precursor detonation wave development in anfo due to...

Precursor Detonation Wave Development in ANFO due to Aluminum Confinement

Scott I. Jackson, Charles B. Kiyanda, and Mark ShortShock and Detonation Physics Group

Los Alamos National Laboratory

Abstract. Detonations in explosive mixtures of ammonium-nitrate-fuel-oil (ANFO) con-fined by aluminum allow for transport of detonation energy ahead of the detonation frontdue to the aluminum sound speed exceeding the detonation velocity. The net effect of thisenergy transport on the detonation is unclear. It could enhance the detonation by precom-pressing the explosive near the wall. Alternatively, it could decrease the explosive per-formance by crushing porosity required for initiation by shock compression or destroyingconfinement ahead of the detonation. At present, these phenomena are not well understood.But with slowly detonating, non-ideal high explosive (NIHE) systems becoming increas-ingly common, proper understanding and prediction of the effects of high-sound-speedconfiners on NIHE is desirable. Experiments are discussed that measured the effect of thisANFO detonation energy transported upstream of the front by a 76-mm-inner-diameter alu-minum confining tube. Detonation velocity and front shape were recorded as a function ofconfiner wall thickness and length. Detonation shape profiles are characteristically differ-ent from records with weak confinement and displayed small curvature near the confiningsurface. This variation was attributed to energy transported upstream modifying the inter-action between the NIHE and confiner. Average detonation velocities were seen to increasewith increasing confiner thickness, while wavefront curvature decreased due to the stiffer,subsonic confinement. Preliminary Dn-κ analysis of the data was performed and requireda modified fitting waveform to properly represent the experimental front shapes. It wasconcluded that the confiner was able to transport energy ahead of the detonation and thatthis transport has a definite effect on the detonation by modifying its characteristic shape.

Introduction

Accurate prediction of non-ideal high explosive(NIHE) detonation has become a topic of significantinterest in recent years. Non-ideal explosives differfrom conventional explosives in that they are usu-ally high-porosity, low-density materials where the

Approved for unlimited release: LA-UR-10-03433

fuel and oxidizer are not mixed on a molecular level.As a result, NIHEs typically exhibit low detonationvelocities. They also have much larger detonationreaction zones that are centimeters in length, ratherthan the 100’s of microns associated with more idealexplosives.

The detonation velocities observed for manyNIHEs are typically below the sound speeds ofstiff confining materials, including common metals.

In Proceedings of the 14th International Detonation Symposium, Office of Naval Research, pp. 740–749.

This is in contrast to conventional or ideal high ex-plosives (HEs), where the detonation velocity ex-ceeds the sound speed of most confiners. In idealHE systems with strong confinement, the detonationdrives a shock into the inert confiner and no infor-mation propagation in the confiner exceeds the det-onation velocity. The confiner is only able to influ-ence the detonation by acting on the reaction zonebehind the detonation shock and ahead of the sonicsurface. Since the confiner is shocked and ideal HEshave small reaction zones, this implies that increas-ing the confiner thickness above a few reaction zonelengths has no effect on the detonation velocity. Forweakly confined systems, a sonic point exists at theHE-inert interface and the inert is unable to influ-ence the detonation reaction zone.

Low-detonation-velocity, stiffly confined systemscontain no inert shock when the confiner soundspeed exceeds the detonation velocity. This allowsthe confiner to transport energy from behind the det-onation shock upstream to the unreacted explosive.Such energy transmission can potentially enhanceor hinder the detonation by modifying the amountof confinement it experiences. In some cases, this“precursor energy” will drive the confiner surfaceinto the NIHE, compressing it. The precompressioncan densify the NIHE, increasing its detonation ve-locity,1 or even igniting it. However, precompres-sion can also crush porosity out of the NIHE, de-sensitizing it and leading to local detonation fail-ure. The precursor energy can also cause loss ofconfinement ahead of the detonation due to fracture,which can also result in detonation failure.2 Finally,the large reaction zone lengths of NIHEs and thesubsonic confinement both allow for a much greaterdependence of confiner thickness on detonation ve-locity.3

