LA-6809CC-14 REPORT COLLECTION

REPFKNXJCTIG:{COPY

UC-34 and UC-45

Issued: July 1977

An Empirical Model to Compute the

Velocity Histories of Flyers

Driven by Electrically Exploding Foils

S. C. Schmidt

W. L. SeitzJerry Wackerle

Ioswalamos~ scientific laboratory

of the University of California

i LOS ALAMOS, NEW MEXICO 87545

An AHirmative Action/Equal Opportunity Employer

UNITED STATESENERGY RESEARCH ANO DEVELOPMENT ADMINISTRATION

CONTRACT W-740 S-ENG. 36

1

r

Printed in the United States of America. Available fromNational Technical Information Service

U.S. Department of CommerceS285 Port Royal RoadSpnrrgtleld, VA 22161

Price: Printed Copy S3.S0 Microfiche $3,00

J ‘“ –1

_ ~——

SCN“~ol.=— AN EMPIRICAL MODEL TO COMPUTE THE~— m~~o, VELOCITY HISTORIES OF FLYERSm—~1=5= DRIVEN BY ELECTRICALLY EXPLODING FOILS-g,d~~~ o$Eo, by~.

~g$—m S. C. Schmidt, W. L. Seitz, and Jerry Wackerle

Oc

-’~m;.—.—

ABSTRACT

A modification of the gas gun (Gurney) formulation is used to computa thevelocity and position histories of flyers driven by electrically exploded metalfoils. The model is based on a numerical time integration of an energy con-servation statement for the flyer and the expanding high-pressure metalvapor. Empirically altered, experimerhal power curves are uzed for thetime-dependent energy term in the conservation equation. Computed bursttimes and flyer velocity histories for 1.5- to 25-mm-square aluminum foilsagree favorably with available experimental data. Comparison of calculatedand measured results for single cases with exploding copper and magnesiumfoils suggests

I. INTRODUCTION

that the model is also applicable for these materials.

——__——__——. ._ ——— ——— ——

During the past decade, electrically driven flyersystems have evolved into effective laboratmy high--pressure shock-wave generators, which are par-ticularly useful for investigations of the short-duration shock initiation of condensed explosives,’ Atypical arrangement for accelerating thin flyers isshown in Fig. 1. A capacitor bank is dischargedthrough a thin metal foil, effecting ita abruptvaporization. This “burst” of the foil generally occurswith a sharp maximum foil resistance and electricalpower input. Tho plastic layer is sheared at the innerradius of the barrel, and the flyer disk so formed issubsequently accelerated by the high-pressurevapor. Flyer velocities as high as 14 mm/ys havebeen achieved in this way.’

The gas gun (Gurney) approximation is a simpleanalysis that has been used to predict the motion ofplates and shells driven by detonated chemicalexplosives,‘-s and recently has been used to treatelectrically driven flyers,‘1’-11 Conceptually, the

Barrel

b

&

Plastic Layer(Flyer) ~\

1t

[

~WppW Conductor ToP

BottomHigh Current Discharge

Fig. 1,Electrically driven flyer assembly.

Layer

and

1

physicalpressure

system modeled is the expansion of high-gas, initially at rest, against confhing

plates or shells. A “Gurney energy” is assumed to bedeposited uniformly throughout the gas before anymotion begins. This energy is taken as an empiricalfraction of the energy of reaction for chemicalexplosives:”’ and has been correlated h the jouleheating near burst for electrically exploded foils.’!’-”

For explosively driven flyers, the gas-gun ap-proach predicts flyer-velocity histories that agreefavorably with both experimental results andhydrodynamic computer code calculations.’”Previous application1!9-11of the Gurney formulationto electrically driven flyers has been limited to thecalculation of terminal velocities, and has notproduced entirely satisfactory results. The standardgas-gun formulation does indeed predict that ter-minal velocity is achieved in typical run distances;however, a much more gradual and continuing flyeracceleration is ob gerved.Since the corresponding ex-ploding foil power histories measured by us andothersl’ll suggest additional energy deposition in themetallic vapor subsequent to foil burst, a formula-tion of the treatment with time-dependent energydeposition is indicated.

