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REPORT NO. 2028

5TUDY OF LINER COLLAPSE, JET FORMATION

AND 9HARACTERISTICS FROM IMPLOSIVET

SHAPED CHARGE SYSTEMS,

0o

IAbdul./Kiwan 2I'. .-i Alvin L fArbuckle

MA17 A1978

Aproedfo pblcrelease; distribution unlimited. n iii~~

ABERDEEN ~~~rOiNGrOUDARLN

USA MAENTEEARH 5D EVEO MNCMADUSA ALLITIC-ESERCHBORTOR



Destroy this report when it is o longer needed.Do not return it to the originator.

Secondary distribution of this report by originating

or' sponsoring activity is rohibited.

Additional copies of this report may be obtainedfrom the National Technical information Service.U.S. Department of Commerce. Springfield, Virginia22161.

The findings in this report are not t'o e construed asan official. Department of the Army position, unless

so designated by other authorized documents~.

The~ use. of t i~iJ namW0 OP'NkMJ~faltwwrB flamfo intiji t11 r'Ot

doann~tfl~taga inovimenttofany ýoon'wroiat pr'odIot;.



UNCLASSIFIEDSECURITY CL ASSIFICATION Of THIS PAGE Who"~ Data XMtIe#@

_______________________________________ BaFREA INSTRUCTIONSOREPORT DOCUMENTATION PAGE BEFOR COMPLECTINFORM

K I. PO0TNUEOf agoT ACSION NO. 3. RECIPIENT'S CATALOG NUMBER

BRL Report-No. 20z8ff____________________~.TITLE rand Subtitle) S. TYPE Of REPORT &PERIOD COVEM90

*STUDY OF LINER COLLAPSE, JET FORMATION ANDCIIARACTERISTICS FROM IMPLOSIVE SHAPED CHARGE Final

SYSTEMS .PERFORMING ONRG. REPORT NUMBER

7. AuTNoRl(e) 11. CONTRACT OR GRANT NIJNBERWe

Abdul R. Kjiwan

Alvin L. Arbuckle

9, PERFORMING ORGANIZATION NMAE AND ADDRESS 10. PRO(URAM ELEMENT. PROJECT, TASK

USA Ballistic Research Laboratory""A-, WR NT UBR

Aberdeen Proving Ground, Maryland 21005 IL161102AH43

I I. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT OATS

US Army Materiel and Development Readiness Command NOVEMBER 19775001 Eisonhower Avenue 13. NUMBER orPAGES

A exandria, Virginia 22333 51,MONITORING AGENCY NAME & ADORESS(II differentrom, Contolting Offic) IS. SECURITY CLASS. lot this eport)

/ UNCLASSIFIED

Tria.O&I-LAiSl FICATION/1OWNRADING

IC. DISTRIBUTION STATEMENT (of this eport)

Approved for public release; distribution unlimited.

17. DIST RI IUTION STATEMF NT (of the .abtract enteredIn E3lock 20, it ditffrat! rom, Report)

I*. SUPPLEMENTARY NOTES

IS. KE Y WORDS (Continue on revere@ side It ecessary and Identity by block number)

Shaped charges Numerical analysisFluid' mechanics Implosion systemsComputational methods Jets

Detonation theory Shock waves

20. -.U~rNAC (C~uhoue srever" elik 11meoawy awdEdeumlfv y block num.ber) krco-mputational fluid

mechanics study of the detonation, collapse, jet formation, flight andproperties of implosive shaped charge warhead systems. The study shows that adifferent liner collapse mechanism occurs from the familiar on e of linear andconical shaped charge systems. The collapse was also seen to deviate from theideal conditions initially envisioned. The resulting jet in some cases does

not possess an inverse velocity gradient as in ost classical cases, The jetin this case has distributions of mass, velocity, and energy along its lengt

D AN7373 3 oTO~IOSIoOEE UNCLASSIFIED (cont)ISECUIRITYLASSIFICATIO" OF THIS PAGE (Wh-a latantered)



* UNCLASSIFIED.WCURNIY CLAAMPICATIOM OF THIS PAGO(WON dMaRnmOe..

different from those of the classical cases. The different je t characteristicsW suggest a different type of target interaction than usual. Some of the

novel features found numerically were confirmed experimentally. A comparativestudy of the properties of different types of shape charge warhead designs isalso made,

