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Cylindrical Explosive Dispersal of Metal Particles: Predictive Calculations in Support of Experimental Trials

Martec Technical Report # TR-07-66

December 2007

20090914172 Prepared for:

Dr. Yasuyuki Horie US Air Force Research Laboratory

Eglin Air Force Base

Florida, USA 32542

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Science & Computing

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4. TITLE AND SUBTITLE

Mode l ing Fragmentation and Reactive Dispersal of Explosively Loaded

Metals

DATES COVERED (From - To ) 19 JUN 2006-31 MAY 2007

5a . CONTRACT NUMBER

5b . RANT NUMBER

FA9550-06-1-0551

5c . PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Robert C. Ripley

5d . PROJECT NUMBER

5e . TASK NUMBER

5f . WORK UNIT NUMBER

7 ERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

US Air Force Research Laboratory

Eglin Air Force Base Florida. USA 32542

Martec Limited 1888 Brunswick St. uite 40 0

Halifax ov a cotia 3J 3J8 Canada Tel: 902.425.5101

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13 . SUPPLEMENTARY NOTES

14 . BSTRACT

The Explosive dispersal of densely-packed metal particles in cylindrical RDX-based charges was studied

numerically in support of experimental trials. Simulations were conducted using a reactive multiphase fluid

dynamic code. undamental studies using a large-scale explosive were performed to show scaling phenomena

while avoiding potential initiation and critical diameter effects. Spherical tungsten particles were applied in

high metal mass fraction cylindrical and spherical charges in two configurations: a particle matrix uniformlv

embedded in a solid explosive versus an annular shell of particles surrounding a high-explosive core. The effe

of particle number density was investigated by varying the nominal particle diameter from 27 to 20 um while

maintaining a constant metal mass fraction. Results were compared with steel particles to evaluate th e influence of material density dispersal. Preliminary laboratory-scale simulations were performed using th e

anticipated experimental configuration fo r the High Explosives R&D facility at Eglin AFB trials. The effect o

particle size and density were investigated, and information to assist in the experiments was obtained. Results were consistent with the fundamental study involving the large-scale explosives, particular} he shape of the

cylindrical dispersed dense particle slug, and the relative performance of th e large and small particles.

15 UBJECT TERMS

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ABSTRACT

Unclassified

18. NUMBER

OF PAGES

19a. NAME OF RESPONSIBLE PERSON

J . F l lerup

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UndS^mdSr&^^rr, 298

(Rev

8-9

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SIGNATURE PAGE

CYLINDRICAL EXPLOSIVE DISPERSAL OF METAL PARTICLES:

PREDICITIVE CALCULATIONS IN SUPPORT OF EXPERIMENTAL TRIALS

Technical Report # TR-07-66 1 1 December 2007

Prepared by: ryU (yC 'kl>liA$_ , ate: bc& I, (Pb~ ] Laura Donahue, P.Eng. Research Engineer

. Ripley, P.ETni. obert C. Research Engineer

, . dtC I I Zwl ate:

Reviewed by : )> A]oLM ate: j 6 "jZ**?-

RobertC. Ripley, P.Eng. Research Engineer ^-

Approved by: r^/cbbs/ £- U^M -u t. ate: (J<-\ ^ 3-ou7 David R. Whitehouse, P.Eng. Manager-Combustion Dynamics Group

T



"•ull.-

EXECUTIVE SUMMARY The explosive dispersal of densely-packed metal particles n cylindrical RDX-based charges

was studied numerically in support of experimental trials. Simulations were conducted using a reactive multiphase fluid dynamic code.

Fundamental studies using a large-scale explosive were performed to show scaling phenomena

while avoiding potential nitiation and critical diameter ffects. Spherical ungsten particles

were pplied n ig h etal as s raction ylindrical nd pherical harges n wo configurations: particle matrix uniformly embedded n solid explosive versus n annular

shell of particles surrounding a high-explosive core. The effect of particle number density was investigated by varying the nominal particle diameter from 27 to 20 urn while maintaining a

constant metal as s raction. esults were compared with teel articles o valuate he influence of material density on dispersal.

Preliminary aboratory-scale simulations were performed using he anticipated experimental

configuration fo r th e High Explosives R&D facility at Eglin AFB trials. The effect of particle

size and density were investigated, and information to assist in the experiments was obtained.

Results ere onsistent ith he undamental tudy nvolving he arge-scale xplosives, particularly he hape f he ylindrical ispersed ense article lug, nd he elative performance of th e large and small particles.

Funding or his project was provided by he U.S . Air Force Office of Scientific Research

under Grant FA9550-06-1-0551.



V^

TABLE OF CONTENTS 1.0 NTRODUCTION2.0 UMERICAL METHODS

3. 0 ARGE SCALE EXPLOSIVE DISPERSAL3.1 PHERICAL EXPLOSIVE DISPERSAL3.1.1 article Morphology Effects3.1.2 article Distribution Effects

3.2 YLINDRICAL PARTICLE DISPERSAL4.0 RELIMINARY LABORATORY-SCALE INVESTIGATIONS 0

4.1 XPLOSIVE DETAILS 0

4.2 5/W-27 RESULTS 1

4.3 5/W-120 RESULTS 4

4.4 5/AL-31 RESULTS 7

5.0 ISCUSSION/CONCLUSIONS 1

6.0 EFERENCES 22



LIST OF FIGURES FIGURE : SCHEMATIC OF MATRIX AND SHELL CONFIGURATIONS. INITIATION LOCATIONS ARE INDICATED BY RED

CIRCLES 3 FIGURE 2: AVE DIAGRAM FOR 2.5 KG SPHERICAL MATRIX CHARGES. THICK LINES, 12 0 HM; THIN LINES, 27 ^M ;

SOLID LINES, TUNGSTEN; DASHED LINES, STEEL; BLACK LINES (N O SYMBOLS) , FIREBALL; LIGHT BLUE

LINES, SHOCK; AND, BLACK LINES WITH SYMBOLS, PARTICLE FRONT

FIGURE 3: WAVE DIAGRAM FOR 2.5 KG SPHERICAL TUNGSTEN MATRIX AND SHELL CONFIGURATION CHARGES.