These types of wall-explosive phenomena are nottypically present in most conventional HE configu-rations. Our current level of physical understand-ing of this interaction prevents accurate modelingof confined NIHE systems. We seek calibrationdata for the Detonation Shock Dynamics (DSD)code to resolve this limitation. DSD is able tomodel detonation propagation when supplied withthe detonation velocity variation versus detonationsurface curvature and the detonation edge angleat the explosive-confiner interface. The velocity-

curvature relationship is derived from experimentalrate-stick data. For ideal HEs with shocked con-finers, the edge angle can be found from shock po-lar analysis.4,5 However, since the confiner flow isshockless and subsonic in NIHEs when the confinersound speed exceeds the detonation velocity, alter-nate methods must be implemented. Experimentalmeasurements are required for the development ofthese new techniques.

In this work, we experimentally characterize theinteractions between the detonation front, a stiffconfiner, and the unreacted explosive. Ammonium-nitrate-fuel-oil (ANFO) was selected as the NIHEand aluminum tubes were used as confiners. Ex-perimentally observed ANFO detonation velocitiesrange from 1.5–4.0 mm/µs depending on the explo-sive properties, charge size and degree of confine-ment,6 while the longitudinal sound speed of alu-minum is in excess of 5.0 mm/µs. Parameters in-clude the confiner wall thickness and detonation runlength. We measure the detonation wave speed aswell as the velocity of the elastic stress wave that isdriven in the metal ahead of the detonation. Deto-nation front profiles are also recorded at the end ofthe tube. We then discuss the novel wave shapes en-countered in these systems due to the HE-confinerinteraction and present a preliminaryDn-κ form forthe data to guide DSD analysis.

Aluminum-Confined ANFO Rate Sticks

Experiments were performed to obtain the deto-nation front-shape and velocity data for aluminum-confined ANFO. All tests used ANFO mixturesconsisting of 94% ammonium nitrate prills byweight mixed with 6% No. 2 diesel fuel byweight. Porous, industrial-grade ammonium nitratewas used from Dyno Nobel with a typical bulk den-sity of 0.80 g/cc and an average prill diameter rang-ing from 1.4–2.0 mm. Mixing was accomplishedby combining the prills and diesel fuel in a ce-ment mixer and mixing for a minimum of 15 min-utes. ANFO was then poured into each tube in200-g increments. Each incremental fill was hand-tamped to prevent significant clumping or void for-mation. This methodology was sufficient to achievean ANFO density of 0.86–0.90 g/cc.

Aluminum tubes were used to confine the ANFOduring the front-shape measurements. Each tube


was 76.2 mm in inner diameter (ID) and wall thick-ness ranged from 6.35–25.4 mm. The tube lengthswere 305 or 914 mm (Tab. 1) yielding length-to-diameter ratios of L/ID = 4 and 12. All were 6061alloy and T6 temper, except for the 25.4-mm-thicktubing, which was T6511. The downstream end ofeach tube was sealed with a 6.35-mm-ID PMMAwindow with an outer diameter matching that of thetube (Fig. 1). A centerline on the window containeda line of PETN paint backed by 80-µm-thick cop-per tape (Fig. 2). Arrival of the detonation shock atthis location initiated the PETN with a bright flashthat was recorded by a streak camera, yielding thefront-shape record.

Ionization pin

Piezoelectric pin

Shorting pin

Booster and tamper

Aluminum tube

Imaging window

Fig. 1. The tube from test 6-305.

