...

Fig. 15 Screen penetration from shot RFS-6. It is interesting to

note the penetration of the 25-ft screen by one of the bars representing the reflector. The bar was apparently in an upright position, as

indeed all of them generally appear to be in Fastax pictures. The

upper left panel of the figure

reflector and pressure-shell

-.

shows some recovered pieces of the

model.

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Www ● ::.:.● 00 ● mm.. .0

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larger fragments at greater distances. This was assumed to be

primarily due to greater relative atmospheric drag on the smaller

pieces.

The pressure shell mock-ups were broken into 5 to 10

pieces, which were recovered at distances of 200 to 500 ft from

zero point. The Duralumin bars representing the reflector

system were recovered unbroken at similar distances. It seems

likely that the reflector model would have shattered, had it been

extensively tubulat ed beryllium rather than solid Duralumin.

Fastax studies of the shots indicated that a smsll portion

of the graphite was projected upward, but the greater portion left

the explosion site radially. The principal motion of the metal

parts was also radial, with virtually no tumbling of the reflector

bars. The initial velocity of the metal parts from the cased

assemblies was about 600 ft /see, with the graphite following

behind. In the uncased shot, the graphite pieces were observed

to have a maximum initial velocity of about 900 ft /see.

● ☛✠ ● .;. :.8+.0 9*.

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APPENDIX B

A SIMPLE FRAGMENTATION DISTRIBUTION

1. Introduction

An attempt is made in this appendix to obtain from probability arguments and a simple assumption (that a probability

per unit length exists for a separation plane) a form for the

expect ed distribution of fractional total volume in particle size.

The form will be the result of a “single shattering process”.

II. The Linear Problem

We shall first treat the problem in detail in one dimension,

since with some simple assumptions, this problem permits an

easy generalization to the full three-dimensional one.

Our experiment consists of taking a stick of length L and

shattering it. There will result n pieces, of length X1, X2, . . . Xn.

Thus, our sample space consists of the discrete random variable

n, and for each n we have n-1 continuous variables, x ~ . . . xn-1’

the variable Xn being fixed by the constraint xl+ . . . +xn = L.

:“p2”: “:” : “:” .“O ● 0 ● 00: : ●:00

● 0 ●

● 0 ●.: ●:0 ●0: ●:0 ● 0

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90

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To obtain the probability density, P(n; xl, . . . . Xn- ~), we

need to make some assumption about the way the stick breaks.

Our fundamental. assumption is that there is a probability, a ,

per unit length of breaking, and that this probability is independent of position on the stick.

Now P(n; xl. . . Xn-l) dxl. . . dxn ~ equals:

of no break in x1) x (probability of break in dxl ) x

J.

the probability of no break in

(Xl /Ax)

Lim ( I-aAx) =

Hence,

-(YX

P(n; xl. ..xl)l) = e

1

adx 1

J.

xl we have

-CYx

1

e .

(probability y

. . . . For

-ax 2

-CYx

e

n

. ..czdx e

n-1

(1)

if L

x < L and is O otherwise.

The probability of having n pieces is obtained by integrating

:::~-~::1 j::l-x:..~::::;2:..xn1,. (2,

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0- .,

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nature

form

A#liw::●::.::.● :● .. ●

900 .:.

:

:*

● ●:0 .

These integrals may be done by recognizing the recursive

of each intermediate integration- That is, we have the

aP

[ dx(a_-x) @/(p-l)!

Jo ~

and p is the number of integrations

upper limit of the last integration.

only because we made the simplest

a.

We have

P, = a /p. ,

P

performed, and a is the

P

This simplification occurs

of possible assumptions about

(3)

U3

Zp(n)=l, t

n= 1

~ nP(n) = l+aL .

n= 1

.“:&#: “:” : “:” .“O

.0 ● 9*

. . .. ma. ● *

(4)

(5)

(6)

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Thus n has a Poisson distribution, as might be expected.

We can also calculate the joint probability of n and x (where

x is any of the xl. . . Xn) and the probability of x by integrating or

summing over the other variables. This yields

P(n, x) = ae

-CYL (QL - @X)n-2 , n>2,

(n-2)!

-aL

= e 6 (x-L),

P(x) = ~e ‘ax + e‘aL 6 (x-L).

n= 1,

(7)

(8)

The conditional probability, P(n, x) /P(n), corresponds

to the probability that a piece selected at random will have

length x, given that n pieces resulted from breaking the stick.

P(x) is the same probability without any condition on n.

We now consider the analogue in one dimension of the

screening process in three dimensions. Given arm, xl. ..xnl

point in sample space, we can construct a function g(=, n, xl. . . xn- ~)

which gives the fraction of total length of pieces that have length

greater than =.