I-,

C Om

. SECURITY CLASSIFICATION OF THIS I'ACE(*P.nDhef E.IE,•ired)

LJ



TABLE OF CONTENTS

Page

LIST OF ILLUSTRATIONS. ............... S

I. INTRODUCTION .................... .... 7

II. HYDRODYNAMICCONSIDERATIONS ........ ............ 8

Ill. COMPUTATIONAL SETUP AN D SIMULATION ..... ......... 12

IV. RESULTS AN D EXPERIMENTAL COMPARISON ........... .... 17

V. COMPARISON OF DIFFERENT DESIGN CONFIGURATIONS. .... 33

VI. CONCLUSION ............. .................. .... 49

DISTRIBUTION LIST....... .................. ... 51

ACCESSION for~

DDC . I1UNANtO0 ;V•'i)D

JUSTI..ICA ,.1. .... ..............

BY.

3s1U tt, Iv., AI1'i ,u,,S, j

r 3,

pIF • l ~ • T1 +il



LIST OF ILLUSTRATIONS

Figure Page

I. Schematic of a Shape Charge Warhead..... ......... 9

2. Idealized Schematic of Imploded Hemisphere Collapse. 9

3. A Schematic of the Computational Setup .... ....... 10

4. Configuration and Velocity Field Shortly AfterDetonation Wave Strikes Liner...... ........... 13

S. Pressure Field at an Early Stage . ......... .14

6. Flow and Velocity Fields Shortly Before Jet Formation. 15

7. Reduced Pressure Field Due to Nonconfinement .... 16

8. High Pressure in Liner Due to Compression .......... 19

9. Early Stage of Je t Formation .... ............ ... 20

10. Early Stage of Je t Elongation ...... ........... 21

11. Early Stage of Je t Flight ............ . . 22

12. Je t Elongation and Flight...... .............. 23

13. Late Stage of Je t Configuration ...... .......... 24

14. History of Velocities of Tracer Particles Placed

on Inner Liner Surface ..... .............. ... 25

15. Velocity Versus Time of Tracers on Axis of Symmetry. 26

16. Velocity Versus Time of Tracers 360 off Axis ofSymmetry ......... .................... ... 27

17. Velocity Versus Ti;.e of Tracers 720 off Axis of

Symmetry ...... ... ..................... ... 28

18. Histories of Average Velocity Components of

Copper Liner ........................... 29

19. Histories of Liner Energies ..... ..... .......... 30

20. Jet Velocity vs. Cumulative Mass of Copper Liner . 31

.,h



LIST OF ILLUSTRATIONS (CONTINUED)

Figure Page

21. View of Je t Being Struck by the Liner Equator at.17 Microsec .......... . . . . ......... 32

22. Various Charge Configurations Studied ............. 35

23. Initial Computational Setup, Charge 22(b). ....... 36

24. Th e Plane Detonation Wave Before Striking the Liner

charge 22(b) ........ ....... .................... 37

25. Early Stage of Liner Collapse, charge 22(b) .... ...... 38

26. Late Stage of Liner Collapse, charge 22(b) ........ 39

27. Early Stage of Je t Formation, charge 22(b) .... ...... 40

28. Je t Formation, charge 22(b) ..... .............. ... 41

29. Early Je t Elongation, charge 22(b) .............. ... 42

30. Je t Elongation and Flight, charge 22(b) ..... ....... 43

31. Comparison of Experimental and Computational Results,charge 22(b) ...... ......... .................... 44

32. Je t and Liner Configuration, Charge 22(c) ..... ...... 45

33. Flow Field Configuration, Charge 22(d) ........... .. 46

34. Je t and Liner Configuration, Charge 22(e) .... ....... 47

35. Flow Field Configuration, Charge 22(f) ........... .. 48

6

6



I. INTRODUCTION

Shaped charge warheads are utilized in a large percentage ofmilitary ammunitions. The processes of warhead design, developmentand testing are rather lengthy, expensive and time consuming.Mathematical modelling and computer simulation of the performance ofwarhead designs can reduce considerably the amount of proof testingrequired and eliminate unnecessary development costs. Parametric

studies of certain configurations or of proposed design changes canbe performed quickly and economically once a basic model has been

validated.