Each aluminum tube also contained three typesof diagnostic pins to detect the transit of variouswaves. These pins were mounted in the wall tobe flush with the tube ID. Dynasen ionization (CA-1040) and shorting pins (CA-1038) pins were usedto measure the ion and shock arrival, while tightlyfitted piezoelectric pins (CA-1136) simultaneouslyrecorded both compression of the tube wall, to de-tect the precursor stress wave in the aluminum, aswell as the arrival of the detonation. Pins were lo-cated 83.1-mm axially apart and were spaced 45◦

deg radially apart (Fig. 3). A piezoelectric pin wasalso located in the end window against the down-stream tube surface. Detonation initiation was ac-complished with 12.7-mm-thick Primasheet 1000

Copper tape PETN paint

Piezoelectric pin

Fig. 2. The downstream end window of the 6.35-mm-thick, 305-mm-long tube filled with ANFO.

booster and an RP-1 detonator, tamped from behindby 12.7-mm of polycarbonate. This booster strengthwas determined to be sufficient in a separate study.7

All pins were sampled at 1.25 GHz. The samplerate coupled with the pin spacing provided velocityuncertainties of 1% for the ionization and shortingpins, and 3% for the piezoelectric pins.

Detonation

Ion Axis

83.1 mmTube

Piezo Axis Shorting Axis

Fig. 3. A schematic of the pin arrangement on the6.35-mm-thick, 914-mm-long tube.

Pin Velocities and Front-Shape Records

Pin Data

An example of the pin data from test 12-305 isshown in Fig. 4. Early in time, at approximately24 µs, the arrival of the precursor stress wave is de-tected by the piezoelectric pin, as denoted by an os-cillating waveform of increasing strength. As thedetonation front arrives at the pin station near 35µs, the pin records substantially increased compres-sion, followed by a rapid release that was likely due


50

40

30

20

10

0

Vo

ltag

e (V

)

35302520

Time (μs)

40

30

20

10

0

36.035.535.034.534.0

P1

Ion Short

Arrival of compressive

wall wave

Fig. 4. Example of pin data traces.

to pin failure. During the period of increased com-pression, both the ionization and shorting pins trig-ger within 100 ns of each other. In every test, allpins at each station triggered within 1 µs of eachother. A pin was considered to have triggered whenthe signal rose above the bit noise associated withthe data acquisition system. Additionally, there isa trigger delay inherent in the mechanical design ofthe shorting pin that requires the shock pressure tomove a brass cap across a 64-µm gap, while no suchdelay exists for either the piezoelectric or ionizationpins. This may explain why the shorting pin triggerslast.

Pin arrival times from each test were analyzed toyield position-time plots of the wave motion in theexperiment. An example of one such plot is shownin Fig. 5 for test 12-914. The progression of the det-onation can be seen from the closely matched ion-ization, shorting and piezoelectric shock pin triggertimes. The propagation of the elastic stress wave inthe metal is also seen ahead of the detonation front.The data from each pin fit well to a line using a leastsquares fit, the slope of which yields the averagewave velocity in the experiment.

These average wave velocity data are reported inTab. 1. The velocity of the elastic precursor rangesfrom 5.1–6.5 mm/µs, which is consistent with thespeed of sound in aluminum. Detonation veloci-

Tim

e (μ

s)

Position (mm)

400200 800600 1000

50

100

150

200

250

300

00

Ion: t = 0.2886x+14.581

Piezo shock: t = 0.2927x+13.471

Short: t = 0.2885x+15.388

Piezo stress: t = 0.1964x+5.4013

Fig. 5. Position-time diagram for the 12.7-mm-thick, 914-mm-long tube showing pin trigger timesand average velocity fits. Ionization, shorting, andpiezoelectric shock data are close to being on top ofeach other.

ties range from 2.7–3.6 mm/µs, increasing with wallthickness up to the maximum 25.4-mm wall thick-ness tested. As mentioned, this trend was expecteddue to the extended length of the ANFO reactionzone and the subsonic confinement condition. Noinert shocks were present to limit the entire confinerthickness from acting on the reaction zone.3

Overall, we find the agreement of the linear ve-locity fit to the elastic precursor wave data to begood, with squared correlation coefficients above0.987. The fit to the detonation pin data is excel-lent, with all squared correlation coefficients above0.996. The lower fit correlation for the elasticstress wave is attributed to multiple issues: The Pri-masheet booster overdrives the precursor wall waveinitially, as evidenced by the higher elastic wavespeeds in the shorter length tubes. Additionally, de-tection of the elastic precursor signal can be difficultdue to its low amplitude, which can be exacerbatedby a poorly fit pin not sensing early compressiondue to insufficient sidewall contact.