In the work described here, a conceptuallysatisfactory mocbflcation of the gas-gun treatment isused to compute velocity histories for flyers drivenby electrically egploded foils. Rather than assumeinstantaneous energy deposition, we empiricallyrelate the joule heating of the foil material to theobserved electrical power histories, with allowancefor energy dissipated in forming the metal plasma.These changes yield computed velocity historiesconsiderably different from those resulting from theusual Gurney model and in favorable agreementwith available experimental data. In many in-stances, the model also affords reasonable estimatesof foil burst time.

The model is strictly empirical. Even thoughmany of the relevant physical processes that occurduring foil heating and expansion are used to incor-porate the empiricism, many more processes (e.g.,plasma recombination, spatially nonuniform energydeposition) are ignored. The principal improvementover previous models of electrically driven flyers isthat a computation of complete velocity historiescan be made for a wide range of foil and flyer dimen-sions,

II. ANALYSIS

A. Simple Gas-Gun Formulation

The usual Gurney model is formulated by the con- .

servation of the total energy (internal and kinetic) ofthe driving gas-flyer system. Initially, the system isat rest and, with compression and internal energy of

*

the flyer neglected, the total energy is the internalenergy of the gas. This Gurney energy, Es, is as-sumed to be generated instantaneously from an ex-plosive reaction or horn electrical heating of a foilvapor. In the subsequent expansion of the gas, theinternal energy, E, density, p, and pressure, p, aretaken to be spatially uniform. The mass velocity, u,is assumed to vary linearly with distarice, r, in thegas and to have the uniform value ur in the flyer.

For electrically driven flyers, slab geometry withthe vapor sandwiched between the ilyer and an in-finitely massive tamper is assumed. With the aboveassumptions, the energy conservation statement is

rf (t)&Q.)m8E(t) + ~ J U2(r,t)dr

+ ~ nI#,2(,) : mgEg ,

(1)

where mr and mr are the gas and flyer masses perunit area and rc the position of the gas-flyer inter-face. With u(r,t) = (r/r~(t))udt) (rind noting thatp(t)rf (t) = mJ, this expression reduces to

(2)

where ~ = mf/mZ. Assuming that the equation ofstate of the vapor is that of a polytropic gas,

(3)

where the gas constant, 7 = 5/3, is chosen on the as-sumption that the metal is monat.omit. When thepressure is considered as an accelerating force ex-erted per unit area of the flyer, .

dufP-mf= , (4)

P

2

the internal energy can be eliminated from Eq. (2),yielding

(5)

The transformation duddt = l/2(du?/drf) convertsEq. (5) to a first-order differential equation foru?(r,), which can be integrated from the initial gas-flyer interface position, rc, to an arbitrary final posi-tion, rf, to give

‘f= [& brg@’1]”2 s ‘6)where @ = 2/3 + 2/(!3@. Aa the flight distancebecomes much larger than the foil thickness, r,>> r~,a terminal velocity

[ 1,1/2

_x&.‘ft - (1/3 +U) (7)

is attained.As mentioned earlier, previous applications of the

Gurney method to electrically driven flyers have allbeen made on the basis of a terminal velocity suchas that expressed in Eq. (7) .lOS-l’The Gurney energywas correlated to the burst current density, ~b,in theform

Eg=KJ: , (8)

where K and n were empirically determined cons-tants for a given foil material and for velocitymeasurements i~t a specfled flight distance. Thismodel successfully predicts the flyer velocitydependence on the burst current density and flyerthickness and is adequate if these are the onlyparameters to be varied.

The consider(kion of only the terminal velocity forelectrically driven flyers is consistent with the as-sumption of the simple model. For typical con-figurations and flight distances of interest, the inputparameter to Eq. (6) would be @ s 1 and rJrf ss0.01, and terminal velocity is nearly achieved.However, under these conditions terminal velocitiesare not usually observed. For example, the velocityhistory measurement of Weingart and coworkers(Fig. 2, curve B, of the present report) has a muchmore gradual acceleration than the trajectory, B’,calculated with the Gurney method and the burst-current correlation. Similar comparisons occur when

the simple analysis is applied to the other flyer/foilassemblies described here.