Most conventional shaped charge warheads consist of a metallicconical liner with a vertex angle of 300 to 900, and a cylindricalcharge which is molded around it and is point initiated at its end.The resulting detonation wave is approximately planar by the time itstrikes the liner and causes the liner to collapse resulting in a lowmass high speed jet moving forward and large mass low speed slugmoving behind the jet. The mass partition of the different linerelements into je t and slug portions takes place at their respectivestagnation points. The theory of je t formation for such warheads wasfirst published in the open literature by Birkhoff, MacDougall, Pugh

and Taylor

1

and was later extended by Pugh, Eichelberger and Rostoker2

.The whole theory was based on simulating the relative motion of themetallic liner during collapse with the steady flow of two jets ofwater impinging upon each other at the stagnation point. The applica-tion of the above theory necessitated assuming the collapse velocityof each liner element or measuring it. Kiwan and Wisnieski enhancedthe above theory 3 by calculating numerically the collapse velocities,jet and slug characteristics from the explosive properties and theassumed geometry. They demonstrated the procedure by calculating theproperties of two wedge shaped charge liners.

Recent interest has been shown in exploiting other technologiesto develop new shaped charge warhead designs for future weaponsof the 1980s. In this report we shall investigate some designs of

interest and study their characteristics through numerical simulationof their performance. The design shown in Figure 1 consists ofa hemispherical metallic copper liner and a hemispherical charge

1G. Birkhoff, D. P. &acDougall,E. M. Pugh, and Sir G. I. Taylor

"Explosives with Lined Cavities" J. Appl. Phys. 19(1948) p. 563.E. M. Pugh., R. J. Eichelberger, and N. Rostoker "Theory of Jet For-

mation by Charges with Lined Conical Cavities" J. AppL Phys. 23,

(1952) p. 532.3A. R. Kiwan and H. Wisniewski, "Theory and Computations of Collapse

and Je t Velocities o f Metallic Shaped Charge Liners" BRL Report No .

1620.

7

'.-.



together with an initiation package. The major portion of this study

will deal with the hydrodynamic simulation of liner collapse, jet

formation, flight and characteristics obtained from the charge shown

in Figuze I. Figure 2 shows an idealized schematic of the anticipated

liner collapse after being hit by a convergent deonation wave. Atypical element E collapses towards the center C with velocity Vcafter being hit by the convergent detonation wave. An observer at

the pole P sees the element E collapsing towards him with velocity Vre

The liner continually get thicker while it is being compressed, until

eventually it starts jetting. The dotted contour shows the actual

liner configuration at that time. The equatorial section of the

liner is elongating du e to the expAnsion of the detonation products atthe unconfined equator.

II. HYDRODYNAMIC CONSIDERATIUNS

The hydrodynamic simulation of the collapse, je t formation and

characteristics of the above referenced charge is made computationally

on the generic charge shown in Figure 3 which does not contain theinitiation package referenced in Figure 1. Only half of the charge

is shown in Figure 3 due to it being axisymmetric. The HELP code 4

was employed to simulate computationally the performance of the chargeshown in Figure 3.

H-ELP is a two dimensional finite difference multi -materialEulerian code capable of treating compressible fluids and solids inthe hydro and elastic plastic regimes. The conservation equationsthat are solved in HELP are:

-P D (pui) (1)

3t ax.

Dui a Ci) (2)

1

DET oj 5

where xi denotes the ith Cooax i.,at, of position, t the time, p denotes

the density, ui the ith velocly ;omponent, ET the total energy.

D stands for the total material derivative, a.. is the stress tensorS13

4L . J. Hageman et al., "HELP A Multi -material Eulerian Program for

Compressible Fluid and Elastic - Plastic Flows in Two Space

Dimensions and Time" Systems, Science and Software Report ?5-2654 (1975).

8



II

[ ULNER--7

Figure 1. Schematic of a Shape Charge Warhead=

Vr

II

CV

FiueIgueal.e Schematic ofaIShploedHaremWarhereClad s

t9

" ......