The detonation, however, does not exhibit anyoverdrive associated with the initiation process. Infact, comparison tests of identical wall thicknessesfind average velocities that are consistently 3–10%lower for the short tubes, relative to the longerlengths tested, indicating that the wave is slightly


Table 1. Dimensional and average velocity data. Asterisk (∗) denotes the T6511 temper tube, all others wereT6.

Test Wall Tube Short Pin Ion Pin Piezo Pin Piezo StressName Thickess Length Shock U Shock U Shock U Wave U

(mm) (mm) (mm/µs) (mm/µs) (mm/µs) (mm/µs)6-305 6.35 305 2.772 2.690 2.814 5.7216-914 6.35 914 2.838 2.797 2.904 5.453

12-305 12.70 305 3.125 3.193 3.092 5.61512-914 12.70 914 3.466 3.465 3.416 5.09225-305 25.40 305 3.383 3.588 3.377 6.480∗

slit PETN paint

76.2 mm

2.0 μs

(a)

(b)

Fig. 6. Still frame (a) and streak image (b) for 6.35-mm-thick, 305-mm-long tube.

underdriven from the booster.

Front-Shape Records: Figure 6 shows the front-shape data for test 6-305. The upper image is a stillframe showing the imaging slit of the window inFig. 2. The lower image is the streak data with timeincreasing downwards. The granular nature of theexplosive is reflected in the streak and some jettingof product gas ahead of the main shock is also evi-dent, particularly at the left wall. Such jetting is alsoobserved in ANFO rate sticks with weaker confine-ment due to air gaps allowing product gases to rushahead of the main front. In Fig. 6, the gap is be-lieved to be due to the subsonic wall pulling awayfrom the explosive ahead of the detonation. A moredefinitive conclusion is not possible in the currentstudy and jetting effects are neglected in the follow-ing curvature discussion.

The front-shape profile shows lowest curvature

Fig. 7. A streak record from Ref. 6 for ANFO con-fined by cardboard.

near the tube center, indicating a locally higherpropagation velocity in the region most isolatedfrom wall expansion. Curvature increases with in-creasing radius to a maximum between the tube cen-ter and the wall, and then decreases near the wall.Different behavior is observed in more weakly con-fined systems (Fig. 7), where the detonation curva-ture is at a minimum at the center and monotoni-cally increases outwards towards the wall. Thus, thealuminum confiner is not only providing additionalconfinement, but also modifying the characteristicshape of the wavefront.

A compilation of all front-shape measurements todate is shown in Fig. 8. All images are identicallyscaled. Similar features as discussed in Fig. 6 areseen in all traces. It is apparent that increasing thewall thickness not only increases the detonation ve-locity, but also results in a detonation profile withless overall curvature. Such behavior agrees wellwith theory.3 Jetting aside, all fronts also appearfairly symmetric.

Comparison of the leading front in each recordshows little difference between the short- and long-


(a) Wall thickness: 6.35 mm, tube length: 305 mm

(b) Wall thickness: 6.35 mm, tube length: 914 mm

(c) Wall thickness: 12.7 mm, tube length: 305 mm

(d) Wall thickness: 12.7 mm, tube length: 914 mm

(e) Wall thickness: 25.4 mm, tube length: 305 mm

Fig. 8. Streak records. Wave propagation directionis up.

length tubes for each wall thickness tested. This in-dicates that the wave shape approaches its steadystate rapidly (within L/ID = 4). In some cases(b, d, and e in Fig. 8), the streak record shows twowaves, with a diffuse or weaker front arriving be-fore the main front. Since the imaging section isPETN paint backed by copper tape, this indicateslow-level PETN ignition followed by stronger re-action. This phenomenon, discussed in detail else-where,7 was attributed to precursor window move-ment separating the inner window surface from theexplosive prior to the arrival of the detonation front.

