DETONATION DIFFRACTION, DEAD ZONES AND THE IGNITION-AND-GROWTH MODEL

G. DeOliveira, A. Kapila and D. W. SchwendemanRensselaer Polytechnic Institute

J. B. BdzilLos Alamos National Laboratory

W. D. Henshaw and C. M. Tarver Lawrence Livermore National Laboratory

13TH DETONATION SYMPOSIUMJULY 23-28

NORFOLK, VIRGINIA

Motivation

Experiments appear to exhibit sustained regions of zero or partial reaction (dead zones) in corner turning experiments, such as in the hockey-puck geometry.

Ignition-and-growth (I&G) reactive-flow model has long provided a framework for simulating a broad class of experiments. Although it captures breakout times well, it does not reproduce dead zones (Tarver ‘05).

Is explicit accounting of desensitization the missing ingredient?

burst time, the optical pin time, the crystal pin time, the timeof firing of all threeX-ray heads and anopticalmarker signalfor the streak cameras on digitizing scopes. This gave us thecross-timing references to tie all of the data together.

3 Results

We start with the basic timing measurements. The time tocross the TATB radius to the crystal pin should be longerthan the time downward on the main axis of symmetry,because of the motion of the air well edge. We estimate anegligible 0.04 ms difference in these times. The distancefrom the edge of the TATB booster edge to the on-axiselectrical pin was 21.36 mm. The average time differencebetween the optical pin and the electrical pin was 2.84!0.02 ms, which is mostly the time to cross the LX-17. TheLX-17 detonation velocity on-axis for four shots was 7.64!0.06 mm/ms for the straight-ahead detonation velocity, ingood agreement with cylinder results.The X-ray picture has the same geometry as Figure 1. A

static picture taken before the detonation is shown inFigure 3. Figure 4 shows the X-ray result at 2.48 ms after theoptical pin. The straight-ahead detonation front is seen asthe circular curve at the lower right. Going around thecorner, however, the light-gray dead zone occupies thespace near the booster.Wemight imagine that the top of thedead zone is the shock wave moving through unreactedexplosive and the bottom is the detonation front, which hasstalled. Figure 5 shows the result at 7.74 ms. The detonationfronts have long since reached the edges and the rarefactionwave has reflected back. Yet the dead zone is still there andis being pushed into the empty air well by the gas products atthe right.

We first consider the streak camera results, which arelisted in Table 1. In terms of Figure 1, the direction runsupward along the right-hand edge from the bottom, thenturns left across the top. This means we begin with thedetonation propagating straight ahead and move progres-sively into the dead zone region. We use the times tocalculate an average wave velocity from the edge of theTATB booster to the breakout point assuming constantvelocity and a 0.04 ms lag for the pin behind the rest of the

Figure 2. Schematic of the X-ray diagnostic geometry showingtop and side views. The X-rays are projected from point sourceson the right to the image plane on the left with the explosivesample being centered on the object plane in the middle. Thecollimation and shielding allowed no measurable cross-talkbetween the three X-ray channels. The image separation on thefilm pack assembly is about 15 mm.

Figure 3. Static radiograph of thick-wall component for compar-ison to dynamic post-initiation images shown below. Note lack ofany structure in the HE except that of decreasing path length withradius of component.

Figure 4. Thick-wall X-ray taken 2.48 ms after the optical pin.The picture has the geometry of Figure 1 with the initial featuresoutlined in white. The detonation spreads left to right and turnsupward around the corner. The oval at top center is the dead zone.The curve at the far right is the detonation front. At the very top isair.