TIME" 0.0 MICROSElC

S 2. 4 cm- 1,27 cm

.19 cm

3

1 2

RADIUS (cm)

0-22.54

5m

a 4

Figurf) 3. A Schematic of -the Computational Setup

10



which can be separated into its hydrostatic stress component (pressure)- ij and a stress deviator tensor Sijp i.e.,

ii isj " 'ij P (4)

Equations (1), (2) and (3) are transformed into conservation forms

and then put into an equivalent integral form before applying finitedifference methods to these equations. The equations that are therefore

solved by finite difference methods for each cell of the computationalmesh and every computational cycle are:

Am -A tpuinidS (5)

A(m ) A .ndS At U - AtAfpuujnidS (6)

S S S

A(ME = A u.n.dS - At Pu.n.dS " AtfPu.EnidS' (7)

S S S

n. denotes the unit vector normal to a surface element dS.

Equations (5) through (7) are supplemented by appropriate initial andboundary conditions to initiate the flow. Material properties arerepresented in HELP by the Tillotson Equation 6 of state for inertmaterials, the ideal gas equation of state, and the JWL equation ofstate for explosion products. The code also contains a burn routinebased on the JWL Equation of state. The above flow equations are

integrated in three phases corresponding to the evaluation of thethree different types of integrals occuring in these equations andcalled the SPHASE (Strength phase), the HPRASE (Hydro phase), andthe TPHASE (Transport phase).

HELP contains a variety of options such as transmittive andreflective boundary conditions at various grid boundaries. It containsalso an artificial viscosity option. Material interfaces are definedin Lagrangian manner and are identified by massless tracer particles.A slide line can also be introduced along a material interface separa-ting tw o materials which permit them to slide against each other.

5P. D. Lax, "Weak Solutions of Nonlinear Hyperbolic Equations andTheir Numerical Computation", Comm. on Pure and Applied Math,Vol XII, P 159 - 193, (1954).

6J. H. Tillotson, "Metallic Equations of State fo r Hypervelocity

Impact," General Atomic Report GA-3216 (1962).

=1

'1ii



Although HELP models the strength properties of materials and containsa yield criterion and a failure criterion our calculations will berestricted to the hydrodynamic phase, with only viscous effectsincorporated. Our experience with calculations incorporating the SPIIASof the code is limited, and we have not investigated the validity of themodel used-in that part of the H-IELP code. Walsh reported that theresults of his calculations using the HELP code in similar problems werenot significantly affected when the strength effects were incorporated.

III. COMPUTATIONAL SET UP AND SIMULATION

The computational simulation of the performance of the charge shownin Figure 3 was made in a computational mesh of 50 x 90 cells. Eachcell was 0.8 mm x 0.8 mm in the region containing the metallic linerwhose thickness is 1.9 mm. The zones were gradually enlarged radiallyand axially to the end of the mesh. The choice of the mesh size had tobe balanced between the dosire for accuracy of the solution obtainedand the speed of the computations. A coarse mesh size is detrimentalto the accuracy of the calculations particularly so if any materialregion consisted of mixed cells only. A fine mesh enhances the com-putational accuracy but requires a larger mesh and reduces the magni-tude of the time step and thus requires longer computational time tosolve a given problem. Te n equally spaced latitude circles (initiation

rings) were selected on the outer hemispherical surface of the charge

shown in Figure 3. The simultaneous initiation of these rings wasconsidered to simulate reasonably well the initiation process of theactual charge.

Figure 4 shows the liner configuration at t=1.92 ps together withthe velocity field. The liner is seen starting to collapse afterbeing hit by the almost convergent detonation wave about 0.46 lis arlier.The lack of confinement on the equatorial plane allows the detonation

products to expand rapidly from that surface causing a departure fromthe idealized collapse depicted in Figure 2. The equatorial section ofthe liner starts to elongate at the explosive-metal-air-interface.

As the equatorial rarefaction wave travels along the surface of the

liner towards the polar region the pressures and velocities are reduced.Figure 5 shows the pressure in the flow field which is found to belarge and rising in the collapsing liner where it has a maximum valueof 0.328 Mbar. About that time (t=1.92 ps) the effect of therarefaction from the nearest unconfined spherical surface of the chargestarts to be felt at the liner surface and the pressure begins todecrease. Figure 6 shows the flow field at t=5.8 Ps. The liner isobserved to be getting thicker at the pole and elongating further inthe equatorial region. The pressure field is seen in Figure 7 to have

7j. M. Walsh, private communication.