Front quality also suffers due to the small di-ameter of the tubes used in this study relative tothe ANFO prill size. The average prill diameterwas approximately 1.7 mm, yielding only about 44prills across a diameter chord. Front records reflectthis discritization of the detonation front. The onlyway to improve the resolution of the front wouldbe to field larger diameter tubes or smaller diame-

ter ANFO, as has been done for cardboard-confinedANFO.8–10

Dn-κ Analysis

DSD analysis is based on the concept that devi-ations of the normal detonation velocity Dn fromthe Chapman-Jouguet (CJ) velocity are a functionof the curvature κ associated with the local wave-front.11 In general, the Dn-κ relationship is derivedexperimentally from detonation velocity and wave-front shape measurements in a rate-stick test. En-ergy loss from the detonation reaction zone to theconfiner wall slows the detonation front near thewall and results in flow divergence and movementof the sonic plane towards the shock. This is mani-fested by increasing curvature with radius from therate-stick center to the edge. Varying degrees of cur-vature can thus be imposed on a detonating explo-sive rate stick by modifying the confining material.

Calculation of Dn and κ

Experimental front shapes are typically fit to ananalytic equation z(r) with a similar characteristicshape. The normal velocity Dn can then be foundfrom

Dn =D√

1 + z′(1)

where z′ = dz/dr, D is the axial detonation phasevelocity obtained from the wall of the rate stick, andr is the radius. Curvature κ can be expressed as

κ =z′′

[1 + (z′)2]3/2+

z′

r√

1 + (z′)2(2)

with z′′ = d2z/dr2. Use of a C2 analytic functionz(r) yields smooth values of the first and secondderivatives z′(r) and z′′(r) and avoids errors thatwould result from direct numerical differentiationof the experimental wave front for the granular ex-plosive used. When using this method, it is criticalthat the specified fit accurately represent the actualwave shape.


Analytical Wavefront Forms

An equation often used to fit the detonation shapeis of the form

z1(r) = −n∑

i=1

ai ln[cos[ηπ

2r

R

]]i(3)

where r is the local radius and R is the maximumradius of the charge (37.5 mm). Parameters ai andη are fitting constants where 0 < η < 1 and n istypically chosen as 1 or 3.8 However, Eq. 3 doesnot allow for the non-monotonic variation in curva-ture present in the outer radii of the wave shapes inFig. 8.

While exploration of the fitting forms that bestrepresent the aluminum-confined ANFO data is stillongoing, a function can be formulated to match theobserved curvature trend. In the present manuscript,we have chosen the Kelvin function Kei(x),

z2(r) = bKei[ζ( rR

)m](4)

as a possible fitting candidate. More explicitly, thisfunction is the imaginary part of a 0th-order modi-fied Bessel function of the second kind. It is able toaccommodate the rapid decrease and possible rever-sal in curvature observed in the wave-shape data.

Unfortunately, the current implementation ofKei(x) is unable to simultaneously recover the non-zero wavefront curvature for small radii and prop-erly fit the outer radii. Our current solution is to uti-lize a composite function zc that smoothly blendsEqs. 3 and 4 together as shown in Fig. 9.

zc(r) = ω1 z1 + ω2 z2 (5)

The weighting parameters ω1 and ω2

ω1,2 =12

[1± cos

(πr

R

)](6)

favor z1 near r = 0 and z2 near r = R.

