Adiabatic expansion of high explosive detonation products

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TID-4500, UC-4 Chemistry

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UNIVERSITY OF CALIFORNIA LIVERMORE

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UC R L - 504 2 2 CI

ADIABATIC EXPANSION OF HIGH EXPLOSIVE DEPOMAPION PRODUCTS E. L. Lee H. C. Hornig

J. W. K u r y May 2, 1 9 6 8

LEGAL This report

was prepared as an account of nor the Commission, nor any person

NOTICE

Government sponsored work. Neither the United States. acting on behalf of the Commission: A. Makes any warranty o r representation, expressed or implied. with respect to the accuracy, completeness. or usefulness of the information contained in this report, or that the use of any information. apparatus, method, or process disclosed In tbls repOrt may not infrlnge privateiy owned rights; or 8. Assumes any liabilities with respect to the use of. or for damages resulting from the use of any information. apparatus, method, or process disclosed in this report. As used in the above. “person acting on behalf of the Commission” includes any employee or contra~torof the Commission. or employee of such contractor, to the extent that such employee or contractor of the Commission. or employee of such contractor prepares. disseminates. or provides acces8 to. any informatlo? pursuant to his employment or contract with the Commission. or his employment with such contractor.

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DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency Thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document.

A

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ADIABATIC EXPANSION OF HIGH EXPLOSIVE DETONATION PRODUCTS Abstract A relatively simple p r e s s u r e , volume, energy ( P V E ) equation of s t a t e has been developed t o d e s c r i b e the adiabatic expansion of detonation products. Specific equations f o r ten explosives have been

p r e s s u r e data and r e s u l t s f r o m metal acceleration experiments.

The thermo-

dynamic and hydrodynamic r e q u i r e m e n t s placed upon this equation of s t a t e a r e discussed and a comparison of calculation

determined using detonation velocity and

and experimental r e s u l t s a r e presented.

Introduction Numerous equations of state

2J

have

r e s u l t s from cylindrical, metal expansion

been proposed for describing the adiabatic

experiments t o develop an equation of

zyxwvutsr zyxw

expansion of detonation products.

How-

s t a t e which c a n a l s o be used for geome-

ever, when these equations a r e used in

t r i e s involving l a r g e expansion of the

hydrodynamic calculations, they do not

detonation products.

accurately predict the performance of an explosive.

To r e m e d y t h i s , Wilkins

4

Section I of t h i s r e p o r t d i s c u s s e s the

form of the equation and d e s c r i b e s the

developed an

procedure used t o evaluate the constants.

equation based p r i m a r i l y on s p h e r i c a l , metal expansion experiments. H i s equa-

Section I1 d i s c u s s e s the experiments

and the hydrodynamic calculations used

tion, when used in hydrodynamic calcula-

in t h e i r interpretation.

t i o n s , accurately predicts r e s u l t s for experimental geometries emphasizing the

Appendixes A-D contain a complete

e a r l y s t a g e s of detonation product expan-

tabulation of the experimental and calcu-

sion.

lational r e s u l t s .

We have extended his work using

A

-1-

Section I. The Equation of State A.

zyx

Contributions of the various t e r m s

FORM OF THE EQUATION

zyxwvu zyxw zyxwvu zyxwv in Eq. (1.3) to the p r e s s u r e a r e shown in

Fig. 1.

The equation of s t a t e used h e r e is empirical.

Its development follows an e a r l i e r 5

1 .o

equation proposed by Jones and Miller and a n equation developed by Wilkins .4 Therefore we r e f e r to it a s the Jones-WilkinsLee (JWL) equation.

0.1

Jones:

0.03

P = Ae-R.V - B + C . T

(I. 1)

0.01

L

0

Wilkins : P =

I)

2

% + B(I - eV) e-R +v V V

a + Be- R V + P(A) = -

Q V

C p+1

0.003

I

UE

a

0.001

0.0003

(1.2)

0.0001

where

0.00003 0 .oooo 1 0.1

JWL:

(

P = A 1 -

(

-R2'V

-R1*V -R2'V P(A) = Ae + Be

1

3

10

30

100

zyx

-R1'V

V

RIU* V) e

+B1- R;V)e

0.3

Fig. 1. Contribution of various t e r m s in JWL equation of s t a t e t o total adiabat p r e s s u r e f o r Composition B, Grade A .

W E

+T

+-p + 1

(1.3)

B.

THERMODYNAMIC-HYDRODYNAMIC CRITERIA P a r a m e t e r s in the equations a r e chosen

V

V stands f o r the relative volume -

t o satisfy the following conditions: 1 ) the

VO

zyxwvutsrqponmlkjih measured Chapman-Jouguet ( C - J ) s t a t e , 2)

following the convention used in hydrodynamic codes. However, substitution of

the measured expansion behavior in the

V (specific volume) * p o (loading density) SP for V w i l l convert these expressions t o

tions at l a r g e expansions, and 4 ) hydro-

specific volume.

dynamic continuity.

cylinder t e s t , 3 ) thermodynamic limita-

The p r e s s u r e s a r e given

in megabars (Mbar) and adiabat is abbreviated as A .