12



LL

Ca

C,b 00 0 0 410 )9 30

R C

STMIi;= 1.92125 MvlIC&OSiC4

C)" t - p.

i,, \ "

, ,,

i N

&> ,

rr

Figure 4. Configuration and Velocity Field Shortly After Detonation

Wave Strikes Liner



CIO

00,j

a4:

cr

w4-J

0 m C

0 m m w

CD)

LL))

LI)

14



jq'MI: S,91113 MICROSFiC

L11

'pO

Figure 6. Flow and Velocity Fields Shortly Before Jet Formation

is



ri00.

AA

ui 00 0

CL-

C:) CH

C))CD V)

II )rj

(U ~at

Llb



decreased significantly by that time. The maximum pressure in theliner material is found to be 0.15 Mbar. As the liner collapseadvances, the pressure starts to increase again due to liner com-

pression and reaches a maximum value of 0.603 Mbar, at t=9.2 usas can be seen in Figure 8. Th e pressure decreases thereafter dueto the influence of the equatorial rarefaction and the expansion ofliner material arising from je t formation and elongation. Therarefaction wave emanating from the equatorial plane reaches the polarregion about tm7.2 4s and the je t becomes distinguishable after that

time. Figures 9 and 10 show the early stages of je t formation. Theshort arrows show the direction of the local flow velocity in the differ-ent layers of liner material. Figures 11 through 13 show the latestages of je t formation and flight. A particularly remarkable featurein those Figures is that the equatorial section of the liner impactsthe je t after its initial elongation. Several other features of these

•jets will be discussed more fully later. Figure 14 shows a plot of thevelocity versus time for ten different tracer particles placed on theinside surface of the hemispherical liner, while figures 15 through 17show plots of velocities versus time of four particles placed across theliner thickness at three different locations, one on the axis of symmetryand the others are placed at locations whose radii make angles of 36*and 720 respectively with the axis of symmetry.

IV. RESULTS AND EXPERIMENTAL COMPARISON

Th e primary advantage of mathematical modelling and computationalsimulation of physical problems is the wealth of information available6nce a successful model has been achieved. Th e values of the variouscalculated physical parameters of the problem are available throughoutthe region of computation in a permanent record form which can subse-quently be retrieved and examined. Parametric studies can also be madequickly and sometimes economically. In this section we shall summarize

our computational results and compare them with some of the availableexperimental data. Figure 18 shows a plot of the average velocitycomponents of the metallic liner as a function of time, while Figure 19shows the different liner energies as functions of time. Th e initialrarefaction wave arriving at the liner surface due to the nonconfinement

of the spherical charge surface reduces the liner acceleration, whilethe equatorial rarefaction wave causes the je t to become distinguishable.

Th e continued liner compression converts the liner radial momentum toaxzal momentum. The total liner energy increases rapidly at first andapproaches an asymptotic value later on . Figure 20 shows a plot ofje t velocity as a function of cumulative mass at various times. Theje t mass continually increases as more metal is accelerated to jetvelocities.

17

11



It was found numerically that about 18.7% of the hemispherical

liner forms the jet (i.e., has velocity _ 2mm/ws). Lxperimental

measurements estimate the je t mass to be about 18% of the liner mass.Th e calculations indicate that about 19.9% of the explosive energy

is delivered to the copper liner of which 11.8% is in kinetic energyform and 8.1% is in internal energy form. Th e kinetic energy of

the je t is 41% of the total energy of the liner (69% of the kinetic

energy of the liner). The je t tip velocity wa s found to be 6.42mm/ws.Two experimental measurements of je t tip velocity were made at BRL of

7.07mm/ps and 7.57mm/us. In the experimental tests the hemispherical

charge used was 0.151 kg of PBX and the initiation package contained0.2685 kg of composition B-3. In the computations only the energy

from the hemispherical charge was incorporated in the calculations.

If one adds the kinetic energy of the flier plate, in the initia-tion package, to the explosive energy of the charge then the resulting

je t velocities will increase on the average by about 8%. The resultant

je t tip velocity will increase to 6.92mm/ps. If in addition oneconsiders the effect of the confinement provided by the flier plate

and scale the jet tip velocity according to the values given in columns(a) and (e) of Table I of this report, the je t tip velocity will. befound to be 7.35mm/ps which is within the range of experimental measure-

ments.