THICK LINES, 12 0 HM; THIN LINES, 27 HM; SOLID LINES, MATRIX; DASHED LINES, SHELL; BLACK LINES,

FIREBALL; LIGHT BLUE LINES, SHOCK; AND, BLACK LINES WITH SYMBOLS, PARTICLE FRONT FIGURE 4: WAVE DIAGRAM FOR CYLINDRICAL DISPERSAL OF 2.5 KG TUNGSTEN CHARGES (2 7 n M DIAMETER).

THICK LINES, CYLINDRICAL CHARGE; THIN LINES, SPHERICAL CHARGE; SOLID LINES, MATRIX; DASHED

LINES, SHELL; BLACK LINES (N O SYMBOLS), FIREBALL; LIGHT BLUE LINES, SHOCK; AND, BLACK LINES

WITH SYMBOLS, PARTICLE FRONT 6

FIGURE 5: FLUID DENSITY (COLOUR) AND PARTICLE CONCENTRATION (LINES - LOG) FOR 27 HM TUNGSTEN

PARTICLES IN 2.5 KG (TOP) SHELL AND (BOTTOM) MATRIX CONFIGURATIONS. HADING INDICATES

STRENGTH OF DENSITY GRADIENT

FIGURE 6: CONCENTRATION OF DISPERSED 27 HM TUNGSTEN PARTICLES IN 2.5 KG MATRIX AND SHELL

CONFIGURATIONS AT (LEFT) T= 1.0 MS AND (RIGHT) T = 8.0 MS

FIGURE 7: RADIAL VELOCITY DISTRIBUTION OF 27 MM TUNGSTEN PARTICLES IN 2.5 KG MATRIX AND SHELL CONFIGURATIONS AT (LEFT) T= 1.0 MS AND (RIGHT) T = 8.0 MS

FIGURES: PREPARED EXPERIMENTAL CHARGES 0

FIGURE 9: CHARGE DIMENSIONS IN MILLIMETRES 0

FIGURE 10: EARLY-TIME EXPLOSIVE DETONATION AND PARTICLE DISPERSAL OF A5/W-27. FLOOD INDICATES PRESSURE LEVEL; SOLID LINES DENOTE PARTICLE CONCENTRATION OF 0 MG/M

3 TO 0.1 KG/M

3 (LOG

SCALE) 1

FIGURE 11: EARLY-TIME PARTICLE SPEED PROFILE FOR A5/W-27. FLOOD INDICATES PARTICLE SPEED LEVEL; SOLID

LINES DENOTE PARTICLE CONCENTRATION OF 0 MG/M3 TO 0.1 KG/M

3(LOG SCALE) 2 FIGURE 12: LATE-TIME PARTICLE DISPERSAL AND SHOCK PROPAGATION OF A5/W-27. FLOOD INDICATES FLUID

PRESSURE LEVEL; SOLID LINES DENOTE PARTICLE CONCENTRATION OF 0 MG/M3 TO 0.1 KG/M

3 (LOG

SCALE) 13

FIGURE 13: LATE-TIME A5/W-27 PARTICLE SPEED. SOLID LINES DENOTE PARTICLE CONCENTRATION OF 10 MG/M3

TO 0.1 KG/M3 (LOG SCALE) 13

FIGURE 14: GAUGE HISTORIES FOR A5/W-27 (LEFT) PRESSURE AND (RIGHT) PARTICLE NUMBER DENSITY 4 FIGURE 15: EARLY-TIME EXPLOSIVE DETONATION AND PARTICLE DISPERSAL OF A5/W-120. FLOOD INDICATES FLUID PRESSURE LEVEL; SOLID LINES DENOTE PARTICLE CONCENTRATION OF 10 MG/M

3 TO 0.1 G/M

3

(LOG) 15

FIGURE 16: EARLY-TIME PARTICLE SPEED PROFILE FOR A5/W-120. FLOOD INDICATES PARTICLE SPEED LEVEL; SOLID LINES DENOTE PARTICLE CONCENTRATION OF 10 MG/M

3 TO 0.1 KG/M

3 (LOG) 5 FIGURE 17: LATE-TIME PARTICLE DISPERSAL AND SHOCK PROPAGATION OF A5/W-120. FLOOD COLOUR INDICATES

FLUID PRESSURE LEVEL; SOLID LINES DENOTE PARTICLE CONCENTRATION OF 0 MG/M3 TO 0.1 KG/M

3

(LOG SCALE) 16

FIGURE 18 : LATE-TIME A5/W-120 PARTICLE SPEED. SOLID LINES DENOTE PARTICLE CONCENTRATION OF 10 MG/M3


FIGURE 19 : GAUGE HISTORIES FOR A5/W-120 (LEFT) PRESSURE AND (RIGHT) PARTICLE NUMBER DENSITY 7 FIGURE 20 : EARLY-TIME EXPLOSIVE DETONATION AND PARTICLE DISPERSAL OF A5/AL-3 1 . FLOOD INDICATES