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mihhiii! ::●::e::o ●

.* ● : ●

● o c.. ●:.

: :e ● ●:, .

dxJ ‘J ‘~** ”xn.l) = L ~ _ ‘“

L

1

Xi>x

~ !i-

= L i=l

Xie(xi-x),

(9)

where e(x) = I(o)ifx>o (<0).

1.0- I 1.0-

I

I

I

I I

I I

9 I I

I I

I I

I

I

~

o 1.0“ o I.0 L

Fig. 16 Examples of g for specific sample points

Two such g-functions are shown in Fig. 16. If ~ L is

large, the first one shown has small probability. It is only for

large numbers of particles that g approaches a continuous function.

Since this is the case in which we shall be interested, we can

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!!-

compute the expected value of this function by weighting the

g’s by P(n, X1. .. xl-l ) and averaging over the sample space.

We have

—

“ax

[

= z

e 1l+ Q; (P-- .

L)

Note that this g(X) differs from the probability that one

piece selected at random has size greater than=. This probJ

L

ability is simply ~ P(x)dx * e-ax .

III. The 3-Dimensional Problem

We consider a cube LxLxL and assume

analysis applies to each

becomes the probability

per unit length. Thus a

axis of the cube. The

that the previous

parameter a

of the occurrence of a separation plane

point Q in sample space (discrete

variables n n n “ continuous variables . . . x

XYZ’ t n-l; yl”””yn -l;

x Y

‘l”” ”zn-l ) corresponds to reducing the cube to a rubble of

z

rectangular pieces. The amount of new area produced in this

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●●☛o+: ● ●: :0

● e ●

● O : : :0

● 0 ●.: ..0 ● ●:e ●

rubbling process is simply

A= (nX-l) L2 + (nY-l) L2 +(nz-l) L2 . (11)

From (6), the expectation value of n-1 is simply a L.

We then give another meaning to a from A = 3 a L3.

1

a= ~ area produced per unit volume.

The assumption of orthogonal separation

(12)

planes should not

be too bad if the major part of the rubble is in small pieces. In

terms of short-range order, the probability that the angle

between two intersecting separation planes is in the vicinity

of 90° is much greater than the

The long range orthogonality is

probability for small angles.

simply a means of sirnplif ying

calculations. If one were dealing with a single crystal, one

would choose the three (or more) most easily cleaved crystal

planes and probably get reasonable answers.

Since the probabilities in the

separable, the probability y of a point

three directions are

Q in permissible sample

space (permissible means ~ X, xy, xz < L) is the

product of the probability densities we obtained for the onedimensional case

--

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● ● e

● : :0 ● ● e ::

● om ● : : ::

● ●:. : .:* ● 00 ● 0

nx+n +n -3

P(Q) = e-3aLa y z .

Similarly we have from(7) and(8)

P(nxnynz, xyz) = P(nx, x) P(n y, y) P(nz, Z) ,

3 -CY(x+y+z) P(xyz) *Q e .

We now construct a function g(v, Q) which gives, for

each point in the sample space, the fraction of the total volume

that resides in particles whose volume is greater than or equal

to v.

1

g(v, Q) = — x Xyz

L3 all particles

for which xyz > v

1

nnn

=— XYZ

L3 z

Xiyizke(x. y .Z -v). l~k

i,j, k=l

(13)

( 14)

(15)

( 16)

Again we are interested in the case where the number of

particles is large and a particular g(v, Q) resulting from an

experiment is likely to be near the continuous function g(v) which

is the expectation value of g(v, Q). We have

g(v) = j dQ g(v, Q) P(Q) . (17)

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● ✎ i-oo

● . 9.: .:. . .:. .

The integration, unlike the probability density, does not

separate because of the presence of the choice function, tl(xyz-v).

However, each of the terms in the sum ( 16) gives a like contribution, and we pick up a factor n n n . We choose 6(x y z -v)

XYZ 111

‘lYIZ1

as the typical term and obtain

L

g(v) = > x nnn

1

dxdydz xyz O(xyz-v) P(n n n , xyz) .

nnn XYZ XYZ

XYZ o

(18)

The n-sums can be done to give

L

g(v) . -!-_

L’ 1

dxdydz XyZ 6(XyZ-V) f(X) f(y) f(z) ,

f(x) = e-ax

[ 1

a2(L-x) + 2a -1- 6 (x-L) .

(19)

We shall be interested in the case where we have a large

number of particles ( a L >> 1). This limit can be conveniently

obtained from ( 19)

m

g(v) = J’dxdydz CY6

0

by L-- co. We then have

-a(x+y+z )

xyz tl(xyz-v)e . (20)

We now define a mean dimension r and a dimensionless

parameter ~ proportional to the mean dimension.