The failure of the flyer to reach a terminal velocityas quickly as predicted can be understood by ex-amining the power curves for the exploding foils,such as curve A in Fig. 2. Contrary to the instan-taneous energy deposition at burst, which is as-sumed when using the Gurney model, the actualpower deposited is not sharply peaked near the timeof burst, but exhibits a moderately fast rise to peakpower and a more gradual decay after burst, Thegradual decay suggests that joule heating of the foilis still occurring at relatively large postburst times.Addition of energy to the expanding gas would sus-tain a greater gas pressure than expected from thesimple model, and would lead to a continuing ac-celeration of the flyer. Thus the energy conservationstatement should be formulated with a time-dependent energy deposition term to allow closeragreement with experimental power curves.

B. Time-Dependent Energy Deposition

If the constant Gurney energy, Es, is replaced by atime-dependent deposited specific energy,Q(t), theconservation statement, Eq. (5), can be rewritten as

duf(t) 1—.Mlrf (t) [( ) 1

- ; +~ u,(t)’ + ‘Q(t) . (9)dt

Initial conditions for the integration are Q(0) = u,(O)= Oand rdO) = r’, With Q(t) specified by observedpower histories, a numerical solution is necessary.Specifically, the set of three coupled differentialequations, Eq. (9),

drf (t)— = u,(t) ,

dt(lo)

and

AJ2#l . p(t) (11)

are integrated numerically using LASL TLIB“ Subroutine ODE. The power history, P(t), is derivedfrom a separate analysis of foil current and voltagemeasurements and a fifth-order polynomial inter-polation scheme (LASL TLIB Subroutine AK-NINT). Initial calculations indicated a need to

3

A.

,u

?

‘O 0.5 LO 1.5 2.0 2.5 3.0-

Time (ps)1 ,.

J&$, 2,

Flyer velocity and foil power us time; 0.051-mm-thick, 25.4-mm-square aluminum foil; 0.25-mm-thick, 25.4-mm-diam Mylar flyer; 40-kV dischurge voltage. Curve A, experimentalpower histo~. Curve B, experimental velocity histov. Curve B’, computed velocity histo~using Gurney model. Curve C, computed velocity history using unultered postburst powerhistory. Curve D, computed velocity hiatow using modified postburst power hhtoqy.

reduce the actual power input. The reduction is ac- A. Energy Used for Fusion, Vaporization, andcomplished by empirical fitting. Ionization

III. EMPIRICAL FITTING

The analysis is carried out with the aid of two em-piriciems: (1) a preburst energy, I, empiricallychosen as the sum of the heata of ~sion, vaporiza-tion, and ionization, is subtracted horn the ex-perimental power curve so that Q(t) = Oin Eq. (8)until the J P(t)dt = I, and (2) modification of thepoatburet portion of the power curve so thatpredicted velocity histories agree with measure-ments.

The first empiricism is suggested from experimen-tal velocity and power histories. As noted in Fig. 2,flyer movement starts very close to the time of peakpower or foil burst, implying that energy depositedin the foil before burst does not contribute directlyto flyer acceleration. Foil melting, vaporization, andionization are possible dissipative processes to ab-sorb this energy.* As a first approximation, I was setequal to the sum of the heateof fusion, vaporization,.—

●l’he actual heating path may not include a preeaure-volumestate which allowe for a vaporization trarwition.

and ionization at atmospheric pressure; values forthe three foil materials of interest are given in Table1.

Calculations were performed for experiments byWeingart and coworkers and by Stantonil by usingtheir measured power curves and the I = 32.3 J/rngvalue for aluminum, with the resultsgiven in Figs. 2and 3. In both cases, 32.3 J/mg corresponded to theintegration of the specific power (curve A) to a timenear burst. In both instances, the calculated velocityhistories (labeled C) gave times of flyer movementcoinciding with both the times of initial motionobserved (curves B) and the times of peak power inthe foils. Following burst, the predicted flyervelocity histories have the correct shape, but areconsiderably larger than those observed. This dis-agreement dictates a further modification of powerinput, P(t) .