Several important observations can be made from the computations,

concerning the je t properties from such systems. No inverse velocitygradient wa s found in the je t produced by such systems as in the caseof most conical systems. Th e lead particle in the je t has as a result

of this a small amount of mass. Examination of Figures 9 and 10 suggeststhat the je t forms from the liner material located on the insidesurface layer of the liner, while the remaining liner material ends

up in the slug. This observation is confirmed from an examination ofthe velocity plots shown in Figures 14 through 17. Figure 14 showsthat the entire inside surface layer of the liner reaches terminal jet

velocities except for the equatorial portion of that layer. Figures15 through 17 confirm this observation. Th e amount of je t mass andkinetic energy from such a system is similar to that obtained fromconical systems (same order of magnitude), although their distributions

along the je t length appear to be different. X-rays from early

experimental tests showed a part of the je t to be missing. It wasthought at the time that that part of the copper je t vaporized. Thecalculations shown in Figures 11 and 12 show the correct interpretation.

It is clear from those figures that the equatorial portion of thehemispherical liner after initially stretching, moves inwards an dpinches off the jet. X-rays of the je t at early times were then

taken in subsequent test firings which confirmed the theoreticalpredictions. Figure 21 shows the je t obtained from one of theexperimental test firings. The equatorial protion of the liner isseen in the process of pinching of f the jet.

18

S . . . . ,7



00.

0I .,00. V0

004-J

W

o c•~~0-

w19)

in'-2

LA 0

IL.

co &n

1-9



I'FTIME 8.99182 MICROSEC

N~00

U

S:--

C ....

I0

0

L0

It~f

Fiur

ci.0 1000 2.00 3.00 4'.00 S'.00 6.0cADIUS (CM)

Figure 9. Early Stage of Jet Formation

20

S•o



UTl 1656 ICOE

tt

X

1100va P.00 3 00 4.00 5'0

RADIUS (CM)

Figure 10. Early Stage of Jet Elongation

21



TIME 17.71877 MICROSIEC

c7a

0

Coy

rn

L)

c-i

C.D

C•)

Cy)

-0.00 i.00 2.00

R-CM

Figure 11. Early Stage of Jet Flight

22

-I.



"TIME u 22.67634 MICROSEC

C"

2i 4R-CM

Figure 12. Je t Elongation and Flight

23 -



TIME 39.90044 MICROSEC

N]

01- j

24--CM

Figure 13. Late Stage of Jet Configuration

24



di

LU

in

.Or4

-LJr 4C'+

~0

"-4

a 04



9

C3

a

0n

fl

no-L~~~ ocU10'0 ~(33083W/o 9A

26



I44

144

44

- 0

4ý4.

0

S f41

u 4

* 0

L r u

27:



9I

4J

4-4

14

C3

0

.4J

00*9 DO"S0 o.,G 0. z no-I O

(33S31W/W)AI3C1A

28-

bb~ 4~



#IS

X.

00

I-L

LU0

0 4.

> 0

00Lu -

zi ui

Z >00

00

2 29



4nIINI04

z z C

w-JJ

.,4

$4.

00

03



00 N4

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'JoJ

(SWIW) A1013A -



Figure 21. View of Jet Being Struck by' the Liner Lqniat oiat HII oo

3 2



V. COMPARISON OF DIFFBHIRNT DESIGN CONFIGURATIONS

The above numerical study dealt exclusively with the hemispheri-cal liner collapse under implosion and the je t obtained from theshaped charge configuration shown in Figure 22(a). In this section

we shall compare briefly the collapse and jet properties of thecharges shown in Figures 22(b) through 22(f) with the above studiedcharge 22(a).

The charge shown in Figure 22(b) is cylindrical in shape, containsthe same mass of explosive as the previous case, but is initiatedat its eid by a plane wave. Figure 23 shows the computational setup,while Figure 24 shows the plane detonation wave at t = 2.2ps shortlybefore striking the liner. Figures 25 and 26 show the early stagesof the liner collapse in this case. Figures 27 and 28 show the earlystages of je t formation for this case, while Figures 29 and 30 showthe late stage jet configurations.

