CP620, Shock Compression of Condensed Matter - 2001edited by M. D. Furnish, N. N. Thadhani, and Y. Horie2002 American Institute of Physics 0-7354-0068-7

ANFO CYLINDER TESTS*LX. Davis & L.G. Hill

Los Alamos National Laboratory, Los Alamos, New Mexico 87545 USA

Cylinder test data is reported for commercially available prilled ANFO (ammonium-nitrate/fuel-oil)at 0.93 g/cc density and ambient temperature. The tests were four-inch inner diameter, with wall-thickness and length scaled from the standard one-inch test (0.4 inch and 48 inch, respectively). Thewall expansion was measured with a rotating mirror streak camera and the velocity was measuredby fine-wire pin switches, in the standard manner. The wall expansion trajectory is much smootherthan for conventional explosives, which show a pronounced jump-off with subsequent ring-up. Thisobservation is consistent with a broadened detonation shock in the granular bed. The data is analyzedfor equation-of-state information and JWL parameters are given.

INTRODUCTIONThe cylinder test has long been the principal

method for obtaining equation-of-state (EOS)parameters for high explosive (HE) detonationproducts. It involves recording the detonationvelocity and wall trajectory of a copper tubefilled with an explosive sample, and detonatedat one end. The standard tube is 1-inch internaldiameter, 0.1-inch wall, and 12 inches long. Thisdiameter is sufficiently large compared to the re-action zone of many HE's that the detonation isessentially planar. The tube length is adequateto ensure that steady flow is achieved during themeasurement, while the wall thickness strikes areasonable balance between maintaining tube in-tegrity and spatial resolution1.

For non-ideal explosives such as ANFO, thestandard cylinder is too small compared to thereaction zone, and must be scaled up accordingly.Previous ANFO cylinder tests2 were conductedat diameters up to 292.1 mm (11.5 inches). Itwas reported that a test diameter of 101.6 mm(4 inches) was the minimum size to scale favor-ably with the large cylinder test; yet, very largefield experiments3 yielded somewhat higher det-

* Work performed under the auspices of the United StatesDepartment of Energy.

onation velocities and pressures than even thelargest cylinder test. Thus for ANFO it appearsthat no practically fieldable test is truly "largeenough"; rather, there is some schedule of di-minishing returns as the size is increased.

The physical origin of this effect is a long re-action tail that is sampled in a different way de-pending on device size and geometry. It is a verydifficult problem to handle computationally; itrequires a fully reactive calculation, for which asufficiently large cylinder test can at best providea sufficiently accurate end state (product EOS).

ANFO is also non-ideal in other ways. Perssonand Brower4'5 characterized several varieties ofcomrnericial ammonium nitrate prills and foundsubstantial variations in performance and prod-uct composition. They attributed this to vari-ations in porosity and pore size distribution inprills obtained from different sources. Thus, dif-ferences may be expected in otherwise identicalexperiments using ANFO from different sources.

In this paper we report the results of two nom-inally identical 4-inch diameter cylinder testsperformed on a large ANFO batch, which we re-blended to assure homogeneity and uniform per-formance throughout. This was done to ensureconsistency with other work reported here6, andalso to test shot-to-shot reproducibility.

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EXPERIMENTALThe experimental configuration is shown

schematically in Fig. 1. The streak camera isplaced with the slit perpendicular to the tube,looking directly into an explosively-driven argonflash. The explosive is detonated at the top, andthe cylinder expands as the wave travels downit. This closes the pin switches, and an imageis recorded on the streak camera as the tube ex-pands across the slit plane. Different sized testsare geometrically similar in all respects. Thusthe present 4-inch tests had a 0.4-inch wall thick-ness, and were 48 inches long.

Liner breaks; detonationproducts escape -™™_-

ing LinerAir ShockDetonation Wave

Tube is electrical ground

FIGURE 1. Schematic diagram of the Cylinder Test.

It is essential to carefully control copper pa-rameters or the tube will break prematurely. Weused Alloy 101 copper (the highest commercialpurity), following standard practice for the 1-inch test. Micrographs of tube samples showedthat the grain size was about 50 /zm (or about200 grains through the thickness), and that thematerial was essentially in an annealed state as-wrought. Hence, heat treating was not required.Despite the granular composition of ANFO, thetube achieved full expansion without breaking.

The ANFO was composed of explosive-gradeprills and 6 wt.% diesel fuel. It was purchasedfrom Titan Energy, Lot $30SE99C.