FLUID PRESSURE LEVEL; SOLID LINES DENOTE PARTICLE CONCENTRATION OF 0 MG/M3 TO 0.1 G/M

3

(LOG SCALE) 18 FIGURE 21: EARLY-TIME PARTICLE SPEED PROFILE FOR A5/AL-3 1 . FLOOD INDICATES PARTICLE SPEED LEVEL;

SOLID LINES DENOTE PARTICLE CONCENTRATION OF 0 MG/M3TO0.1 KG/M

3 (LOG SCALE) 8 FIGURE 22 : LATE-TIME PARTICLE DISPERSAL AND SHOCK PROPAGATION OF A5/AL-3 1 . FLOOD INDICATES FLUID

PRESSURE LEVEL; SOLID LINES DENOTE PARTICLE CONCENTRATION OF 0 MG/M3 TO 0.1 KG/M

3(LOG

S C A L E ) 19

FIGURE 23 : LATE-TIME A5/AL-31 PARTICLE SPEED. SOLID LINES DENOTE PARTICLE CONCENTRATION OF 0 MG/M3


FIGURE 24 : GAUGE HISTORIES FOR AS/AL-31 LEFT) PRESSURE AND (RIGHT) PARTICLE NUMBER DENSITY 0



^B

LIST OF TABLES

TABLE 1 : ETALIZED EXPLOSIVE CHARGE COMPOSITION

TABLE 2: HARGE DETAILS 1




1 .0 NTRODUCTION

Some heterogeneous explosive formulations consist of a condensed explosive surrounded by a

dense metal particle ayer. The dispersal of inert particles rom high explosive charge s investigated numerically n th e current work. The modeling is motivated by an experimental

effort at the High Explosives R&D acility at Eglin AFB hat aims to simulate dispersal and

afterburning effects using dense metal particles as casing surrogates. Modeling calculations are

used to predict th e arrival time and duration of the dispersed particle cloud including its time-

varying concentration and velocity. This nformation will allow optimal configuration of th e

diagnostics and optics n order to avoid the obscuring effects of th e ireball while capturing

particle kinetic ffects n he near ield. nert particles are he ocus of th e present work o

study undamentals nd o calibrate equipment, while avoiding complexities ntroduced by

reactive particle luminescence and reaction products in the flow field.

TR-07-66




2.0 UMERICAL METHODS All simulations are performed using Chinook, a 3D parallel unstructured mesh CFD code or

th e simulation of time-accurate explosive events. This code, developed by Martec Limited, ha s been validated and used fo r spherical nert particle dispersal 1], cylindrical eactive particle

scenarios [2 ] and multiphase explosions [3 ] featuring high metal mass fractions.

The governing equations are the Euler equations fo r conservation of mass, momentum, energy,

material concentrations and particle number density (number of particles per unit volume). t

features th e second-order HLLC approximate Riemann solver [4 , 5] which is used fo r both the

fluid and particle phases, each of which ha s independent velocity and temperature fields. The

Godunov-type solver can handle all sound speeds in a generalized Riemann solver framework

fo r th e condensed explosive, multicomponent detonation products, granular material, discrete

particle system and air. The particle model developed in [1 ] is used, capable of simulating th e

solid flow from solid continuum to a highly dilute particle system, with th e associated variance

in sound speed (from 0 m/s o 0 /s). Gas-particle nteractions re simulated using phase exchange ource erms, hich re ased n raditional mpirical orrelations or rag

(momentum), eat ransfer convection) nd as s ransfer particle ombustion). he governing equations and particle exchange source terms are described in [6 , 7] .

Equations of state EOS) re equired o model ach material nd o close he ystem of equations:

• Mie-Griineisen EOS fo r condensed reactants [8 ] with Walsh and Christian temperature

fitting [9 ]

• Jones-Wilkens-Lee ( JWL) fo r gaseous detonation products [10]; explosive fitting

parameters calculated using Cheetah [11]

• Ideal Gas Law fo r surrounding atmosphere and air-blast (gamma = 1.4)

• Phenomenological EOS fo r solid particles (both dense and dilute) [1 ]

To ccount or arly-time article oading, omentum cceleration actors or hock interaction ith acked etal articles re mployed. he ear-field ense ranular heterogeneous low effect is ncluded in th e governing equations and drag model; n he ar

field, drag is the main driving force within th e expanding detonation product gases and air.

TR-07-66




3.0 LARGE SCALE EXPLOSIVE DISPERSAL The effect of particle morphology and distribution were nvestigated through eries of D

and D alculations.

lthough mall-scale

harges 25

50 ) re lanned or he

preliminary experiments at Eglin AFB, metalized explosive charge sizes of 2 .5 and 20 kg are

studied n hi s ection o how dispersal phenomena while avoiding potential nitiation and

critical diameter ffects. The explosive ormulations considered are given n Table W =

tungsten, Fe = steel).

Table 1: Metalized explosive charge composition Comp % vol.

%wt.

A5/W

%wt.

A5/Fe

A5 (98.5% RDX) 60.3 11.5 24.2

Meta l 39.7 88.5 75.8

Figure llustrates he harges nvestigated n he urrent tudy. n he irst harge configuration, matrix of metal particles s embedded uniformly n olid high explosive,

while n he second configuration n explosive core s surrounded by n annular hell f particles. Both 2 .5 and 20 kg charges were analyzed. The charge outer diameters ranged from

5.7 to 9 .0 cm fo r th e 2.5 kg charge and from 1.4 to 8 .0 cm fo r the 20 kg charge depending

on configuration. The shell thickness was 0.3 and 21.0 mm in th e 2.5 and 20 kg A5/tungsten

spherical charges, respectively. For th e cylinders, the charge length is twice th e outer diameter.