LX-17 Corner-Turning 361

! 2004 WILEY-VCH Verlag GmbH&Co. KGaA, Weinheim Propellants, Explosives, Pyrotechnics 29 (2004), No. 6

pin tells when the detonation starts to leave the booster andturn the corner. Above the TATB booster is a cylindrical airwell of radius 19.05 mmand length 15 mm,whichdefines thecorner of interest. The length from the detonator to thebottomof the LX-17 part is 40.45 mm. Two radii of cylinderswere used. The thick-wall version has a 44.45 mm radius sothat the LX-17 extends 25.4 mm beyond the edge of theTATB. The thin-wall version has a 31.75 mm radius so thatthe LX-17 extends 12.7 mm beyond the edge of the TATB.Figure 1 is set so that the origin is at the point of the corner-turn rather than the axis of symmetry. The Z-axis is positivefor corner-turning andnegative for straight-aheadmotion ofthe front.The diagnostics used on this experiment included streak

cameras which measured shock break-out on the surface ofthe explosive part, an optical pin for absolute timing, time-sequence x-ray imaging to examine the details of thedetonation corner-turning, and a crystal pin for cross-timingpurposes. The crystal pin proved critical for knowing theabsolute timing. At the start, the streak camera and X-raywere thought to be equal in importance. By the end, the X-ray had clearly become the more important technique. Ashort description of these diagnostics as applied to thisexperiment follows.Themain streak diagnostics looked at the top and sides in

Figure 1. Poly-methyl-methacrylate flasher blocks weremounted on the edge such that 0.076 mm gaps existedbetween the LX-17 and the plastic. When the detonationwaves break out on these surfaces, a flash of light occurs inthe gap and is imaged on the photocathodes of twoelectronic streak cameras located just outside the tank.The camera viewing the outer edge of the sample had a3.0 msec window and the camera viewing the top edge had a1.0 ms window.

To determine the time interval between the arrival of thedetonationwave in theTATBat the corner and thebreakouttime at the edges of the LX-17, we used an optical pintechnique. A probe normally used for Fabry-Perot experi-ments was placed in the aluminum holder arm so that laserlight from the probe impinged upon the corner of analuminized mirror surface in intimate contact with theexplosive. We monitored the laser pulse with a Hamamatsus3071photodetectorwith a 532 nmbandpass filter in front ofit.When the detonationwave reached the corner, themirrorwas destroyed and the return laser pulse reflection disap-peared.Modern X-ray systems have sub-millimeter spot size

combined with high flux. Our equipment had greater than3.44 grays (30 milli-roentgens) radiation dose per pulse at1 m with 0.5 mm full-width-half-maximum spot size. Theset-up used for these experiments consisted of three450 keV flash x-ray units set at angles of 11 to 15 degreesfrom each other about the axis of symmetry of the high-explosive charge as shown schematically in Figure 2. TheX-rays are projected from point sources on the right of thefigure to the image planes on the left with the explosivelocated on the object plane in the center. In the lowerdiagram, the explosive sits just as it does in Figure 1, with theair well facing upward. Each X-ray unit projected a distinctnon-overlapping image onto a common film pack. Magni-fications from the three projections varied from 1.34 to 1.35.The temporal resolution was 25 ns as defined by the flashduration and was constant for all shots. The spatialresolution varied from shot to shot, but was typically inthe range of 0.1 mm to 0.5 mm. As each of the three unitscould be independently triggered on a given shot, a timesequence could be obtained for the same shot/experiment.The diagnostic was heavily collimated to insure absolutelyno cross-projections between the three X-ray channels.Each channel projected a well- defined region of the objectplane to the image plane with full image separation asillustrated in Figure 2 below. To confirm this, sourceintensity was compared vertically across the image sets.Vertical lineouts taken from these images have the sameslope at the same image location.The contrast was optimized primarily by adjusting the

high voltage of the diagnostic. Multi-plane film packassemblies allowed a range of imaging sensitivities foreach shot. As the high explosive detonated in these shotswas uncased, there was minimal fragmentation to possiblydamage the film pack. Therefore, we did not have to useheavy or complex shielding to protect either the x-ray headsor the film packs. We were able to use minimal shielding tomitigate the effects of blast and focus on minimizingbackground with absorbers to further optimize the contrastratio.Finally, to monitor the arrival of the detonation wave at

the LX-17 surface on the cylindrical axis directly in line withthe initiation point, we placed a crystal pin detector at thatpoint and recorded the results on a digitizing scope. Thisgave us a clear timing fiducial in the experiments. Wemonitored the current start to the detonator, the bridgewire

Figure 1. Schematic of the corner-turning geometry. The originis the optical pin at the booster/air/LX-17 boundary. The thickwall is 25.4 mm right from the optical pin; the thin wall is 12.7 mm.