The tube was loaded in stages, or "lifts." Us-ing approximately 20 lifts per cylinder yielded liftheights and masses that could be convenientlymeasured to good accuracy. We obtained bulk

densities of 0.936 ± 0.002 g/cm3 and 0.925 ±0.002 g/cm3. A two-inch thick CompB boosterwas placed at the top of the tube and initiatedwith an SE-1 detonator. We aligned the slit withthe tube 16 inches from the bottom. This dimen-sion was also scaled from the one-inch test. Itis far enough from the booster to ensure thata steady structure has been achieved, yet farenough from the other end that reflected wavesdon't perturb the measurement. Assembly de-tails for the standard 1-inch LANL cylinder testare given in a recent report7.

Velocity pins consisted of 4-mil diameter var-nished copper wires, bent in a check mark shapeand taped to the tube in equal intervals, withpoints facing the oncoming detonation. The lo-cations of the pin tips were then measured usinga dial caliper. When the detonation passes, theshock-accelerated tube surface crushes the insu-lation and fires an electrical circuit.

Streak camera measurements used a LANLWinslow-Davis combination camera writing at£30.5 mm//xs. The argon flash was a box 4 feetlong, lined with DetaSheet on its top and bot-tom inner surfaces, to produce a flash of «150/zs duration. Both sides of the film record weredigitized using an optical comparator.

DATA PROCESSINGThe detonation velocity DQ is the slope of a

linear fit to the pin switch x-t points. We assumethe measurement uncertainty to be the standarderror due to random scatter about the line.

The streak camera measures radial wall ex-pansion versus time at a fixed axial position, forboth sides of the tube. When the motion of thetwo sides is digitized and overlaid, there is gen-erally systematic deviation beyond experimentalscatter. The culprit is tilt—due to slit misalign-ment, detonation wave skew, or some combina-tion of the two. A linear tilt correction providesan exact correction for the first cause, and a sen-sible correction for the second. It generally rec-onciles the sides to within random scatter.

The following equation8 provides a nearlyideal smooth fit through cylinder expansion data:it cuts symmetrically through shock ring-up atearly time, and follows the data to within exper-

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imental noise at late time:

p _- Kg - 2Vo (i)

where RQ is the initial outer tube radius, ao isthe initial radial acceleration of the smooth fit,VOQ is the asymptotic radial velocity, and

(2)

where a is a fitting parameter. Because we seeka smooth fit through the shock ring-up, Eq. 1 isallowed a virtual origin to as an additional fittingparameter. Once the other parameters are deter-mined to may be dropped—except in situationswhere the data and fit are overlaid directly.

The tilt-corrected expansion data for one ofthe two shots is shown in Fig. 2, together withthe 10 x fit residuals. The standard deviation infit residuals is 175 /mi. In contrast to Cylindertests on conventional explosives, there is no defi-nite jump-off point. The reason is evidently thatthe effective detonation shock thickness is a fewprills, which is of order the wall thickness.

140

120

j 80

£ 60}

40

20

0Standard Deviation: 175 urn

0 25 50 75 100 125 150 175t (|isec)

FIGURE 2. Tilt-corrected wall expansion data forShot#AC88-3926s with analytic fit and lOx fit residuals.

The standard Cylinder test performance met-rics are Cylinder Energy, J5ig, and Gurney En-ergy, Gig, The subscript indicates that both areevaluated at E = 19 mm for the 1-inch test. Eigis the radial component of liner kinetic energyper unit liner mass, i.e.,

Gig is the kinetic energy of the HE productsplus the liner, per unit mass HE, obtained fromthe cylindrical Gurney approximation9.

(4)

where pw and pQ are the wall and initial HE den-sities, respectively, and TQ is the initial inner tuberadius. Neither £19 nor Gig use £>Q, but only thedifferentiated fit to Eqs. 1 & 2 and, in the caseof Gig, initial densities and dimensions.

To scale performance metrics from larger teststo match those obtained from the standard 1-inch test, one must make the following scalingargument. If RQ is sufficiently large compared tothe reaction zone thickness then: 1) DQ is vir-tually independent of test size and 2) all tubeshapes are equivalent when expressed in the di-mensionless coordinate system R = R/RQ, z =Z/RQ. Since the flow is steady, z = D$t. Divid-ing both sides by RQ gives the corresponding di-mensionless time: f = (Do/J?o)t. Consequently,dirnensionless velocities scale as v = V/DQ.

Scaling between sizes requires similarity, i.e.,comparison at equal values of the dirnensionlessvariable(s). Noting further that DO must be size-independent for scaling to hold, one concludesthat times and distances both scale with the testsize, and velocities are unaffected. Thus "JSig"is obtained from a 4-inch test by using the mea-sured radial velocity evaluated at E = 76 mm.

The detonation velocity, wall expansion fittingparameters, and performance metrics (scaled to1-inch diameter) are listed for both tests in Table1. The two agree to within a few percent.