Because of the cylindrical charge aspect atio, he spherical charge of th e am e mass ha s

smaller outer diameter.

MATRIX SHELL

o 0 vol% A5

40 vol% W 100vol%A5 56vol%W

44 vol% Ail

Figure 1: Schematic of matrix an d shell configurations. Initiation locations are indicated

by red

circles.

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3.1 SPHERICAL EXPLOSIVE DISPERSAL

3.1.1 Particle Morphology Effects The ffect f particle aterial nd iameter n he ispersal ynamics as nvestigated through D alculations nvolving pherical harges ontaining 7 nd 20 rn iameter tungsten nd teel articles. he etal articles ere istributed n niform atrix

throughout the charge, with voids filled with A5 explosive. This configuration is similar to that

studied by Zhang et al. [1].

Figure llustrates he effect of particle diameter and material. ue o greater nertia, he

dispersed ront of larger particles emains t nearly constant velocity onger than hat of the

smaller particles, which decelerate and are overtaken by th e shock ront. Charges containing

steel particles have aster shock peed nd arger ireball ndicating ess momentum and

energy ransfer to he particles n heir acceleration and heating s compared o he heavier tungsten particles of the same size. However, because of th e lower steel particle inertia, arge

steel particles are dispersed ahead of th e ungsten particles until r > 4.0 m, and mall teel

particles pass th e same size tungsten particles at r = .3 m fo r th e same explosive fraction.

6-

E _

E

£

-

1 Fireball

V \r x

Shock

- j*

j \<-'' Particle Front

1 « iL-^*^ - * * Tungsten

Steel

i ....

0 2 Radius (m )

Figure 2: Wave diagram fo r 2.5 kg spherical matrix charges. Thick lines, 120 urn; thin lines, 27 urn; solid lines, tungsten; dashed lines, steel; black lines (n o symbols), fireball;

light blue lines, shock; and, black lines with symbols, particle front. 3.1.2 Particle Distribution Effects The effect of th e distribution of particles within he harge was nvestigated or he am e

weight fraction of tungsten to A5 as that of th e matrix charge specified in Table . The matrix

configuration was compared with n annular particle hell surrounding he explosive core

TR-07-66



••


(Figure ). The blast performance of shell versus matrix configurations was previously studied

fo r aluminized explosives in a chamber [3]. For metal particles in th e shell configuration, th e

tap density was used to determine a metal volume fraction of 55.7% with th e voids filled with

air.

Figure 3 llustrates th e wave diagram fo r the 2 .5 kg spherical matrix and shell configurations.

At early times in th e near field, the particles overtake the shock front fo r th e interval 0.3 < r < 1.0 m. The time at which th e particles cross the shock occurs later for th e shell configuration

than fo r th e matrix, and th e crossing distance is greater fo r increasing particle size.

Particle Front

Matrix

Shell

2 Radius (m )

Figure 3: Wave diagram fo r 2.5 kg spherical tungsten matrix an d shell configuration charges. Thick lines, 120 um: thin lines, 27 um: solid lines, matrix; dashed lines, shell; black lines, fireball; light blue lines, shock; and, black lines with symbols, particle front. For th e matrix configuration elative o he hell configuration, he shock s slightly arther

ahead nd he ireball s arger. This s due o he detonation ransitioning o n air blast

immediately at the en d of th e charge, without th e confinement effect of a dense particle bed.

The hell configuration provided more confinement nd he ireball ecompression s more

pronounced and occurs ater as indicated in Figure 3. Consequently, the particles n the shell

shocked by th e detonation are 8 00 K hotter initially and th e dispersed particles in the shell are

up to 450 K hotter.

For oth article izes n eneral, he ar-field ispersed article ront rom he atrix

configuration s ahead of that fo r the shell configuration. One exception s th e 20 kg charge

with small particles, where the dispersed particles from the shell are ahead of the matrix fo r r > 3.25 m. Otherwise, th e results obtained fo r the 20 kg charge exhibit similar behaviour to that

of the smaller charge.

TR-07-66




3.2 CYLINDRICAL PARTICLE DISPERSAL Two-dimensional alculations ere performed o alculate he dispersal f particles rom

centrally-initiated ylindrical harges. he last low ield as xpected o eature igh directional dependence, particularly n he near-field. Results along adial slice rom he

charge entre re ompared with pherical ispersal esults o tudy he ffect of charge geometry on th e blast (Figure 4). This comparison is no t simply a change in th e degree of blast

expansion odelled n ne dimension, ut ather he ull harge hape nd xpansion s resolved. Only a single cylindrical charge aspect ratio was simulated; esults are expected to

vary fo r other charge geometries.

The cylindrical charge has a faster particle front and shock velocity than th e spherical esult,

despite having smaller nitial diameter. n both he pherical nd cylindrical charges, he

shock nd article ronts re aster or he atrix harges s ompared ith he hell configuration, although at later t imes the shock and particle fronts fo r th e shell case eventually

pass th e equivalent matrix positions.

The cylindrical harge lso hows greater nfluence of particle distribution shell versus

matrix) on ireball ize. he maximum ireball xtent or he cylindrical matrix charge s approximately .2 , he ireball xtends only 0.6 m n he adial direction or he hell configuration. everberations n he ireball vident n he hell onfiguration re ot s distinct in the matrix charge results due to a more diffusive multiphase flow field.

£ g ) E

Particle Front

Sphere

Cylinder

2 Radius (m)

Figure 4: Wave diagram fo r cylindrical dispersal of 2. 5 kg tungsten charges (27 um diameter). Thick lines, cylindrical charge; thin lines, spherical charge; solid lines, matrix; dashed lines, shell; black lines (n o symbols), fireball; light blue lines, shock; and, black

lines with symbols, particle front.