The measured C - J conditions a r e directly entered into the equations.

-2 -

zy 8

The

cylinder t e s t expansion behavior is entered

Moreover, for m o s t H E s , the entropy a s s o -

by a repetitive t r i a l and e r r o r procedure

ciated with the C - J adiabat is higher than

using two-dimensional hydrodynamic calcu-

for the two phase region; thus water w i l l

lations. This procedure is described in Section 11.

not condense during the adiabatic expansion.

zyxw zyx zyxwvut zyxwv

The f o r m of the J W L equation allows

US

Secondly, in the J W L equation, the pro-

t o impose two sensible thermodynamic

file of the expansion at l a r g e values of V

limitations at l a r g e expansions.

is dominated by the value of w.

Firstly,

valueof I?

we fix the total available energy, Eo(Mbar

E

(

- -

Since the

should approach

c c / c c ) , a t a value consistent with the

CV a t l a r g e expansion, and s i n c e T' = o + 1

available chemical energy.

for V

This energy

is obtained either from detonation calorim8 etry6a7 o r RUBY calculations .". 4 ,

of w to 0.20 < (u < 0.40, which is consistent

with the heat capacities of the gaseous

products f o r the explosives discussed in

Calorimetric E o ' s and the JWL values a r e given in Table I.

1 0 , we a r b i t r a r i l y l i m i t the choice

this report.

The c a l o r i m e t r i c

P r o p e r hydrodynamic continuity is

values a r e based on H 2 0 ( g a s ) since it i s

doubtful whether water vapor c a n condense

a s s u r e d if P is everywhere a monotonical-

t o the liquid s t a t e in the time it takes for the high explosive g a s e s to expand initially.

ly decreasing function of the relative vol-

*RUBY,

ume.

This is the s a m e a s requiring

r to

be g r e a t e r than z e r o and continuous, a

C-J-adiabat composition at a relative volume of 10 is used to calculate the available chemical e n e r g y

Table I.

condition which cannot be predetermined by limitations on the selection of

Comparison of EO used in JWL calculations and detonation calorimetric results. Eo (Mbar c c / c c )

JWL

Detonation calorimetry

0.105

0.109

Nit rornethane (NM)

0.051

0.050

PETN

0.101

0.101

0.07

0.070

Composition a, b

HMX

.

TNT

zyxwvuts

Comp B, G r a d e A

RDX, TNT (64/36)

0.085

0.081

Cyclotol

RDX, TNT (77/23)

0.092

PBX 9011

HMX, Estane (90/10)

0.089

-

PBX 9404

HMX, NC, C E F (94/3/3)

0.102

0.098

LX-04-1

HMX, Viton (85/15)

0.095

0.097

LX-07-0

HMX, Viton (90/10)

0.096

-

aAbbreviations a r e NC phosphate.

=

Nitrocellulose, C E F = T r i s 8-chloroethyl

bNumbers are approximate weight percent. -3 -

zyxwvutsrq zyxwvut zyxwvut zyxwvuts the initial guess for R1, R 2 and w used in

coefficients, but must be checked for each turned out that R1 the value of

r has

the hydrodynamic calculation resulted in

In practice, it has

specific equation.

p

4 and R1

Z

1, and that

a metal kinetic energy 10% too high, for example, a new guess f o r which E - Eo

always been g r e a t e r

than 1 f o r the explosives we have investi-

a t the s a m e V is 10% l e s s would give

gated.

agreement with experiment.

Near the C - J point the high p r e s -

A computer code was used t o calculate

s u r e behavior is dominated by the coeffi-

E - E 0 for systematic variations in R1, R2, and w and t o then compare the values with the E - Eo values calculated using

cient R1 as can be s e e n in Fig. 1. Even

is

f o r compressions n e a r 2 ( V F 0.5), still g r e a t e r than 2 .

the initial guess. An adiabat that varied

At v e r y l a r g e compressions, the p r e s s u r e behavior would be dominated by w.

f r o m the initial guess by the s a m e amount

This is probably an incorrect description,

that the initial guess v a r i e d from experi-

but is well outside of the range of p r e s -

ment was then used in the next hydrody-

s u r e s normally encountered in experi-

namic calculation.

ments on explosives.

with experiment w a s usually within 1%. If

C.

Resultant agreement

not, the procedure was repeated.