TABLE 1. Fit and Performance Parameters

R- RQ=19mm(3)

ParameterShot #

R0

PQD0

aoVooa

EWGig

Unit—

mmg/cmd

mm//ASmm/fj,s2

mm/^s—

kJ/gkJ/g

ShotlAC88-3926

60.960.9364.0620.14121.065

0.63760.3731.753

Shot2AC88-3927

60.960.9254.2580.15451.220

0.53940.3831.821

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EOS ANALYSISWe now compute JWL parameters, necessar-

ily assuming that the 4-inch test is large enoughcompared to the reaction zone that the detona-tion is nearly Chapman-Jouguet (Do & DCJ).Expansion then follows the principal isentrope,the empirical JWL expression for which is

P8(V) = (5)

where V = V/VQ and v is specific volume, withVQ the initial value. The other quantities are fit-ting parameters, of which only w—the ideal gasGriineisen gamma—has physical significance.

The internal energy on PS(V) is obtained byintegrating the pressure using the isentropic re-lation P8(V) = -dEs/dV, where E = e/vQ. Thefunctions (V, P8(V), E8(V)) then define the prin-cipal isentropic curve in EOS space. The e(P, v)EOS surface can be approximated in the neigh-borhood of the principle isentrope by a linear(Mie-Griineisen) expansion away from it. JWLfurther assumes that Griineisen gamma is equalto (jj everywhere. This is not really true; rather,it is a convenience that allows the EOS surface tobe approximated from cylinder test data alone.

There are two basic strategies by which JWLparameters have been inferred. The most ro-bust calculates the cylinder wall expansion byhydrocode, iterating on the JWL parameters un-til satisfactory agreement is achieved. The othercomprises various simplified methods, which ap-peal to hydrocode calculations for validation.

Our method employs elements of both strate-gies; it is a simplified, quasi-analytic calculationof the cylinder test that explicitly generates theisentrope. (In fact, this method was first pro-posed by G.I. Taylor in 1941, some 20 years priorto JWL and the cylinder test.10) The present im-plementation is a refinement of that outlined inRef. 8. Taylor's method generates a numericalisentrope, to which JWL must be fit. This is astraightforward nonlinear least squares optimiza-tion subject to thermodynamic constraints.

Our JWL, inferred from both cylinder testscombined (using average values DQ = 4.160mm//zs and po = 0.931 g/cm3), has parameters:Pcj = 5.150 GPa, Vcj = 0.6802, A = 49.46 GPa,

B = 1.891 GPa, C = 0.4776 GPa, RI = 3.907, R2= 1.118, u = 1/3, and EQ = 2.484 kJ/cm3 (E0being the energy of detonation computed fromthe product Hugoniot). It is plotted in Fig. 3along with three curves derived from the 11.5-inch test of Ref. 2, and a BKW Cheetah11 cal-culation. Our JWL has a total energy slightlybelow Ref. 2; moreover, energy is released laterin our expansion, our curve falling below at highpressures and above at low pressures. This be-havior suggests that flow reaction persists duringour measurement. The Cheetah JWL assumesthat reactions go to equilibrium, and has about25% more energy than Ref. 2. This suggests thatreaction also persists at 11.5-inch diameter—andperhaps for all laboratory-scale configurations.

O

Present studyCheetah BKW

LLNL study, Eef. 2 (3 ea.)

0 1 2 3 4 5v/vo

FIGURE 3. JWL expansion isentropes.

ACKNOWLEDGEMENTSWe thank R. Hixson, C. Necker, & J. King for

test support, & R. Flesner for funding support.

REFERENCES1. Hill, L.G.; These proceedings.2. Helm, P., Finger, M., Hayes, B., Lee, E., Cheung, H.,

& Walton, J.; LLNL Report No. UCRL-52042 (1976)3. Petes, J., Miller, R., & McMullan, P.; DNA Technical

Report No. DNA-TR-82-156 (1983)4. Brower, K.R., O'Connor, E., & Joshi, V.; RCEM

Semiannual Technical Report A-02-94 (1994)5. Persson, P.A., & Brower, K.R.; RCEM Semiannual

Technical Report A-01-95 (1995)6. Catanach, R.A., & Hill, L.G.; These proceedings.7. Catanach, R.A., Hill, L.G., Harry, H., Aragon, E., &

Murk, D.; LA-13643-MS (1999)8. Hill, L.G.; Proc. 21st issw (1997)9. Kennedy, J.E.; Explosive Effects & Applications,

Ch. 7, J. Zukas & W. Walters, Eds. (1998)10. Taylor, G.I.; Collected Works V3, Paper #30 (1963)11. Pried, L.E., Howard, W.M., & Souers, P.C.; LLNL

Report UCRL-MA-117541 Rev. 5 (1998)

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