It is apparent from examining Figures 23 through 30 and the restof the computational plots (not shown) that the liner turns insideout in this case. The resulting je t from this shaped charge design,

which is defined to be that part of the collapsed liner with

velocities > 2mm/ps, is seen to be a short thick jet. Some instabilityis seen to occur near the base of the slug. The je t takes a longertime to form, its mass is about the same as the previous case 22(a)

(11.6 xlO- 3kg), but is considerably sliwer moving, the je t tip velocity

being only (3.6mm/us). The total energy communicated to the liner is(8.9 x 104J) which is about 52% of the energy communicated to theliner in tho previous case 22(a). Figure 31, views (a) through (c),show the je t obtained experimentally from a copper hemisphere whoseradius is 1.9 cms with a cylindrical charge which is point initiatedat its end along the axis of symmetry. Figure 31(d) shows ourcomputational prediction of the liner configuration at t = 28.7psafter initiation for the charge shuwn in Figure 22(b) with a planewave as described above. The similarity between the experimental andcomputational results is encouraging and provides some validation ofour computational model.

The charge shown in 22(c) is similar to 22(a) except that some ofthe explosive in the equatorial region was shaved off in the hope thatthe equatorial portion of the liner will take a longer time beforeit interrupts the jet. The interruption of the je t was delayedabout 6ps, but it was not possible to eliminate it. The je t obtainedin this case was similar to that obtained from 22(a). Table I containsthe characteristics of the jets obtained from charges 22(a) through22(f), while Figures 32 through 35 show some profiles of the jetsand liners obtained from charges 22(c) through 22(f) respectively atthe times indicated on the Figures.

33

S . .... . . , , ,, i i i i



Table I. Summary of the Computational Results.

CHARGES GEOMETRY

FIGURE 22 (a) (b - c) (d)* (e) Cf.Jet Mass (Kg) 3I10

311.7 11.6 11.8 9.6 12.6 18.3

Je t Tip Velocity

(mm/ps) 6.4 3.6 5.0 6.1 6.8 5.7Kinetic Energyof Je t (J)

-4x10 6.36 3.72 5.81 5.74 8.35 9.83

Total LinerEnergy (J)

* -5xlO 1.68 0.89 1.63 1.17 1.94 2.90

The charge shown in Figure 22(d) has an iron flange 6.35 mm(0.25 in) thick to confine the expansion of the detonatioa productsat the equatorial surface of the charge and delay the rarefactionemanating from that surface. The results of that computation aresummarized in column 4 of Table 1, owever those numbers listed arebelieved to be in error because parts of the je t flowed out of thecomputational mesh at the top transmittive boundary of the computa-tional mesh before stablizing into a final state. Normally such aproblem is avoided through constant monitoring of the calculationsand a timely rezoning of the computational mesh. The numerical resultsgiven in column (d) hould therefore be considered as lower boundsfor this case. In the numerical simulation of the performance ofthis configuration, the detonation gases were not allowed to expandbetween the liner and the flange as it is the case in practice. Itwas observed in the computational model that the flange prevents theje t disruption by the liner's equator. Figure 33 shows the flowfield configuration at

t = 13.49ps.The charge shown in 22(e) is similar to 22(a) but has a confining

case on the outer surface of the charge. The je t obtained in thiscase has 31% more kinetic energy than the unconfined charge 22(a).The je t has a larger mass and a faster je t tip velocity. A larger

portion of the explosive energy is communicated to the liner in thiscase. The results of this computation are summarized in column S

*•The results reported in this column are inaccurate due to a

computational oversight.

34



.. ý aEXPJF LINER

,I

(a) (b)

(c)FLANGE (d)

CAIN

\LINER LINER

(.) (fM

Figure 22. Various Charge Configurations Studied

35

lil



C) TIME 0.03818 MICROSEC

0

c:)

=0

Line

I

o

o • Liner

Explosive

\Initiation Surfaces

b00 1 00 2.00 3.00 4.00 5.00

R-CM

Figure 23. Initial Computational Setup, Charge 22(b)

36



000

000

44

U-) CDi

U, C)

ir 4-J

CD 041

41)

CDC

4-)

LO 1-4

I?0CIOi

37)



So TIME 5.95841 MICROSEC

C0

00

C)

0D.00 1.00 2 .00 3.00 4 00 5 .00

P-CM

Figure 25. Early Stage of Liner Collapse. Charge 22(b)

38



TIME 11,12312 MICROSEC

F.,.

R-?