B. Modified Power History

Even though the correction is empirical, somerationale for a modification of the measured powerhistories can be argued. Following burst, thematerial accelerating the flyer is a highly ionized,highly conductive plasma; however, a region ofhigher resistance liquid and un-ionized vapor mustexist between the plasma and the solid lead (see Fig.4). Because voltage probes must be positioned sothat the melt/vapor transition region is included inthe measurement, the electrical resistance andpower observed do not properly reflect the energydissipated in the plasma.

Another source of disagreement between theoryand experiment is the assumption of an infinitelymassive tamper in the development of Eq. (9) sothat the kinetic energy (and velocity) of the flyer isnot diminished by the kinetic energy of tampermaterial. This assumption is unrealistic, particular-ly during the period just following burst, when pres-sures of several gigapascals are estimated in the foilplasma. A calculation to correct for this effect wasmade with a “growing tamper” model, in which themass per unit area of the confining tamper materialwas assumed to be zero at burst and to subsequentlyincrease according to its density multiplied by itscharacteristic sound speed. Appropriate modifica-tion of the energy conservation relation and explicituse of momentum conservation gave a tractableproblem, and calculated velocity histories had theexpected improved agreement with observation.Still, the need for a large empirical correctionremained; consequently, we included the effect oftamper motion in a correction rather than employ-ing the more complicated formulation of the growingtamper model.

A correction factor applied to the postburst powerdensity was chosen to force agreement for cases with25.4- and 9.53-mm-square aluminum foils (Figs. 2and 3). The form used was

Correction Factor = [0.958 - 0.166 V]

(12)x [1.0+ ,- $]’”0 .

Here W is the width of the foil in millimeters, T isthe time from foil burst (calcdat ed as describedabove), and b is chosen as 0.1 pa for the large foils

TABLE I

MATERIAL PROPERTIES OF FOIL METALS(Taken from Ref. 12)

Heat ofDensity Fusion

Material (mg/mmS) (J/mg)

Aluminum 2.79 0.40

Magnesium 1.74 0.37

Copper 8.89 0.21

Heat of Heat ofVaporization Ionization

(J/mg) (J/mg)

10.5 21.4

5.42 30.3

4.80 11.7

5

350 u a v 8 1 9 I

A

u AAAAA

-300 -A

A,A t

AE’ A

g 250 “ A

A

T Irne (ps). ..

Fig. 3.

Flyer velocity and foil power us time; 0.051-mm-thick, 9.53-mm-sqmre aluminum foil; 0.127-mm-thick, .9.53-mm-diam Myhar flyer; 18-k V discharge voltage. Curve A, experimentalpower hbtoqy. Curve B, experimental velocicy history. Curve C, computed vebcit:$ histo~

using unultered postburst power histow. Cume D, computed velocity histo~ using modifiedpostbumt power hktory.

I

- Volt age Probes

1

~Melt and vaporRegion

Fig. 4.Melt and vapor region of exploding foil.

under discussion and 0.026 pa for the smaller foils

described later. The results of applying this post-buret correction factor are shown by curves D inFigs. 2 and 3. Although the results are superior tothose obtained with the simple Gurney formulation,the real test of the model is ita ability to simulatevelocity histories for foil/flyer geometries much dif-ferent from those used to calibrate the empirical cor-rection factor.

IV. COMPARISON OF MODEL WITH AD-

DITIONAL EXPERIMENTAL DATA

In this section the empirical fit structured above isapplied to a variety of different foil/flyer conf@ra-tions to validate its usefulness as a predictive tool

.

1

F

6

and also to determine, as well as possible, its rangeof applicability.

A. Large Aluminum Foil Data

Weingart and coworkersi’ls have studied flyersdriven by aluminum foils of different dimensionsand exploded with different firing-set voltages.F@res 5A and 5B give an experimental powerhistory and a single velocity datuml’ for a foil/flyerconfiguration and discharge voltage similar to thatgiven in Fig, 2, except that the aluminum foilthickness has been increased by a factor of 3. Alsoshown are the predicted velocity history and thevelocity-distance dependence computed using theempirical fit discussed above. Both the computedvelocity and the estimated burst time agreefavorably with experimental results. Even thoughthe exploding foil for this case has tripled inthickness from the example shown in Fig. 2, thepostburst velocity historiesof the two conilgurationsare comparable. The specific power in the thinnerfoil is considerably greater than in the thicker foil,but the total energy deposited is approximately thesame for the two contlgurations. The thicker foil re-quires more time and three times the electricalenergy to burst, but since I is a relatively small frac-tion of the total electrical input energy, thevelocities attained are comparable. This againemphasizes the importance of considering the post-burst power input.