TR-07-66




t = 0.5 ms t = 1.0 ms t = 2.0 ms

t = 0. 5 ms t = 1.0 ms t = 2. 0 ms Figure 5: Fluid density (colour) an d particle concentration (lines - log) for 27 uni tungsten particles in 2. 5 kg (top) shell an d (bottom) matrix configurations. hading

indicates strength of density gradient.

TR-07-66




m4

10'3

t

Sphere, Shell 10

,J

C10

2

„E 10 > ic V

fio

-

— n E

« to c V

1 °

I Jio 3

2 S—A

&

|0° _

41

oicr2

- m 10? -

E 3 Z

i V o

§10;

o

K . C\ 10 s -

E

u f ~ ~ ; ; \\ . .2

S i 2 r»ia

4 - 1 1 1 10\s

o tr e 0.

g r«10«

Ii| ' 0 i o C r e a

1CT6

10s

J , I 1 ) 1 10 5

'"0 2 3 4 5 1tr

Radius (m) Radius (m )

Figure 6: Concentration of dispersed 27 fim tungsten particles in 2.5 kg matrix and shell configurations at (left) t = 1.0 ms and (right) t = 8.0 ms.

Sphere, Matrix Sphere, Shell Cylinder, Matrix Cylinder, Shell

2 Radius (m )

900

1 600

1 >

1 r e Q.

300

t= 8.0 ms Sphere, Matrix

Sphere, Shell Cylinder, Matrix Cylinder, Shell

2 Radius (m )

Figure 7: Radial velocity distribution of 27 um tungsten particles in 2.5 kg matrix and shell configurations at (left) t = 1.0 ms and (right) t • 8.0 ms.

TR-07-66



Cylindrical Explosive Dispersal of Metal Particles: Predictive Calculations in Support of Experimental Trials 10

4.0 PRELIMINARY LABORATORY-SCALE INVESTIGATIONS A series of simulations were performed using th e proposed configuration fo r th e experimental

trials to be performed at the High Explosives R&D facility at Eglin AFB. Only cylindrical A5 charges surrounded by an annular shell of metal particles were considered. Both tungsten and

inert aluminum particles were simulated to investigate th e effect of particle size and material

density on th e dispersal. Figure 8 illustrates the charges used in the experiments with nominal

200 g mass.

Figure 8: Prepared experimental charges.

4.1 EXPLOSIVE DETAILS

A schematic of the charge is given n Figure 9 , with component mass raction details of th e

three harges nvestigated isted n able . ll harges nvolve n 5 xplosive ore surrounded by a shell of monodisperse particles, with inter-particle voids illed with air. The

explosive detonation is initiated by a small region of hot products on th e centre axis at one end

of the charge.

The volume fraction of ai r and metal in the shell is relatively constant throughout all charges

(approximately 44% ai r and 56% metal), s s th e explosive mass 10.5 g). The densities of

A5, ungsten, nd aluminum re assumed to be 65 0 kg/m3, 9250 kg/m 3

, and 2700 kg/m3,

respectively.

Hot Spot

Axis of

Metal " 1

-

1

:5.0

Explosive ;e.3

Symmetry * 0.8 l Figure 9: Charge dimensions in millimetres.

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Cylindrical Explosive Dispersal of Metal Particles: Predictive Calculations i n Support of Experimental Trials II

Table 2: Charge details Charge Identification Label

A5/W-27 A5/W-120 A5/A1-31 Particle Diameter (jim) 27.0 120.0 31.0

Shell Composition (% vol) A ir 44.16 44.16 44.76

Metal 55.84 55 . 84 55.24

Total Mass (g) Explosive 10.5 10.5 10.5

Metal 151.0 151.0 20.9

4.2 A5/W-27 RESULTS

Select results for th e A5/W-27 charge are illustrated in Figures 10-14. The early-time (1-10 ns ) detonics phenomena are shown n Figure 0. This image illustrates th e explosive detonation,

normal nd blique hock ransmission nto he article ayer, nd nitial article ayer dispersal pattern. The form of the dispersed particle cloud is affected by both th e asymmetric

end nitiation ocation, and th e open nds of th e charge. The patial particle speed profile s

given n Figure 1, and shows that maximum particle speeds of approximately 500 m/s are

located at th e ends of th e shell, while particle velocities are relatively constant along th e outer

length of th e shell. There is a considerable velocity gradient present through th e thickness of

the particle cloud, as th e particles on th e outer edges of the shell are less confined and are thus

accelerated more quickly by th e shock.

Axi»! Dlitanca m) Axla) Dbtinea m )

t = 0.0070 m«

0.04

t =0 10O ms

0 4

Axial Distance m) Axial Dittance 1 1 1 )

Figure 10: Early-time explosive detonation an d particle dispersal of A5/W-27. Flood indicates pressure level; solid lines denote particle concentration of 10 mg/ra

3 to

0.1 kg/m 3 (log scale).

TR-07-66



Cylindrical Explosive Dispersal of Metal Particles: Predictive Calculations in Support of Experimental Trials 1 2

t = 0.0100 m s

0 <

o 1

Axial Distinct (m )

Figure 11: Early-time particle speed profile fo r A5/W-27. Flood indicates particle speed level; solid lines denote particle concentration of 10 mg/rn

3 to 0.1 kg/m log scale).