METHOD F O R DETERMINING COEFFIC IEN TS

Final values f o r R1, R2, and w give calculated w a l l velocities ,within 1%of the

zyxwvutsrq

To u s e Eq. 1.3, s i x constants must be determined.

experimental w a l l velocities. The detailed

The l i n e a r coefficients A ,

comparisons of calculation and experi-

B, and C a r e determined f r o m Eo, D, PcJ

mental r e s u l t s a r e given in Appendixes

and po once a guess is made for t h e nonl i n e a r coefficients R1, R2, and w. A

A and B.

hydrodynamic calculation is then c a r r i e d

D.

out and the r e s u l t s a r e compared with experiment.

A procedure based on calculated energy change (Eo - E ) along the adiabat w a s evolved which minimizes the number of g u e s s e s required t o obtain agreement with experiment.

To a f i r s t approximation,

A = - e O R1

(See Table 11.) F o r some of the explosives listed w e have given two o r t h r e e s e t s of coefficients.

The best s e t is labeled AA.

zyx zyxwvut report.

Where PcJ has not been m e a s u r e d , we

-RIV

B +-e R2

-R2V

+ - -C

wVw

have made an estimate assuming that

2.7 < rc,

EO

f o r a given expansion.

C

2.8.

A simple multiple of

10 kbar, causing r t o fall in this range, w a s chosen as the C - J p r e s s u r e . These values a r e x t d by an a s t e r i s k (::). Table 111 gives a l i s t of coefficients f o r

(I.4)

f o r a volume of the detonation products characteristic

been determined f o r ten high explosives.

which w i l l be r e f e r r e d to later in this

0

E - E

JWL equation-of-state coefficients have

The other s e t s a r e given f o r comparisons

the energy delivered t o a metal shell at a given expansion is proportional to E - E evaluated from

RESULTS

Wilkins' equation applied t o LX-04-1 and

If -4 -

zyxw zyx zyxw zyxwvutsrqp zyxwvutsrqponmlkjihgfe zyxwvutsrq zyxwvutsrqpo zyxwvutsrqponm Table 11. J W L p a r a m e t e r s .

HMX'

-4

B

NM

DA

7,7828 0.01071428

2.0925

0.00~0 4 2

0.0077042 4.4

0.056895

PETN AA

AB

PBX 9404

AA

5.24229

6.03414

0.09112357

6.34717 0.079982

8.5445

0.076783

0.20193

0.0104527

O.OIO~IB

4.8

4.15

4.2

'0.010753 4.7

0.007zio 4.2

0 . 0 0 8 ~ ~ 3 10.011585 0.006a631 4.25 4.65 4.07 1.45 1.30 1.00

0.1Y241 0.0064342 0,006651

Cyclorol

AA

PBX 9011

LX-

LX-04-1 AB

3.71213 0.032306

7.9653

1.352, 0,030284

Comp Grade B. A

AB 6.12023 0.206750

TNT

8.4984

0.15277

6.11834 0.016672

07-0

AC

5.94143

0,050039

6.8674 0.0790406

0.0094815 4.0 0.9

0.0114438 4.2 1.0

1.0

1.2

1.0

1.2

0.3

0.275

0.25

1.10 0.34

1.1 0.35

1.0

0.3

0.95 0.30

0.00754 4.6 1.35

0.3

0.25

0.25

0.35

0.25

0.3

0.4

(Mbar cc/ccl

0.105

0.051

0.051

0,101

0.07

0.085

0.092

0.089

0.102

0.102

0.095

0.095

0.095

0.096

cgc,

1.891

1.128

1.128

1.77

1.63

1.717

1.154

1.77

1.84

1.84

1.885

1.865

1.865

1.865

PCJ (hibar)

0.4Za

0.12510

0.1409

0.3211

o,2112

0 . 2 0 5 ~ ~ 0.3Z1'

0.34a

0.37"

0.3904

0.34"

0.364

0.37a

2.7105

2.5386

2.1875

2.812

2.72i

2.706

2.7307

2.7611

2.85

2.658

2.9355

2.69

2.69

2.7621

0.8311

0.693

0.798

0.825

0.85

0.88

0.88

0.847

0.847

0.846

0.864

c n

- - ~

-.I

K2 Y(

0.6

Eo

I'cJ

0.6287

(cm~sec)o.sii

'PCJ aasunled fruni P =

0.6287

A,

2.7 < I'cJ > 2.8

,

Table 111. C o e f f i c i e n t s f o r Wilkins a n d T - l a w e q u a t i o n .