Fit to the Aluminum-Confined ANFO data

Fitting the composite function to the data ofFig. 8 obtained from the 305-mm-long tubes onlyyields the wave shapes shown in Fig. 10 and the fit-ting parameters shown in Tab. 2. While apparent inthe streak records, the decrease in overall wavefrontcurvature due to the increased confiner thickness is

0 5 10 15 20 25 30 35

0.5

1.0

1.5

2.0

2.5

3.0

Radius (mm)

Hei

ght

(mm

)

z1(r)

z2(r)

zc(r)

Fig. 9. Wavefront fits for test 12-305.

5 10 15 20 25 30 35

1

2

3

4

5

6

Hei

gh

t (m

m)

0

Radius (mm)

6-mm wall (6-305)

13-mm wall (13-305)

25-mm wall (25-305)

Fig. 10. Front shape variation with confinement.

much more obvious when the fits are plotted relativeto one another.

Application of Eqs. 1 and 2 to each fit then yieldsDn and κ as a function of radius. The variationin these parameters across the wavefront is shownin Fig. 11 test 25-305. The normal detonation ve-locity is highest at the center of the charge and de-creases with increasing radius as the normal to thewavefront diverges from the longitudinal tube axis.The normal velocity then increases slightly near theconfining wall as the wavefront normal turns back

Table 2. Wavefront fitting parameters.

Test a1 η b ζ mName (mm) (mm)6-305 105 0.223 9.54 2.27 2.0512-305 8.24 0.591 12.5 1.09 1.7425-305 5.49 0.604 4.58 2.06 2.21


0 5 10 15 20 25 30 35

0.002

0.000

0.002

0.004

0.006

0.008

0.010

0.012

3.35

3.36

3.37

3.38

Radius (mm)

κ (

1/m

m)

Dn (

mm

/μs)

Fig. 11. Dn and κ versus r for test 12-305.

toward the axis. Curvature is seen to start at a posi-tive value that decreases to a local minimum near 10mm, increases to a global maximum near 23 mm,and then crosses to a negative value near the confin-ing wall.

A plot of Dn as a function of κ for all of the305-mm-long tests is shown in Fig. 12. The trends

-0.005 0.005 0.010 0.015 0.020

2.8

2.9

3.0

3.1

3.2

3.3

κ (1/mm)

Dn (

mm

/μs)

2.7

0

25-mm wall (25-305)

13-mm wall (12-305)

6-mm wall (6-305)

Fig. 12. Dn versus κ versus r for all 305-mm-longtests.

seen in Fig. 11 are evident in all traces and aremarkedly different from prior ANFO data obtainedwith light confinement.8 In particular, each Dn-κcurve exhibits two rollovers that are due to a lo-cal minima or maxima in curvature along the ra-

dius. The local maximum in κ is apparent in thestreak records and demonstrates the effect of thealuminum confinement. However, we believe thatthe local κ minimum is an artifact of the compos-ite fitting form (particularly the weighting function)and is not present in the experimental data. Ongoingstudy of the best fitting form will explore this issue.

The Effect of Confinement on the Front Shape

Variations in confinement will obviously affectthe curvature of the detonation wavefront. It is in-structive to consider the resulting wave shapes forconfiners that (a) remove energy from the reactionzone (sink confinement), (b) neither remove norcontribute energy (perfect confinement), and (c) addenergy (energetic confiner) to the subsonic region ofthe reaction zone.

Most confiners for high explosives yield at pres-sures well below those produced by the detonationshock. For these materials, arrival of the detonationat the HE-confiner interface drives an inert shockinto the confiner, causing the HE-confiner interfaceto move outwards. The outward motion of this in-terface expands the partially reacted HE materialsand removes energy from the flow, inducing wavecurvature and resulting a decreased bulk detona-tion velocity (D < D∞) as shown in Fig. 13a.For a given detonation, lower impedance confinersare accelerated to higher velocities (up to a limit-ing maximum), allowing for more interface move-ment, translating to increased reaction zone energyloss and more wavefront curvature.