Figure 2 llustrates he ater-time first millisecond) particle dispersal nd shock pressures. The form of the dispersed particle cloud is quite different than th e early-time orm shown n

Figure 0, with he maximum particle displacements occurring mid-length along th e charge. This appears to be due to colliding waves along the charge center, and may be dependent on

the charge aspect ratio.

Three coalescing hocks are evident in Figure 2, especially at th e later times. These shocks

originate rom he nitial xpansion t he nitiation nd , he shock ransmitted hrough he

particle bed, and the transmitted shock out the far end of the tube. Differences in th e speeds of

these hocks du e o changes n he particle bed condition confinement) are examined n

subsequent sections. The results indicate that th e incident shock is followed by a second high

pressure region at the leading edge of the particle slug, seen most prominently in Figure 2 at

t= 1.0610 ms. This may be a ballistic effect, as the high-drag dense particle slug compresses

th e air ahead of it.

As hown n igure 3, he peak particle peeds n he bulk of the lug have decayed o approximately half of th e earlier-time speeds shown in Figure 11 .

TR-07-66



'••r


t = 0.0110ms t = 0.3610 m s

Early-time solution

Preoure (Pa) 170000 160000

150000

140000 130000 120000

—| 10000

— 100000

Axial Distance m )

Prewjrt(Pa)

1 170000

„_ laoooo E ieoooo

- ' r—

140000 130000 c 120000

$ 05 110000

tooooo

a 0000 •o o o o • 0000

M•a _^^^^^^ e

°0 1 : Axial Distance m)

1 = 0.7110 ms t = 1.0610 ms

170000 160000 150000 140000 130000

120000 110000

Axial Distance m) Axial Distance m)

Figure 12: Late-time particle dispersal an d shock propagation of A5/W-27. Flood indicates fluid pressure level; solid lines denote particle concentration of 10 mg/m to

0,1 kg/m 3 (log scale)*

t = 0.3610 ms

Axial Dktanci m)

Figure 13 : Late-time A5/W-27 particle speed. Solid lines denote particle concentration of 10 mg/m

3 to 0.1 kg/m 3

(log scale). Numerical gauges were placed t adial distances rom he mid-length of th e explosive cylinder (r = 0.2, 0.3, 0.4, 0.5 and 0.75 m). Figure 4 plots th e pressure and particle number

density (number of particles per cubic metre) histories at these locations. The pressure results

show airly significant econd peak, especially t th e 0.4 o 0.75 m gauge ocations. This

second peak is th e result of the ballistic shock discussed earlier.

With the definition of a "particle window", number density nformation can be converted o

determine he ime-dependent umber f particles assing hrough olume or ater comparison to experimental PIV data.

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K 4 0 0 0 0 0

£ a .

I

r>0.3m

rtlii

f » 0.75 m

"

1 0 0005 001 0015 0 001 0015

Figure 14: Gauge histories fo r A5/W-27 (left) Pressure an d (right) Particle number density

4. 3 5/W-120 RESULTS In rder o tudy he ffect f particle iameter on he article ispersal haracteristics, simulations er e erformed ith 20 rn ungsten articles hile aintaining he ame explosive and metal mass fractions. The explosive detonation and early-time dispersal pattern

are llustrated n igure 5. he arger particles equire dditional ime o ccelerate s compared to th e smaller particles du e to th e greater inertia.

The resulting lower particle speeds are also very evident with a comparison of Figure 1 and

Figure 6, which hows a drop in particle speed as compared with the smaller particles. The

velocities n he centre of the slug range rom approximately 200-300 m/s n th e case of th e

12 0 um particles, compared with peak particle velocities of approximately 8 00 m/s at th e same

location n the 27 um particle slug. The particle velocities through th e thickness are also ar

more uniform than observed fo r the small diameter particles.

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t- gimmi

^B «•;*•<$ — 1 5E-09 — 1E*09

* H 7E*08 —| 3E*09

| H e*OB J s e - o e •6*08

i

t • m 4 1

S 1 - AMDtabrwt i

Figure 15: Early-time explosive detonation an d particle dispersal of A5/W-120. Flood indicates fluid pressure level; solid lines denote particle concentration of 10 mg/m o

0.1 kg/m 3 (log).

t = 0.0100 m s

0.04

0l*ance(n1

Figure 16 : Early-time particle speed profile fo r A5/W-120. Flood indicates particle speed level; solid lines denote particle concentration of 10 mg/m

3 to 0.1 kg/m 3

(log). The ater-time ressure nd article oncentration rofiles or he 5/W-120 harge re illustrated n Figure 7. The adial hock peed s greater fo r th e arger particle iz e du e o lower overall drag forces compared to the smaller particles. Although the drag of an individual

large particle s greater than the drag of a smaller particle, he total drag on a cloud of large

diameter particles s ower han or n qual volume raction of small particles, herefore influencing th e strength of the shock transmitted through th e particle layer.

While th e radial hock strength is increased fo r th e arger particles, the end shock speeds are

reduced. t s hypothesized ha t his s du e to he ncreased confinement effect of th e mall

particles. Drag orces re greater fo r the shell of smaller particles, also resulting n greater

confining orce. s consequence of the greater confinement, igher strength nd aster shocks expand from the ends of the charge in th e case of the smaller diameter particles. This

theory also explains he absence of the ballistic hock present n he mall diameter results.

Because of th e lower particle cloud drag forces, th e strength of th e compression wave ahead of

the particle cloud is also reduced.

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Figure 7 lso llustrates he educed displacement of the arge diameter particle loud s compared with the cloud of small particles (Figure 2) . The slug of small particles has high total drag forces and low inertia, and therefore the small particles are accelerated more quickly.