360 P. C. Souers, H. G. Andreski, C. F. Cook, R. Garza, R. Pastrone, D. Phillips, F. Roeske, P. Vitello and J. D. Molitoris

Propellants, Explosives, Pyrotechnics 29 (2004), No. 6 ! 2004 WILEY-VCH Verlag GmbH&Co. KGaA, Weinheim

Dead zone

Souers et al ‘04

Detonation front

Outline

•A description of the standard I&G model.

•A proposed enhancement of the I&G model to include desensitization.

• 1-D shock-initiation results for the standard and enhanced I&G models.

•Hockey-puck corner-turning results for the standard and enhanced I&G models.

The I&G Model

• Proposed by Lee and Tarver (1980), refined in later studies.

• Calibrated for a variety of explosives including PBX 9501, PBX 9502, LX 17, ... .

• Model particulars...

- Explosive is a homogeneous mixture of two constituents (reactant and product).

- Separate, JWL equations of state for each constituent.

- Mixture energy and volume are weighted sums.

- Closure conditions: pressure and temperature equilibrium.

- Mixture variables satisfy reactive Euler equations.

- A single progress variable (product fraction) measures reaction progress.

- Single reaction rate with multiple terms (ignition and growth), switched on and off, calibrated to experiments, mimics hot-spot formation and growth.

- Used to simulate a variety of experiments.

- Parameters may need adjusting, depending upon the experiment.

Governing Equations

Ut + f(U)x + g(U)y = h(U)

E = e +1

2(u2 + w

2)

e = (1 ! !)es + !eg, v = (1 ! !)vs + !vg

es

vs0

=psvs

!s

! Fs(vs/vs0) + Fs(1),eg

vs0

=pgvg

!g

! Fg(vg/vs0) ! Q

ps =!s

vs

[CsTs+Gs(vs/vs0)+Fs(vs/vs0)], pg =!g

vg

[CgTg+Gg(vg/vs0)+Fg(vg/vs0)]

ps = pg, Ts = Tg

EOS: Mechanical

EOS: Thermal

Mixture Rules Closure Rules

U =

!

"

"

"

"

#

!!u!w!E!"

$

%

%

%

%

&

, f =

!

"

"

"

"

#

!u!u2 + p!uwu(!E + p)!u"

$

%

%

%

%

&

, g =

!

"

"

"

"

#

!w!wu!w2 + pw(!E + p)!w"

$

%

%

%

%

&

, h =

!

"

"

"

"

#

0000!R

$

%

%

%

%

&

,

EOS Data Set (LX-17)

Gi(V ) =Ai

R1i

exp(!R1iV ) +Bi

R2i

exp(!R2iV )

JWL parameters Unreacted ProductsA (Pa) 778.1e11 14.8105e11B (Pa) -0.05031e11 0.6379e11

R1 11.3 6.2R2 1.13 2.2! 0.8938 0.50

Q (Pa-cc/cc) 0.069e11C (Pa/K) 2.487e6 1.0e6

vs0 (m3/kg) 1/1905

+Bi

!

V

!i

!

1

R2i

"

exp(!R2iV )

Fi(V ) = Ai

!

V

!i

!

1

R1i

"

exp(!R1iV )

i = s, g

Parameter ValueI, (s!1) 4.0e12

b 0.667a 0.22x 7.0

G1, (1011 Pa)!y s!1) 4500e6c 0.667d 1y 3

G2, (1011 Pa)!z s!1) 30e6e 0.667g 0.667z 1

!igmax 0.02!G1max 0.8!G2min 0.8

Rate Law

R = RI + RG1 + RG2

RI = I(1 ! !)b(vs0/v ! 1 ! a)xH(vs0/v ! 1 ! a)H(!igmax ! !)