A perfect confiner is able to constantly match theflow pressure and velocity along the HE-confinerinterface such that no energy is transmitted to orfrom the reaction zone. The result is that the det-onation front shape is perfectly flat (Fig. 13b), as itwould be in a charge of infinite radius and the det-onation velocity is D = D∞. In general, the onlyperfectly matched confiner for a given HE is itself.For gaseous detonations at atmospheric pressures,metal walls also approximate an ideal confiner dueto their much higher impedance.

Energetic confiners are actually able to add en-ergy at or ahead of the detonation reaction zone nearthe HE-confiner interface. As shown in Fig. 13c,this energy addition accelerates the detonation nearthe interface and results in negative curvature rel-


(a)

(b)

(c)

D < D 8

D = D 8

D > D 8

Confi

ner Detonation

Fig. 13. Wave curvature that would result from(a) sink, (b) perfect, and (c) energetic confinement.Shocked confiners are shown for simplicity.

ative to the case of weak confinement. Unlike theprevious two cases, this converging wave configu-ration is unsteady; for constant energy injection, thewave shape will transition to that of Fig. 13b, withD > D∞.

The observed front shapes in Fig. 8 appear to be acombination of cases (a) and (c). Positive curvatureis obviously present in the central region of the flow,however near the edge of the charge negative curva-ture appears. It would be presumptuous to assumethat the front shapes are a steady-state phenomenongiven that negative curvature is unsteady and thatthe charges tested were short in length. However,the observed waveforms are definitely quasi-steadyor, at least, persistent given their presence in boththe shorter (L/ID = 4) and longer (L/ID = 12)tubes tested. In a related work, Short et al.12 nu-merically explore this problem in further detail.

We also note that the wavefront shapes observedin the current study are markedly different than theresults from Belcher and Eden1 in that their pre-cursor edge effects not only modified the detona-tion shape near the wall, but spread across the en-tire wave profile after propagating approximatelytwo charge widths. However, their difference be-tween D and the confiner sound speed was much

larger (5.2 mm/µs) than in the present study (∼2.1mm/µs).

Conclusion

Detonation waves were propagated in aluminumtubes filled with the non-ideal high explosiveANFO. Tube wall thickness varied from 6.35 to25.4 mm while lengths of 305 and 914 mm wereused. This configuration was of interest because thesound speed of the aluminum confiner exceeded thedetonation velocity, preventing a shock from form-ing in the tube wall and allowing the aluminum totransport energy from behind the detonation front tothe undisturbed explosive upstream.

Front-shape records showed maximum curva-ture away from the wall, with different character-istic wave shapes than observed in weakly confinedANFO. Detonation and aluminum stress wave ve-locities were recorded with shorting, ionization, andpiezoelectric pins embedded in the tube wall. Inall cases, increasing the tube wall thickness led tohigher detonation velocities and less wavefront cur-vature, as predicted by prior work.3 The precursormotion of the aluminum tube and window aheadof the detonation front is discussed in a separatestudy.7

Calculation of the Dn-κ relationship for the 305-mm-long tubes tested indicated that prior wavefrontfits of the form ln [cos (r)] did not properly accountfor the decrease in curvature near the wall. A newanalytical fitting form was proposed. The maximain wavefront curvature with increasing radius re-sulted in a rollover on the Dn-κ plot. The proposedfitting form also was found to exhibit a second arti-ficial minima in curvature, which was not present inthe experimental data and highlighted the need forfurther development of a fitting form able to repre-sent the new wave shapes.

The velocity, front-shape, and Dn-κ data pre-sented are essential to understand and accuratelymodel the behavior of low-detonation-velocity ex-plosives in higher-sound-speed confiners. Futuretests will further explore the observed phenom-ena in larger-diameter, longer-length tubes to verifythe propagation behavior and obtain higher-fidelityfront-shape measurements that are unaffected by theearly wall motion.