These timeframes occur relatively early in the overall expansion, and it is anticipated that after sufficient time, the large diameter particles will overtake the small particle position, as shown fundamentally in Figure ( r < m). As shown in Figure 18 , the average particle speeds for the large diameter particles is still lower than the small particle speeds.

t = 0.0110 m s t = 0.3610 m s

P»wure(Pa) P<tUuri(P|) UO0O0

1 170000 _ 160000 „ 160000

• j j

Early-time

solution =

150000 140000 130000 120000

B • 0 c

-S 05

= 150000 1*0000 130000

120000 — 110000 110000

o m

\ 100000 100000

\ 1 0000

e o o o o V5V 1 0000

80000 70000

B

\

K

smt^ : 05 l 2 °0 u5 Axial Distance m ) Axial DIttane* m)

t = o.; 11 0 ms t = 1.0610 m s

Pr»s«jre(P«) Pitnurt (P w

_ ^ 1 170000 160000 1 170000

i e o o o o E 150000 E i500oa

140000 •-> 140000 130000

g ^>w 130OO0 - M— 120000 • s X. 120000

-8 05 ^ ^W '10000 « 05 * — ~ > 110000 100000 > -afe \

§ / ±v 90000

80000 • /*— > i 90000 80000

a . /yj g * X *0000 f ^nttm • 70000 ° f \ 0

, • p

05 15 O S 2 Axial Distinct m) Axial Distance m )

Figure 17: Late-time particle dispersal and shock propagation of A5/W-120. Flood colour indicates fluid pressure level; solid lines denote particle concentration of 10 mg/m

3 to 0.1

kg/m3 (log scale).

125 AKUI Dktanct m)

Figure 18: Late-time A5/W-120 particle speed. Solid lines denote particle concentration of 10 mg/m

3 to 0.1 kg/m 3

(log scale). Figure 9 gives he numerical gauge esults or ive measurement ocations n he adial direction. The aster adial hock peed s vident when omparing o Figure 4, nd he

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second pressure peak du e to the ballistic hock does not occur with th e arger particles. The

relative particle number density trends are very similar to th e mall particle results, however

the number densities re everal orders of magnitude ower du e o he educed number of

particles in the shell. Specifically, there should be 9 0 times th e number of smaller particles per unit volume as larger particles.

i800000

j KKMOO

Q.

r • 0 m r •0.3 m r « 0 4 m r.OSm r • 0V4 m

1 r a 0.3 m

2 5E-09 r.04mi "O.itn raQVSm

2E*09 " — .§ 1 SE'OS

z

1E->08

A

5E»08 -

1 1 1 1 1

0001 0 00005 0001 00015 0002 00025 0003 00035

Figure 19: Gauge histories for A5/W-120 (left) Pressure and (right) Particle number density

4.4 A5/AL-31 RESULTS

The effect of particle material density was nvestigated hrough simulations nvolving nert aluminum articles. he luminum articles er e odelled s nert o emove otential reactivity ffects rom he analysis nd ocus on particle material ffects only. The 1 m

aluminum articles er e f comparable ize o he 7 m ungsten articles, owever

represented only approximately 4% of the ungsten particle mass. Figure 20 llustrates he detonation propagation, oblique shock formation, and particle dispersal or the first 0.01 ms.

The particle layer disperses much more quickly than in either of the tungsten cases, du e to th e

reduced article nertia. he articles av e ee n ispersed o pproximately wice heir original adius before he detonation reaches th e nd of the charge. The particle speeds are

approximately double those observed fo r the small tungsten particles, as shown in Figure 21 .

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t = 0.0010 ms

Axial Dtitanct (m ) Axial Dlstane* (m )

Axial Distance (m ) Axial Dlitanca (m )

Figure 20: Early-time explosive detonation and particle dispersal of A5/A1-31. Flood indicates fluid pressure level; solid lines denote particle concentration of 10 mg/m to


Axial Distance (m )

Figure 21: Early-time particle speed profile for A5/A1-31. Flood indicates particle speed level; solid lines denote particle concentration of 10 mg/m

3 to 0.1 kg/m3 (log scale).

Figure 22 llustrates the pressure and particle concentration contours fo r times between 0.01 and 1.0 ms. In contrast to the tungsten particle results, the aluminum particle cloud travels with the leading shock, with some particles travelling ahead of the shock. The results show leading trails of low concentration particles that begin at early time due to detonation pressures nd

dense drag forces at the corners of the shell. These may be numerical artifacts and should be investigated further. The radial hock speed is greater than or the 27 um tungsten particles, and there appears to be lower confinement given the relative shock strengths along the axis of symmetry. This seems to indicate that the lower mass and lower inertia particle shell results in greater acceleration and a net decrease in the drag force.

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t = 0.0il0ms

Axial Dist inct (ml Axlt! Dlittnce (m )

Figure 22: Late-time particle dispersal and shock propagation of A5/A1-31. Flood indicates fluid pressure level; solid lines denote particle concentration of 10 mg/m

3 to


Figure 3 llustrates the particle peeds t 0.36 ms. The aluminum results appear to how large difference n velocity t he entre of the particle loud between he nner nd outer surfaces, however the area with large speed (approximately 500 m/s) occurs in a region with a relatively low particle concentration.

t = 0.3610 ms

J . 7 5

3 a ,0 2 5

Speed (mrs) H • 1500

1250 ' V 1000

790

5 0 0 E 25 0 0

0 05 1 .5 2 Axial Distance (in)

Figure 23: Late-time A5/A1-31 particle speed. Solid lines denote particle concentration of 10 mg/m

3 to 0.1 kg/m 3

(log scale). TR-07-66




The pressure nd particle number density histories t ive numerical gauge ocations re plotted in Figure 24 . The secondary shock which is most pronounced at 0.2 m appears to no t be due to a ballistic-type shock as observed in the 27 um tungsten case, but is due rather to a

secondary recompression fluid shock (as seen in Figure 22). This wave may be stronger than in ither of the tungsten cases as the particle cloud travels with the incident shock, nd the second wave is no t impeded by a lagging particle cloud.