PBX 9404

LX-04 - 1

I? -law

Comp B Simulated BKW

a

0.0045 6 3

0.008335

-

0.02771

0.059937

0-

0.00526 6

0.009435

0.126

0.04645

0.09270

B

6.572

5.943

-

0.01191

0.3427

C

0.029 4.0

-

Q

0.032 4.0

0.08085 3.785

0.03515 3.43

R

4.0

4.0

-

0.6486

3.054

w

0.35

0.40

-

1.1235

0.8588

0.1343

0.1126

0.0865

0.0903

0.0836

1.84

1.865

1.717

1.717

1.714

(Mbar)

0.39

0.36

0.295

0.280

0.259

VCJ D (cm/psec)

0.7266

0.7316

0.7302

0.749

0.763

0.880

0.848

0.798

0.807

0.799

EO ( M b a r cc/cc)

pCJ

P B X 9404.

2.706

Simulated LJD

zy

2 3 w i t h t h e BKW,15 LJD, a n d T-law e q u a -

In t h e c o u r s e of o u r w o r k t h e

BKW a n d L J D a d i a b a t s f o r C o m p B w e r e

t i o n s of state. For LX-04-1 a n d P B X 9404

simulated'

b o t h t h e J W L a n d Wilkins' r - b e h a v i o r are

w i t h Wilkins' e q u a t i o n of

state to f i t t h e m i n t o a format suitable f o r

zyxw

input i n t o t h e H E M P Code.14 T h e s e coef-

(For t h e r e m a i n i n g HE'S, I? vs V p l o t s a r e g i v e n

f i c i e n t s a r e also l i s t e d in Table 111 a l o n g

i n A p p e n d i x D.)

w i t h the I?-law c o e f f i c i e n t s .

V c u r v e s have characteristic d o u b l e m a x i m a . If o n e treats t h e

p l o t t e d i n F i g s . 3a, b, c, d.

All the

(i:F)s

By p l o t t i n g T = - - v e r s u s v f o r t h e C o m p B a d i a b a t , t h e J W L e q u a t i o n is c o m p a r e d g r a p h i c a l l y in F i g s . 2a, b , c ,

r versus

high d e n s i t y g a s e o u s d e t o n a t i o n p r o d u c t s

as h a v i n g some of t h e p r o p e r t i e s of a -5-

4

zyxwvutsrqp

zyxwvutsr I

I

I

8

r(

CI

r 2

r

I

0

zyxwvutsrqponm zyxwvutsrq zyxwvu JWL EquationJ

1

I 1

I

I 10

3

1

30

V

Fig. 2a.

4

Fig. 2b.

Comparison of I? calculated f r o m the JWL equation and the BKW equation f o r Composition B , Grade A.

Comparison of I? calculated f r o m the JWL equation and the L J D equation f o r Composition B , Grade A.

the c o m p r e s s e d l a t t i c e expands approach-

I

I

I

ing the equilibrium distance. The logar i t h m i c derivative of the l a t t i c e p r e s s u r e alone will exhibit a singularity at Plattice = 0 , since

r T h e r e f o r e , r e s u l t s f r o m lattice plus

zyxwvuts zyxwvu zy t h e r m a l p r e s s u r e derivatives will exhibit

L W L Equation

a maximum f o r the usual intermolecular

-

l t 0

potential descriptions such as 6 - 1 2 , expo-

1

3

10

V Fig. 2c.

nential 6 o r modified M o r s e .

30

The locations of the first o r high den-

Comparison of r calculated from the JWL equation and the r - l a w for Composition B, Grade A.

s i t y m a x i m a shown i n t h i s r e p o r t a r e at

g a s densities somewhat higher than one

would expect f r o m t h e equilibrium dis-

t a n c e s derived f r o m t h e condensed phases

solid 1attice:j2

the I? v e r s u s V curve

of the product g a s e s .

It is suggested that

should exhibit a maximum n e a r a volume

the p r o p e r equilibrium distances t o u s e

corresponding to the equilibrium l a t t i c e distance. This is simply because the

m a y be those f o r high p r e s s u r e allotropic

A s an example, water e x i s t s as ice VI1 at 2 1 kbar and h a s a density of 1.56 g / c c .

f o r m s of t h e condensed phase.

l a t t i c e p r e s s u r e , which c a n be a m a j o r

p a r t of the total p r e s s u r e , falls to z e r o a s

-6-

A

zyxwvu 4

3

zyxwvutsrq zyxwvuts zyxwvutsrqponm i - 2

A0 I

0

1

-- PCJ =

0.36

10

3

V

Fig. 3a.

zyxwvu I

I

1

30

Comparison of JWL r calculations f o r LX-04-1 adiabats AA and AB.

(

I 3

1

10

V

r for

Fig. 3b.

4,

I

3

LX-04-1, Wilkins equation.

I

I

I

Wilkins equation

zyxwvutsr r

2

PcJ = 0.37 Mbar

I ---- 0.39 I m 3 A0

0

PcJ =

Mbar

10

1

V

V

Fig. 3c.

Fig. 3d.