Figures 6A and 6B show a power history and singlevelocityia datum for a foil/flyer configuration inwhich the foil width is half that of the conf@rationof Fig. 2 and the capacitor discharge voltage is alsodecreased by the same factor. As can be seen fromthe predicted velocity history, a good estimate of thefoil burst time is obtained because initial flyermovement occurs at approximately the time of peakpower. Figure 6B also shows that the velocity com-puted using the empirical model agrees favorablywith the measured velocity.

B. Large Magnesium and Copper Foils

To assess the model’s range of validity, it wascompared with Stanton’sli observations of flyers

driven by electrically exploded magnesium and cop-per foils with geometries and firing-set conditionssimilar to those of the aluminum foil experiment(Fig. 3). The empirical postburst specific power cor-rection, calibrated using the aluminum foil observa-tions, was applied to the cases of magnesium andcopper foils.

The predicted velocity history for the magnesiumfoil (Fig. 7) is in reasonable agreement with obser-vation—the small discrepancy being due mainly tothe calculated later start for the flyer motion. Thisdisagreement occurs despite the fact that the com-puted burst time corresponds to the peak in thepower history.

For the copper foil, the computed flyer velocityhistory (Fig. 8, curve C), predicts a burst time andinitial flyer motion that occur considerably laterthan the peak in the power history or initialmeasured flyer movement. If the ionization energyof copper is not included in the determination of I,the computed velocity history (curve D) agrees withthat observed. Conceivably, the lower specitlc powermight provide some argument for assuming in-complete ionization of the foil; however, this deduc-tion should be accepted with caution because of thehighly empirical character of the analysis.

C. Small Aluminum Foil Data

We have measured velocity, current, and voltagehistories for seven 1.52-mm-diam Mylar flyersdriven by O.011-mm-thick, 1.52-mm-squarealuminum foils. A 2-YF capacitor discharge unit,charged to 3 kV,was used to explode the foils. Fourtests were fired with 0.75-mm-long, 1.52-mm-diambarrels attached to the Mylar surface (see Fig. 1).Velocities at the end of the barrels were determinedfrom streak-camera records of the flyers striking-0.15-mm Lucite step flashers. The other three ex-periments were performed without barrels, withvelocity histories obtained using a modification ofthe streak-camera reflection technique.i’ Flyer mo-tion was recorded by observing, at an oblique angle,the light emitted from the exploding foil and trans-mitted through uncoated slits on the flyer surface.Barrels were not used in these experiments becausethey would partially obscure the flyer surface atsmall travel distances. In the absence of a fiducial

7

I20

40

20

0,

A

ExperimentsPower

●●o*

●●

●

.0 Computed

A

● Velocity●

●

●

J\●

6

●

s

0.5 Lo 1.5 2.; 2.5 3.0 3.5 4Time (~s)

61 m , 1 , , , , 1

t

B .?5 ● ° Experimental

z ● **

● Velocity<4

●●

g ●● Computed Velocity

I3 “*

●

2 -0●

I ;

a00123456 78

1 m m n n n

Distance (mm)

Fig. 5.Flyer velocity and foil power us time (Fig. 5A) and flyer velocity us travel distance (Fig. 5B);0.152-mm-thick, 25.4-mm-squure aluminum foils; O.%-mm-thick, 25.4-mm-dium Mylarflyers; 40-kV discharge voltage.