C"

C2)

co

O0.0 1 ,00 2,00 3.00 4 .00 5,00R-CM

Figure 26. Late Stage of Liner Collapse, Charge 22(b)

39



C)

TIME u12.87821 MICROSEC

Q

ca~

LD

I

04

- R' M~



S~0

0

0~

!-.-

r• • I I i i0•;O.O0I.O02 O 3 O '.O0S.O06,O

I 4-4

0,__ _ __ _ __ _ _

0 ,

0,001,002.003.001.005.006.0



0

TIME 18.23331 MICiROSEC

K7r

N 0

00

cmm

0CD

, C)

S~CD

S~0-

! ~C.

0

000 1 0 2.00 3.00R-CM'

Figure 29. Early Jet Elongation,Charge 22(b)

42

L*l



TIME 28.7201b MICRO-SEC

ci_00

coi

C)

'0,01'02003 0

c-JC

Fiue30 e Eogtinad lgthre 2b

c43



(a) (b)

29-.0 /.sec

IM



cl)

0,

C*)C

Fiur 2.Jt ndLne onigrtin Care22c

C45



CD TIME 13.48655 MICROSEC

0* 0

CD

L)

C?

MI

oh I o0 2.00 3.00 4,00 5.00

R-CMFigure 33. Flow Field Configuration, Charge 22(d)

46

I i



TIME 12.84828 MICROSEC

0.00 1.00 2.00

R-CM

Figure 34. Jet and Liner Configuration, Charge 22(e):•

47



II

=13.01705 MICROSEC

i?"

408

S•0OO .00 2'O00 3.00 4'.00 5.00 • 00 7.00

::/• •R-CM

:•:. ,Figure 35, Flow Field Contfiguration, Char~ge 22(f')

• 48

i" I'.

I ' •,,

-. I I llll~ - ii i i i • " ii .' , ,



of Table 1. Unfortunately the equatorial section of the liner inter-rupts the jet at an early stage of its formation. Figure 34 showsthe liner configuration at t w 12.85s.

The charge shown in 22(f) has a 3.81 mm (0.150 in) thick linerwhich is double the thickness of the liners used in the previouscases. The charge thickness was also increased to 24.13 i (0.95 in).The initiation points were distributed over a 1200 sector of the charge

surface instead of the 1800 hemispherical surface. The calculations

revealed that the equatorial portion of the liner interrupts the je tabout 18ps after initiation. The je t has more mass, but the jet t'I

velocity is slightly lower than case (a). A summary of the results

in this case is given in column 6 of Table 1, and Figure 35 showsthe flow field configuration in this case at t = 13.02ps.

VI. CONCLUSION

The above study explained the collapse and je t formation processesof a hemispherical liner with a hemispherical charge which is surfaceimploded. It is clear from the preceding study that the collapse an dje t formation processes are fundamentally different from those ofa cone. The various hemispherical liner elements converge towards a

single point as they collapse. The je t forms du e to the compressionof liner material which squeezes out the je t materials as in an extrusionprocess. Conical liners collapse along a line. The study has shownthat the je t originates from the inner surface layer of liner material.It has been shown that such jets have no inverse velocity gradients.The above study revealed the cause of the jet pinchoff as being due

to the equatorial portion of the liner striking the jet. The designmodifications discussed in Figures 22(c) an d 22(d) alleviate thisproblem.

The second part of the study dealt with the effects of variationsof the charge geometry and initiation mode as in charge 22(b) anddealt with the effects of confinement, and variations of the chargean d liner thicknesses. The study of charge 22(b) revealed that the

hemispherical liner turns inside out in this case an d forms a short,thick, and slow moving je t which might be suitable foe use against acertain class of targets.

In conclusion the above computational study has provided a wealthof quantitative values of various physical parameters most of whichagree quite well with experimental measurements. This agreement inaddition to the qualitative agreement of our computations withexperimental results provides validation of our computational modeland reveals the benefits of such studios as a design tool. Inpractice many experimuntal design parameters were based on similarhydrodynamic computations. Such computational studies can often bemade quickly, economically and can result in considerable financialan d time savings.

49

_,A



The authors wish to acknowledge several helpful suggestions by

Dr. Philip Hlowe and Dr. Clifford Mseltino who also provided soma of

the experimental data. Special thanks'are due to M'r. V. oyl

for providing the photograph-shown as Figure 21.,-

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abdul r. kiwan and alvin l. arbuckle- study of liner collapse, jet formation and characteristics...

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