Comparison of JWL I? calculations for PBX 9404 adiabats AA and AB.

E.

I? f o r PBX 9404, Wilkins equation.

DENSITY DEPENDENCE T h e JWL equation contains the assump-

We cannot explain the second (low dens i t y maximum) but have observed that it

tion that the Gruneisen p a r a m e t e r (G) is

falls roughly at the c r i t i c a l density of the

constant* whereas it is a function of E and

g a s e s produced by CHNO explosives.

V in the most general description.

It

*I t

is v e r y difficult t o investigate this possi-

zyxw

is possible to make the JWL equation consistent with the measured dependence of D on p by removing the constraint onG, i. e . , allow G = G(V) o r G = G ( E , V ) , a s described in U C R L - 7 0 8 0 9 .

ble c o r r e l a t i o n quantitatively since t h e r e

a r e no simple , reliable descriptions of fluid behavior n e a r the c r i t i c a l density. -7

-

zyxwvutsr zyxwvutsrqponmlkj zyxwvu zyxwv where

With the single additional assumption

that Eb = Eo * p b / p o one can calculate the

C - J s t a t e and adiabatic expansion f o r v a r ious values of p b in a range within *IO% po.

C.

of

zyxwvut zyxwvutsrq

The only coefficient which changes is However, the usual procedure is t o

u s e a m e a s u r e d value of D' and the original value of

r to

specify the C - J state and

determine new values f o r A , B, and C . Original values for HI, R 2 , and

u),

I?,

are

USES AND LIMITATIONS

retained and Eb is determined a s above.

The principal value of the J W L equation

Using f3bJ from

of s t a t e lies in i t s ability t o give an accu-

r a t e description of' the C-J adiabat.

The

coefficients we have determined for a J W L equation should b e considered a condensed and

s u m m a r y of m e a s u r e d C-J adiabat expansion p r e s s u r e s f o r the high explosives l i s t e d . 0ril.y to a f i r s t approximation are

zyxwvutsrq they a description of' the equation of state

the determination r e q u i r e s the solution of

of the high rtsplosive product g a s e s a t

the following s e t of t h r e e l i n e a r equations f o r A',

El,

points removed f r o m that adiabat ( i . e . ,

and C ' .

points which are reached by experiments

at other than the listed loading density o r by reshocking the detonation products).

+

However, since the J W L equation satis-

C' (U,+lj

f i e s the c r i t e r i a in Section IIR, the uncer-

vcJ

tainty involved in using t h i s description o v e r a limited r a n g e outside of the fitted experiments i a , hopefully, niiriimized. F u r t h e r m o r e , since these c r i t e r i a a r e satisfied, this eyuatioii of s t a t e should not

where

only be useful as an "engineering" equation t o be used i n various calculations f o r the high explosives 1.isted h e r e , but should a l s o s e r v e as a description of the t h e r m o dynamic behavior of the expanding g a s e s . The lack of t e m p e r a t u r e information l i m i t s the kind of thermodynamic informa-

and

tion one can deduce d i r e c t l y , hut the properties of the equation allow it t o be used either in a t e s t of proposed P, V, T -8

-

zyxwvuts zyxwvutsr zyxwvut zy

equations, o r in the construction of a P,

and have applied t h i s information t o gener-

V, T equation.

a t e equations of s t a t e for CHNO explosives

where hydrodynamic m e a s u r e m e n t s w e r e

W e have observed that the nonlinear

lacking.

However, we caution against

coefficients R1, R 2 and w do not v a r y

using such a procedure f o r other c l a s s e s

appreciably f r o m one explosive to another

of high explosives.

zyxwvu

-9 -

Section 11. Experiments and Hydrodynamic Calculations Experimental accuracy and the validity

zy

0.57~ for radius-time d a t a , and 1%for

of our calculation procedures determine

wall velocity, provided the tube surface

how well the adiabats listed in Section I

is electropolished o r chemically cleaned.

actually do r e p r e s e n t the behavior of the

Detonation velocities a r e measured by

detonation products.

placing pin switches 23 c m a p a r t on the

In this section, we

a

surface of the tube.

describe the standard t e s t s and, in addi-

The effect of explosive diameter on

tion, give r e s u l t s from t e s t s and calculascaling, and the effect of metal yield

cylinder t e s t r e s u l t s h a s been investigated. One-in., 2-in. and 4-in. d i a m , scaled

strength.

experiments have been c a r r i e d out for

tions designed to investigate stability,

PBX 9404 and TNT. Also, 1-in. and A.

EXPERIMENTAL CONFIGURATIONS FOR MEASUREMENT O F ADIABATIC EXPANSIONS

2-in. diam, scaled experiments were done with Comp B.