1

8

280 r I 1 1 0 1

A● 7

●

240 - ●● - 6

G

E 20(3 -> “ 5g ~

‘ 160 -z

- 4 ;,

d?-+

w

“ 120-.- - 33

i ~g80- - 2

40 “ - I

00m

0A5 LO 1.5 2.0 2.5 3.0 3.5°

7

2

I

o

T I me (~s)

, , m v 1 , , ,

B

●●

●

Computed ● ‘bExperimental

Velocity . ● Velocity*

●

●

Distance (mm)

Fig. 6,Flyer velocity and foil power us time (Fig. 6A) and flyer velocity us trauel distance (Fig. 6B);0.061-mm-thick, 12. 7-mm-square aluminum foils; 0.25-mm-thick, 12. 7-mm-diam Mylurflyers; 20.4-kV dhcharge voltage,

9

/- I‘Computed Velocity 6 ~

350 “ /Experimental VelocityGE 300 -2

: /w

6~ Zjo

●

1‘m / ●

●

“ 150 -.-+.-% 100 -(s)

50 - - I

# n 9 1 tIJ3 1.5 2.0°

b“ “

11/=Power 11?

Experimental

Time (~s)

Fig. 7.

Flyer velocity and foil power us time; 0.051-mm-thick, 6.35-mm-square0.127-mm-thick, 6.35-mm-dium My&r flyer; 18-kV dhcharge voltage.

I20

100

80

60

40

20

a I I I 1 8

A

●

A

rA 1 I m b

0.5 Lo L5

magnesium foil;

Time (~s)

Fig. 8.

Flyer velocity and foil power us time; 0.036-mm-thick, 9.53-mm-squure copper foil; 0.127-

.

I

mm-thick, ~53-mrn-d&m My fur fZyer; 18-k V dischurge voltage. Curve A, experimentalpower hido~. Curve B, experimental velocity hktoqy. Curve C, computed velocity historyincluding ionization energy. Curve D, computed velocity histov not including ionizationenergy.

10

on the streak-camera film, the electrical currentand voltage records were related to the optical ob-servations by correlating the maximum in thevoltage measurement with the first observation oflight from the bursting foil.

The velocity and specific power histories and thechange of velocity with travel distance deduced fromthe above data for 0.025-, 0.051-, and 0.127-mm-thlck flyers are given in Figs. 9 and 10. The differentvelocity curves correspond to the measurements atdifferent points on the flyer surface. The initialvelocity of each of the flyers corresponds to themeasured velocity at the time sufficient light is firstobserved from the bursting foil, Because all threeunconfined flyers were first observed with a nonzeroinitial velocity, these histories have been shifted0.06 ILSto the right of estimated foil burst time. Theestimated error for the velocity measurements is ap-proximately *1OYO,except for small travel timesand distances which have somewhat larger errors.

The calculated velocity histories and velocity-distance relationships agree with observations towithin experimental error, even though the calibra-tion of the specific power correction factor was madeusing much larger foil configurations. The agree-ment for the small systems could be improvedfurther by altering the empirical correction factor tomatch the small-foil data.

The step-flasher measurements taken with barrelassemblies agree within experimental error with thereflection technique observations taken without bar-rels and with the computed velocities. However, thesuggestion that the confhing effect of barrels is un-important should be accepted with caution.

Because the specific power histories in Fig. 9 differslightly, the flyer thickness, d, is the principalparameter varied in this series of experiments.Observed late-time velocities are roughly propor-tional to@, so that the simple gas-gun model, us-

ing a correctly selected Gurney energy, would ap-pear to provide a decent approximation for this par-ticular parameter variation. However, terminalvelocities computed with Eqs. (7) and (8), usingmeasured burst currents and constanta calibrated tolarge aluminum foils, are larger by a factor of 2 thanthose observed experimentally.

v. SUMMARY

A version of the gas-gun (Gurney) model that al-lows continuous electrical energy deposition hasbeen developed and used to calculate velocityhistories of flyera driven by electrically explodedfoils. The time-dependent energy input is related toobserved power histories, with a semi-empiricaltreatment of the energy required to form the foilmaterial plasma and a purely empirical correction ofthe postburst contribution. Agreement with experi-ment is obtained for aluminum-foil systems varyingby an order of magnitude in foil and flyer dimen-sions and for assemblies with magnesium and cop-per foils. Presumably, the tested range of ap-plicability of the model can be extended to include agreater variety of geometrical configurations andother flyer and foil materials.

ACKNOWLEDGMENTS

The authors are indebted to Richard Weingartand Richard Jackson of Lawrence LivermoreLaboratory for the large-foil, step-flasher velocityand power history data used in this work. Specialthanks go to Robert Mowrer for his assistance withthe small-foil experiments and other aspects of thework. We also appreciate the support efforts ofBeverly Clifford and William Hicks.