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.-.

● ● e**

● *****8 . .

● 9* ● : :

●

:: ●:0 : ●:0 ● ** ● *

~=v113

.

(21)

v=~r . (22)

If we make these substitutions in (2 O) and let CYX-- x,

we obtain a universal function, g( n), to describe the volume

fraction. Thus a enters as a scaling parameter on the mean

dimension of a particle for the case where a L>> 1. We have

m

g(q) = f ddydz 6(XyZ-TJ3) e

-(x-l-y+z)*YZ

.

0

The z-integration can be done

m

dq) = f dxdy (xy + Y13)e

-(x+y+r?3/xy) .

0

(23)

(24)

If one uses x = r cos (@/2), y = r sin (?5/2), this may be

transformed into:

- 7r12

Sf

-r(l+sin9)1/2

g(q) = dr d @r (r2sin #/2 + q3) e

- 2q3/(r2sin +)

00

(25)

a form suitable for numerical integration.

The function g(q ) was computed in the r, ~ plane using

Simpson’s rule in the regions of maximum contribution. It is

‘- .._

‘Nc~$/F/[j, i- .

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— . . . . . . . . ...000 ● 0

● 9

::.; : .:0.

● * ● ●

● . : :0

● 0 ●.: .:0 ● .:0 ●

listed in tabular form in Table X and shown in Figs. 17 and 18.

IV. Comparison with Experimental Results (Qualitative)

If we try to scale experimental data to obtain a best fit

to Fig. 17, we find in general that the theoretical g(x) is too

steep, and that the data for the

cutting the theoretical curve at

most part fall in a broad band

the 50% level (a result of scaling)

and having approximately half the slope of the theoretical curve.

These features can probably be traced to the neglect of

(1) an CYthat varies radially because of the radial decay of the

pressure wave and (2) the abrasion and secondary breakage that

occur from the tumbling about and impacts created by the outpouring of the explosive gases after the explosion proper. Both

of these effects, if somehow incorporated in the theoretical curve,

would cause the theoretical g(x) to flatten out in better agreement

with the experimental data.

In particular, effect (2) above should be more noticeable

in a geometry

configuration.

of many small parts when compared to a solid

This is indeed found to be the case, the former

giving a considerably flatter curve.

These effects could be incorporated by (1) assuming an

a (r) to vary as the radial stress, and then taking a weighted

-- .

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● ● ☛

● ✚ :0 ● ● 0 ::

● 9*9 ● O ● : ● 9

● ●:0 : ●:0 :00 co

TABLE X. THE INTEGRATED VOLUME

g(n)

v g(r?)

0.1

0.2

0.3

0.4

005

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

2.2

2.3

2.4

2,5

2.6

2.7

2.8

2.9

3.0

3.1

3.2

3.3

3.4

3.5

3.6

3.7

3.8

3.9

4.0

0.99501

0.99483

0.99344

0.98908

0.97975

0.96377

0.94009

0.90840

0.86911

0.82314

0.77183

0.71668

0.65925

0.60102

0.54331

0.48723

0.43367

0.38327

0.33649

0.29358

0.25465

0.21968

0.18853

0.16101

0.13689

0.11587

0.09769

0.08204

0.06865

0.05725

0.04758

0.03942

0.03257

0.02683

0.02205

0.01807

0.01477

0.01205

0.00981

0.00796

● ☛✎ ❊✛ ~ee

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DISTRIBUTION FUNCTION,

-lng

0.0050

0.0052

0,0066

0.0110

0.0205

0.0369

0.0618

0.0961

0.1403

0.1946

0.2590

0.3331

0.4166

0.5091

0.6101

0.7190

0.8355

0.9590

1.0892

1.2256

1.3679

1.5156

1.6685

1.8263

1.9886

2.1553

2.3260

2.5006

2.6788

2.8604

3.0453

3.2333

3.4243

3.6181

3.8145

4.0135

4.2149

4.4187

4.6247

4.8328

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APPROVED FOR PUBLIC RELEASE
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average of g(x) ‘s. and (2) assuming that each of the rectangular

parallelepipeds considered is abraded to an ellipsoid, or broken

in half if the longest dimension exceeds some factor of the

smallest diameter. In view of the unpromising nature of such

assumptions,

Rosin’s Law.

the fit of the data has been left to the semi-empirical

In Fig.

plotted in a fashion to

that Wackerle obtains

19, the theoretical curve g(q) has been

permit direct comparison with the shapes

from his experimental data. For the

purposes of plotting, a vslue for a

chosen. Note that in this appendix

to Wackerle’s F.

of 1.8 planes per mm was

the function g(q) corresponds

. .

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