The r e s u l t s (Tables' IVa-

IVc) s c a l e hydrodynamically within e x p e r In o r d e r to describe the adiabatic expansion of the detonation products it is n e c e s s a r y to obtain experimental data f o r

imental e r r o r .

T h e r e f o r e , for the explo-

the initial point (assumed to be the

behavior.

Chapman-Jouguet point) and f o r points

explosives with long reaction zones.

s i v e s t e s t e d , the standard 1-in. diam t e s t closely approximates infinite diameter This conclusion is not t r u e f o r

during the subsequent expansion. The

In particular, recent experiments with p e r -

C - J p r e s s u r e and detonation velocity

chlorate-containing explosives indicate

experiments characterizing the initial point have been described elsewhere.12

diameter effects even with 2-in. diam

zy zyxw zyx zyxwvuts zy charges.

The cylinder and s p h e r e t e s t s used t o

The change in cylinder wall velocity a s

c h a r a c t e r i z e the expansion behavior a r e

a function of position along the cylinder

described below.

was also investigated. Data f o r LX-04-1

The standard cylinder t e s t geometry

in the standard copper cylinder a r e p r e -

used for these experiments i s shown in

sented in Fig. 5 . For R - Ro < 2.5 c m , radius-time behavior is independent of

Fig. 4 . It is s i m i l a r t o the t e s t configurations used in e a r l i e r work.16,17 The

axial position if L / D 2 4.5.

radial motion of the cylinder wall is r e -

d a r d t e s t , m e a s u r e m e n t s a r e made at an

corded by a s t r e a k c a m e r a using shadow-

L / D of 8.)

graph techniques.

The viewing slit is

20 cm from the booster explosive.

(In the stan-

The arrangement f o r the spherical

The

charge experiments4 is a l s o shown in

r e c o r d is read o n a precision comparator

Fig. 4 .

which punches the coordinate data directly

H E inside a c l o s e fitting hemispherical

onto IBM c a r d s . A computer code then

aluminum shell, the other half of the

u s e s these data to calculate radial wall

s p h e r e being simulated by a cylinder of

velocities a t specified values of R

-

It c o n s i s t s of a hemisphere of

the s a m e H E .

Experimental reproducibility is within

The charge is initiated a t

the center with a spherically divergent

-10-

n

zyxwv zyxwvu zyxwv zyxwvutsrqp cm

Plane wave llens ens2

I

Comp B

Cylinder:

OFHC Copper, ASTM-B-187, density = 8.93 g/cc, i .d. = 2.55 cm, 0 . d . = 3.07cm, wall = 0.26 cm, length = 30.5 cm

Explosive:

0.d. = 2.54 cm, length = 30.5 cm

Initintcr:

5F.-1 detocatsr, Tetryl pellet, P-22 plane wave lens, 1 .27 cm thick !lump

B bcsster

0.65 cm A I Shell

I_ I

4

30.5cm

zyxwvu zyxwvut zyx

t-leniispherical s h e l l : Aluminum, ASTM-6061-16 i . r . = 15 cm, density z 2 . 7 0 g/cc, 0 . r . = 15.65 cm, w a l l =0.65crn.

Explosive:

Hemisphere, 0.r. = 15 cm, cylinder m a t e , 0 . d . = 3 0 . 5 cm, length = 15 c m .

Initlo:or:

SE-3,

sphcrically divergent

"

point"

detonator.

Fig. -1, Standard experimental t e s t geometries.

detonator.

The compilation of r e s u l t s f o r both the

Fliotogrliphy a i d data reduction

were the same a s f o r the cylinder t e s t s .

standard cylinder t e s t and the s p h e r e t e s t

To obtain good film r e c o r d s , it w a s neces-

is to be found in Appendixes A and

s a r y t o have a polished finish on the metal,

B.

t o illuminate the s p h e r e with a parallel light beam, a n d to eIic.iixe the experiment in a vacuum

CksiTibCr.

HYDRODYNAMIC CALCULATIONS The hydrodynamic codes KO"

HEMP,14 w e r e used to determiric -11-

and .tii(
E-Ol

2.7174

I .72XlE-0:

2.6228

1.5451E-01 1.3916E-01 1.2639E-01 1.15743-01 1 :0683E-01 .).9355E-02

2.7844 2.9380 3.0826 3.2170 3.3397 3.4494 3.6236 3.7285 3.7554 3.7016 3.5721 3.3804 2.8[133 2.4065 1.9470 1.6723 1.5277 1.4569 1.3999 1.3987 1.3902 1.3994 1.3996 1.3998 1.3999