RG1 = G1(1 ! !)c!dpyH(!G1max ! !)

RG2 = G1(1 ! !)e!gpzH(! ! !G2min)

density threshold for ignition

ignition shut offfirst growth shut off

second growth switchTarver ‘05, LX-17 detonation set

• First growth term does not have an activation delay. Once ignition begins, first growth term switches on immediately and reaction must go to completion in due course as long as p > 0.

• No explicit accounting of desensitization due to weak shocks.

• Need for an enhanced model.

• A desensitization variable to measure the degree of compaction caused by the desensitizing shock.

• A dependence of the density threshold for ignition on the desensitization variable.

• A reaction extinction mechanism controlled by the desensitization variable.

• A negligible effect of desensitization on the propensity to initiate when the stimulus is sufficiently strong.

Ingredients of an Enhanced I&G Model

Proposed Enhancement of I&G

• Introduce desensitization parameter , and the associated evolution equation and rate law.

- and are positive parameters, and any positive pressure drives from (no desensitization) to (full desensitization).

• Modify the reaction rate in two aspects.

- Allow density threshold for ignition to be a function of .

- Introduce a delay .

!

(!")t + (!u")x + (!w")y = !S

S = Ap(1 ! !)(! + ")

A ! !

!

a(!) = a0(1 ! !) + a1!, a1 > a0

RG1 = G1(1 ! !)c!dpyH(! ! !G1min(!))H(!G1max ! !), !G1min = !c"

!G1min(")

delay in activating first growth term

a0 = 0.22, a1 = 0.50, A = 1000, ! = 0.001, "c = 0.01.

0

1

Numerical Method

• Godunov-type, shock-capturing scheme on a domain discretized using composite overlapping grids (overset grids).

• Riemann problems handled using Roe and HLL approximate solvers (extended to the mixture JWL equation of state).

• Reaction source term handled using an Runge-Kutta error-control scheme.

• AMR used to resolve fine-scale structures.

1 + a(!)

1D Initiation by a Weak Shock (12.54 GPa)

Standard model: successful initiation. Augmented model: desensitization prevents successful initiation. Ignition begins, but is shut off by the density threshold for ignition,rising above the post-shock density. Growth begins, but is shut off by the first-growth delay rising above the available .!

1 + a(!),

1D Initiation by a Strong Shock (14.97 GPa)

1 + a(!)

Successful initiation with standard model (dashed line), augmented model (full line).

Ignition begins, and is shut off by rising above the post-shock density, as for the weak shock case. But the growth term is no longer deactivated, as the available exceeds the delay Thus desensitization is unable to prevent initiation to detonation.

! !G1min.

1 + a(!)

ignition deactivated

pressure progress schlieren

Display of Axisymmetric Results

Typical post-corner-turning result. Numerical schlieren image carries more information, and will be the display mode of choice in the movie.

lead shock dead zonelead shock dead zone

Hockey-puck Computations for LX-17

dimensions in mm, time in microsec

Reaction product at 31.46 GPa

t = 0 t = 1.6

Unreacted explosive

Show movie.

Pressure Density lambda

phiPressure Density lambda

No desensitization

Desensitization

t = 2.6

Pressure Density lambda

phiPressure Density lambda

No desensitization

Desensitization

t = 2.8

Pressure Density lambda

phiPressure Density lambda

No desensitization

Desensitization

t = 3.0

Pressure Density lambda

phiPressure Density lambda

No desensitization

Desensitization

t = 3.2

Pressure Density lambda

phiPressure Density lambda

No desensitization

Desensitization

t = 3.4

Pressure Density lambda

phiPressure Density lambda

No desensitization

Desensitization

t = 3.6

Pressure Density lambda

phiPressure Density lambda

No desensitization

Desensitization

t = 3.8

Pressure Density lambda

phiPressure Density lambda

No desensitization

Desensitization

t = 4.0