800000 -!

t* 0.2 in r«0.3m

"04m iiljai-orsm

86*10

r t.llK

r • 1.4 m

imt.im

r«f/4m

Pre

ePa

*

D

" 8E-10

"E _ « Z

4E-M0

_

•

200000 . 26*10

0 0 i

0 0005 0 00 1 «s)

0 0015 0 02 3 00005

«• 0 001 0X15

Figure 24: Gauge histories for A5/A1-31 (left) Pressure and (right) Particle number density

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5.0 ISCUSSION/CONCLUSIONS In he current tudy, he explosive dispersal of densely-packed metal particles n cylindrical

RDX-based charges was studied numerically n support of experimental rials. imulations

were conducted using Chinook , a reactive multiphase CFD code.

Fundamental tudies nvolving arge-scale xplosives er e erformed o how caling phenomena while avoiding potential initiation and critical diameter effects. Spherical tungsten

particles were applied n high metal mass raction cylindrical nd spherical charges n wo

fundamental configurations: a particle matrix uniformly embedded in a solid explosive versus

an annular shell of particles surrounding a high-explosive core. The effect of particle number

density was investigated by varying th e nominal particle diameter from 27 to 20 um while

maintaining constant metal mass raction. esults were compared with teel particles o

evaluate th e influence of material density on dispersal. The dispersal dynamics are recorded on

wave diagrams nd re observed t adial ocations n erms of arrival ime, elocity and particle concentration.

Preliminary aboratory-scale simulations were performed using he anticipated experimental

configuration fo r th e High Explosives R&D facility at Eglin AFB trials. The effect of particle

size and density were investigated, and information to assist in the experiments was obtained.

Results er e onsistent ith he undamental tudy nvolving he arge-scale xplosives, particularly he hape f he ylindrical ispersed ense article lug, nd he elative performance of th e large and small particles.

Particle emperature nformation s available o estimate aluminum eactivity n blast lows.

The nfluence of other actors uch s particle hape, ize distribution and nitiation ocation

may be investigated in the future. The initial momentum transfer is accounted for in th e current

simulations by applying a momentum acceleration factor to th e particle drag force fo r a short duration during th e detonics and near field phases. To improve th e predictability of early time

particle oading, he omentum cceleration actor eveloped or hock nd etonation

interaction with packed metal particles will be employed in the future.

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6 . 0 REFERENCES [I] hang, F., Frost, D.L., Thibault, P.A., and Murray, S.B., Explosive Dispersal of Solid Particles, Shock Waves, 10 : 431-443 (2001).

[2 ] rost, D. L., Goroshin, S., Levine, J ., Ripley, R. C, and Zhang F. , Critical Conditions fo r gnition f luminum articles n ylindrical xplosive harges, hock Compression ofCondensed Matter-2005, pp. 972 -975 (2006).

[3 ] ipley, R.C., Donahue, L., Dunbar, T.E., nd Zhang, F. , Explosion performance of aluminized NT n hamber, roc. 9th Military Aspects f Blast nd Shock, Calgary, Canada (2006).

[4 ] oro, .F . 19 97 ) iemann olvers nd umerical Methods or luid ynamics,

Springer-Verlag.

[5 ] atten, P., Clark, N., Lambert, C. and Causon, D. M.., On th e choice of wavespeeds fo r th e HLLC Riemann solver, SIAM J . Sci. Comput., 18(6) , pp. 1553-1570, Nov 1997 .

[6 ] hang, F. , Tran, D. and Thibault, P. A., Multiphase models fo r detonation propagation in a dusty or porus medium, Combustion Canada '96, Ottawa, Ontario, June 996 .

[7 ] aer, M. R. and Nunziato, J. W., A two-phase mixture theory fo r th e deflagration-to- detonation transition (DDT) in reactive granular materials, Int. J. Multiphase Flow, 12,

pp . 8 6 1 - 8 8 9 , 986 .

[8 ] ader, C. L. , Numerical Modeling ofExplosives and Propellants, 2 n d Ed., CRC Press,

Boca Raton, Florida, 9 9 8 .

[9 ] alsh, . . nd hristian, . . quation f tate f metals rom hock ave

measurements, Physical Review, 97(6) , pp . 1544-1556 , 955 .

[10] ee , . ., ornig, H. . nd Kury, . ., Adiabatic expansion of high explosive

detonation roducts, CRL-50422, awrence ivermore aboratory, niversity f California, 96 8 .

[II] ried, L. E., Howard, W. M., and Souers, P.C., "Cheetah 2.0 User's Manual," UCRL- MA-l 17541 (Revision 5), Lawrence Livermore National Laboratory, 9 9 8 .

[12] ipley, R.C., Zhang, F., and Lien, F.-S., "Detonation nteraction with Metal Particles in Explosives," Proc. 13th International Detonation Symposium, Norfolk, VA (2006).

[13] ichards, D.W., De Angelis, R.J., Kramer, M.P., House, J.W., Cunard, D.A., and Shea, D.P., Shock-Induced Deformation of Tungsten Powder", Adv. X-ray Analysis, 47, 351-356(2004).

robert c. ripley- cylindrical explosive dispersal of metal particles: predictive calculations in...

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