zyxwvu zyxwvutsrqponm

7.0000E-01

0.GCIOJE-UI

,,~,~oLlk:-ol

I.(IUUUE 00 1.1000E 00 1.2000E 00

1 . J548E-01

I.fA34E-01 1.3865t:-01

9.99203-02

7.33753-02

1.3000E 00 ~.~

5.50523-02

00

4.229OL-02 3.33OOE-02 2.6877E-02 1.8757E-02 1.4118E-02 1,06443-02 8.42t,7E-0? 6.8576E-03 5.C7311E-03

1.40011E 1.5000E I.hUO11E 1.80003 2.0000E

z.mu

LX-04-1 adiabat A B

1.4405E -01 1.5513E -01 1.3674E -01 1,21423 .01 1.08643 -01

LX-04-1 adiabat A C 7.2900E-01

~

2.1, !; 2. >I,.,.> 2.7 3 7 0

zyxwvutsrqponmlkjih 8,65163-04

00

LX-04-1 adiabat A A 7.2900E-01

I .H7 i,; 1.. - 'J ! I . !J84 : ; l -~U !

i __

OU 00 00

00 2.25003 00 2.500OE 110 2.7jOOE 00 9.WUOE 00

1.0000E 01 1.5000E 01

4.81683-04 2,80766-04

9.i960E 02 tI.H'J89E 02 H.I:35E 32 6.9629E -02 6.1047E-02 5.4681E-02 ~.~ 4.985LE -32 4.6098E 32 4.3107E . J 1 3.86243-02 3.53763-02 3.23183-02 2.8952E 02 2.805lE -02 2.6491E.02

l.5857E-02 1.4035E-02

312644

3.3604 3.5054 3.5814 3.5853 3.5205 3.3981 3.2350 2.8642 2.5389 2.2803 2.1731 2.1620 2.1986 2.3756 2.3303 2.1059 1.8419 1.6276 1.3987 1.3030

~L~OOOE-O~

2.25003 00 2.5000E 00 2.7500E 00 3.0000E 00

8.7670E-02

8.7753E-02

7.0900E-02 5.2522E-02 3.9821E-02 3.UY70E-02 2.4738E-02 1.70733-02 1.2916E-02 1.0009E-02 8.28133-03 7.1148E-03 6.2505E-03

7.94083-02 7.3294E-02 6.87163-02 6.52023-02 6.2435E-02 5.8336E-02 5.53763-02 5.25463-02 5.0276E-02 4.83593-02 4.6693E-02

1.9009E-03 1.5769E-03 1.1539E-03 6.54 11E-04

3.32723-02 3.1542E-02 2.8849E-02 2.4530E - 0 2

4.0000E 00 5.0000E 00

fi.OOOOE 00 7.0000E 8.0000E 1.OOOOE 1.5000E

-31 -

00 00

01 01

Pressure (Mbar)

V

LX-07-0 7.34233-01 7.0000E-01 7.50003-01 8.00003-01 8.50003 - 01 9.00003-01 9.50003 -01 1.0000E 00 1.10003 00 1.20003 00 1.30003 00 1,40003 00 1.50003 00 1.60003 00 1.80003 00 2.00003 00 2.25003 00 2.50003 00 2.75003 00 3.0000E 00 4,00003 00 5.00003 00 6.0000E 00 7.00003 00 8.00003 00 1.00003 01 1.5000E 01

zyxw zyxw

Energy (Mbar cc/cc)

3.70 0 0 3 - 0 1 4.21163-01 3.48743-01 2.897 03-01 2.41513-01 2.02133-01 1.69913-01 1.43503-01 1.03993-01 7.7 130E-02 5.86183-02 4.58293-02 3.67343-02 3.0110E-01 2.16683-02 1.65723-02 1.25483-02 9.85003-03 7.89563-03 6.41653-03 3.091 23-03 1.73493-03 1.1 2743-03 8.22723 -04 6.49173-04 4.59173-04 2.5 8283-04

1.45173-01 1.58693-01 1.39503-01 1.23593-01 1.10353-01 9.92943 -02 9.00203 -02 8.22063-02 6.99603-02 6.09893-02 5.42553-02 4.90683-02 4.49653-02 4.16373-02 3.65323-02 3.27473-02 2.91443-02 2.63643- 02 2.41573-02 2.2377E-02 1.78803-02 1.55613-02 1.41 683-02 1.32083 - 02 1.24803-02 1.13933-02 9.68443-03

r

2.7 627 2.6623 2.8071 2.9403 3.8604 3.1 660 3.2556 3.3283 3.4193 3.4364 3.3844 3.2762 3.1302 2.9668 2.6581 2.4392 2.3110 2.2993 2.3490 2.4217 2.6194 2.5052 2.1994 1.8906 1.6696 1.4672 1.4013

zyxwvuts

-32-

Appendix D

r

zyxw zy

Versus Volume Behavior for JWL Adiabat

-33-

4

I

I

NM

HMX

3

z

zyxwvutsrqp zyxwvutsrqp zyx -adiabat A 0

r 2 -

r 2

1 0

zyxwvuts 3

1

10

3

1

30

V

Fig. D-1.