Acknowledgements

The authors are grateful to Robert Mier, JohnMorris, and Larry Vaughan for their assistance field-ing these experiments and to Matt Briggs, SteveHare, and Mike Shinas for their expertise with thePDV system. This work was supported by the DOEand managed by Jim Koster and David Robbins.

References

1. G. Eden and R. Belcher, “The effects of inertwalls on the velocity of detonation in EDC35,”in Proceedings of the 9th International Sym-posium on Detonation, pp. 831–841, Office ofNaval Research, 1989.

2. H. Arai, Y. Ogata, Y. Wada, A. Miyake,W. Jung, J. Nakamura, and T. Ogawa, “Deto-nation behavior of ANFO in resin tubes,” Sci.Technol. Energetic Mat. 65, pp. 201–205, 2004.

3. G. Sharpe and J. Bdzil, “Interactions of in-ert confiners with explosives,” Journal of En-gineering Mathematics 54, pp. 273–298, 2006.

4. T. Aslam and J. Bdzil, “Numerical and the-oretical investigations on detonation confine-ment sandwich tests,” in Proceedings of the13th International Symposium on Detonation,pp. 761–769, Office of Naval Research, 2006.

5. T. Aslam and J. Bdzil, “Numerical and theo-retical investigations on detonation-inert con-finement interactions,” in Proceedings of the12th International Symposium on Detonation,pp. 483–488, Office of Naval Research, 2002.

6. J. Bdzil, T. Aslam, R. Catanach, L. Hill, andM. Short, “DSD front models: Nonideal ex-plosive detonation in ANFO,” in Proceedingsof the 12th International Symposium on Deto-nation, pp. 409–417, Office of Naval Research,2002.

7. S. Jackson, C. Kiyanda, and M. Short, “Ex-perimental observations of detonation inAmmonium-Nitrate-Fuel-Oil (ANFO) sur-rounded by a high-sound-speed, shockless,aluminum confiner,” in Accepted to the Pro-ceedings of the 33rd International CombustionSymposium, The Combustion Institute, 2010.

8. R. Catanach and L. Hill, “Diameter effect curveand detonation front curvature measurementsfor ANFO,” in Shock Compression of Con-densed Matter, pp. 906–909, American Insti-tute of Physics, 2001.

9. M. Short, T. Salyer, T. Aslam, C. Kiyanda,J. Morris, and T. Zimmerly, “Detonationshock dynamics calibration for non-ideal HE:ANFO,” in Shock Compression of CondensedMatter, pp. 189–192, American Institute ofPhysics, 2006.

10. T. Salyer, M. Short, C. Kiyanda, J. Morris, andT. Zimmerly, “Effect of prill structure on det-onation performance of ANFO,” in Acceptedto the Proceedings of the 14th InternationalSymposium on Detonation, Office of Naval Re-search, 2010.

11. J. Bdzil and T. Aslam, “Detonation front mod-els: Theories and methods,” Tech. Rep. LA-UR-02-942, Los Alamos National Laboratory,Los Alamos, NM, 2002.

12. M. Short, J. Quirk, C. Kiyanda, S. Jackson,M. Briggs, and M. Shinas, “Simulation of det-onation of Ammonium Nitrate Fuel Oil Mix-ture Confined by Aluminum: Edge angles forDSD,” in Proceedings of the 14th InternationalSymposium on Detonation, Office of Naval Re-search, 2010.

Discussion

Matei Radulescu, U. of Ottawa

Your x-t diagram of the detonation positionand elastic wave in the confiner show an in-planesequence of acceleration and deceleration. Whatare these due to?

Reply by S. Jackson

We currently are unable to provide a definitive ex-planation for this phenomenon. It could simply bean initiation transient. Alternatively, the oscillationsmay be due to a coupled interaction between theconfiner and the detonation, which is not predictedto reach steady-state, but rather a quasi-steady prop-agation condition.12


precursor detonation wave development in anfo due to...

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