.

4

11

Time (ps)

320 4

ElzE>240 .Esperimenlal

W-

;J k~

3

g Power Measured ~velocity o

■■ sL o

z 160m -.

. Computed2<

&Velocity :

.2

.- ● *~ 80 Is

(n

0.5 1.0 15 0Time (/.4S)

320 -4

/-c—

I Time (ps) .!

Fig. 9.

Flyer velocity and foil power us time; O.011-mm-thick, l.524-mm-square aluminum foils;1.524-mm-dium MyZur flyers; -3-kV didwge voltage.

Figure 9A,0.025-mm-thick flyer; open circle indicates step flasher data.Figure 9B, 0.051-mm-thick flyer; open squares indicate step flasher data.Figure 9C, 0.127-mm-thick flyer; open triangle indicates step flasher data.

12

EE

3“ A

2“

I

AA AA AAA

~~0 0.2 0.4 0.6 0.8

Distance (mm)

Fig. 10.Flyer velocity us travel distance; O.011-mm-thick, l.524-mm-square aluminum foils; 1.524-rnm-diam Mylur flyers; 3-k V dischurge voltage. Curves A, O.O%-mm-thick flyer; solicf circle,computed velocity; open circle, step flasher data. Curves B, O.051-mm-thick flyer; solidsquares, computed velocity; open squares, step flasher data. Curves C, O.127-mm-thick flyer;solid triangles, computed velocity; open triangle, step flasher data.

REFERENCES

1. R. C. Weingart, R. S. Lee, R. K. Jackson, andN. L. Parker, “Acceleration of Thin Flyers by Ex-ploding Metal Foils: Application to InitiationStudies, ” Sixth Symposium (International) onDetonation, Preprints, p. 201 (August 1976).

2. R. W. Gurney, “The Initial Velocity of Frag-ments from Bombs, Shells and Grenades,” BallisticResearch Laboratory report No. 405 (September1943).

3. I. G. Henry, “The Gurney Formula and RelatedApproximations for High Explosive Deployment ofFragment,” Hughes Aircraft Corp. report PUB-189(April 1967).

4. M. Defourneaux, “Transport of ‘Energy in Com-bustion and Detonations with Confinement, ”Astronaut. Acts 17, 609 (1972).

5. J. E. Kennedy and A. C. Schwmz, “DetonationTransfer by Flyer Plate Impact, ” Eighth Sym-posium on Explosives and Pyrotechnics, TheFranklin Institute Research Laboratories,Philadelphia, PA (February 1974).

6. J. E. Kennedy, “Gurney Energy of Explosives:Estimation of the Velocity and Impulse Imparted toDriven Metal, ” Sandia Laboratories report SC-RR-70-790 (1970).

13

7. S. J, Jacobs, ‘The Gurney Formula: Variations “ 11. P. L. Stanton, “The Acceleration of Flyer Plateson a Theme by Lagrange, ” Naval Ordnance by Electrically Exploded Foils, ” SandiaLaboratory report No. 74-86 (June 1974). Laboratories report SAND-75-0221 (1976).

8. J. Wackerle, “Applied Initiation Studies: Sim-ple Considerations for the Design of Flying-PlateInitiation Systems,” LASL Group WX-7 internalreport (October 1974).

9. T. J. Tucker and P. L. Stanton, “ElectricalGurney Energy: A New Concept in Modeling ofEnergy Transfer from Electrically Exploded Con-ductors,” Sandia Laboratories report SAND-75-0244(1975).

12. Handbook of Chemistqy and Physics, 51st Ed.(The Chemical Rubber Company, Cleveland, OH,1970).

.

*

13. R. K. Jackson, Lawrence Llvermore Laboratory,personal communication (November 1976).

14. W. C. Davis and B. G. Craig, “Smear CameraTechnique for Free-Surface Velocity Measurement,”Rev. Sci. Instrum. 32, 579 (1961).

10. T. J. Tucker and R. P. Toth, ‘The ElectricalBehavior of Small Exploding Foil Flyer Assemblies,”Sandia Laboratories report SAND-75-0445 (1975).

,

}

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