10

30

V

r vs relative volume (V) for HMX f o r the JWL equation of state.

r v s relative volume (V) f o r NM: f o r the JWL equation of s t a t e .

Fig. D-2.

4 3

r 2

r

1

3

10

30

1

V

Fig. D-3.

3

10 V

I? v s relative volume ( V ) for

Fig. D-4.

P E T N for the JWL equation of state.

-34-

I? v s relative volume (V) f o r T N T f o r the JWL equation of state.

30

4 3

r 2

z

zyxwvutsrqp zyxwvutsrq -’ k

zyxwvutsrq 1

4

I

I

I

n

PBX-9011

r

2

zyxwvutsrqponm 1

1

0

1

3

3

1

30

IO

10

V

V

Fig. D-5.

I

3

1

0

I

r vs

Fig. D-6.

r e l a t i v e volume (V) for Cyclotol f o r the J W L equation of s t a t e .

4

r vs

30

r e l a t i v e volume (V) f o r PBX-9011 f o r the JWL equation of s t a t e .

zyxwvutsr I

I

3

r 2

1

1

0

~

3

1

10 V

Fig. D-7.

r

v s r e l a t i v e volume ( V ) for LX-07 for the JWL equation of s t a t e .

-35-

30

Distribution L R L I n t e r n a l Distribution

zyxw

Michael M. May

R. Batzel/G. Dorough R. Elson

J. Kury H. Hornig

3

E. L e e

50

C. Chapin

zy

P. Urtiew TID Berkeley

30

TID File E x t e r n a l Distribution

5

D. O r n e l l a s (D. Clark, AWRE, England, 2 copies) M. T. Abegg L. M. Bickle J . A. Hornbeck C. B. McCampbell D. Webb Sandia Corporation Albuquerque, New Mexico W. T . A s h u r s t

L . Bakken Sandia Corporation L i v e r m o r e , California

zyxwvuts zyxwvut

I. B. Akst E. Poynor M. Ott Mason and Hanger - Silas Mason C o . , Inc A m a r i l l o , Texas

R . Holmberg J . Polson Mason and Hanger - Silas Mason C o . , Inc Burlington, Iowa C. N. E. L. A.

Mader E. B r a d b u r y Eyster C. Smith Popolato R. Spaulding A. W. Campbell W. Fickett Los Alamos Scientific Laboratory Los Alamos, New Mexico L. V . J o n e s H. R . McGraw Monsant o R e s e a r c h C o r p o r a tion Mound Laboratory Miamisburg, Ohio -36-

zyxwvutsr zyxwvut zyxwvu zyxwvutsrq

Ext e m a 1 Distribution (Cont inued)

@

Maj. Gen. E. B. Giller Division of Military Application Washington, D. C.

E . C . Shute San F r a n c i s c o Operations Office B e r k e l e y , California L t . Gen. H. C . Donnelly Albuquerque Operations Off i c e Albuquerque, New Mexico J. McDonnel

Defense Atomic Support Agency L i v e r m o r e , California 13. F r a z i e r

Army Ammunition Procurement. ti Supply Agency Joliet , Illinois J. R . Kaufman J. Hershkowitz

Army Picatinny Arsenal Dover, New J e r s e y

D. Price J . Ablard S , Jacobs M . Kamlet U. S. Naval Ordnance Laboratory White O a k , Silver Spring, Maryland H . Pfeifer Air F o r c e Armament Laboratories Eglin Air F o r c e B a s e , Florida

D. Lind U . S. Naval Ordnance T e s t Station China L a k e , California P. C. U n d e r w o o d

A r m y Holston Ammunition Plant Kingsport, T e n n e s s e e M. W. Evans Stanford R e s e a r c h Institute Menlo P a r k , California S . M. Taylor T e r m i n a l Ballistics Labor a t o r y Aberdeen, Maryland

N. Hoskin

zyxwvu

United Kingdom Atomic Energy Authority Atomic Weapons R e s e a r c h Establishment Alder maston, B e r k s h i r e , England

-37

-

External Distribution (Continued) E. E. F i s h e r Honeywell, Inc. St. Paul, Minn.

zyxwvut zy

C. S. Godfrey P h y s i c s International Company San Leandro, California

A . H. Makomaski G a s Dynamics Laboratory National R e s e a r c h Council Conseil National de Recherches Ottawa, Canada

TID-4500 Distribution, UC-4, Chemistry

255

c

Printed in USA. Available f r o m the Clearinghouse f o r F e d e r a l Scientific and Technical Information, National Bureau of Standards, U. S. Department of Commerce, Springfield, Virginia 22151 P r i c e : Printed Copy $3.00; Microfiche $0.65.

RS/ rt -38-