PETN Ignition Experiments and Models - The Journal of Physical

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PETN Ignition Experiments and Models Michael L. Hobbs,*,† William B. Wente,‡ and Michael J. Kaneshige‡ Engineering Sciences Center and Energetic Components Realization, Sandia National Laboratories, Albuquerque, New Mexico 87105 ReceiVed: January 25, 2010; ReVised Manuscript ReceiVed: March 10, 2010

Ignition experiments from various sources, including our own laboratory, have been used to develop a simple ignition model for pentaerythritol tetranitrate (PETN). The experiments consist of differential thermal analysis, thermogravimetric analysis, differential scanning calorimetry, beaker tests, one-dimensional time to explosion tests, Sandia’s instrumented thermal ignition tests (SITI), and thermal ignition of nonelectrical detonators. The model developed using this data consists of a one-step, first-order, pressure-independent mechanism used to predict pressure, temperature, and time to ignition for various configurations. The model was used to assess the state of the degraded PETN at the onset of ignition. We propose that cookoff violence for PETN can be correlated with the extent of reaction at the onset of ignition. This hypothesis was tested by evaluating metal deformation produced from detonators encased in copper as well as comparing postignition photos of the SITI experiments. Introduction Predicting the response of pentaerythritol tetranitrate (PETN) during an accident, such as a fire, is important for high consequence safety analysis. The response depends on many factors such as the thermophysical properties of PETN as well as temperature-sensitive decomposition kinetics. Knowledge of properties associated with solid, liquid, and frothy PETN is necessary to predict and mitigate inadvertent thermal ignition. Some of these properties have been measured in Sandia’s instrumented thermal ignition (SITI) experiment1 and Lawrence Livermore’s one-dimensional time-to-explosion (ODTX) experiment.2 The present work increases our understanding of complex preignition reactions and thermophysical changes in PETN leading to thermal runaway. An overview of thermal runaway leading to ignition can be found elsewhere.3–5 Postignition burning and resulting violence is beyond the scope of the current paper. However, an empirical method to assess the potential for cookoff violence, such as reported by Zucker et al.6 for PETN filled detonators, is discussed. PETN has two solid polymorphs, referred to as PETN I (tetragonal) and PETN II (orthorhombic), and starts to decompose at about 75 °C before melting at 142 ( 2 °C.7 PETN II is the more stable polymorph at the melting point.8 The polymorphic phase transition is reported to occur at 130 °C, although no latent energy is given9 or observed using differential scanning calorimetry (DSC) data. However, in the current work, DSC data does show an endothermic process commencing at about 136 ( 2 °C. As PETN melts, bubbles filled with gaseous decomposition products form froth, with an effective thermal conductivity close to that of the decomposition gases. PETN changes from a smoking solid to a bubbling liquid. In contrast, TNT melts before decomposition products are formed and changes to a clear liquid with no gaseous decomposition * To whom correspondence should be addressed. E-mail: mlhobbs@ sandia.gov. † Engineering Sciences Center, Nanoscale and Reactive Processes Department. ‡ Energetic Components Realization, Explosive Projects/Diagnostics.

products or bubbles observed until the liquid temperature is greater than the melting point.10 A variety of experimental observations are used to develop a decomposition and ignition model for PETN. DSC experiments were used to determine specific heat and latent enthalpy. The SITI experiments were used to determine the thermal conductivity. Ignition time, temperature, and pressure from SITI experiments were used to obtain decomposition rates for the model. Ignition times from the ODTX experiments were used to determine liquid reaction rates. Reaction products, overall gas molecular weight, and reaction enthalpy were determined by assuming equilibrium. The remainder of this paper describes the various experiments used to characterize PETN. A simple model is formulated based on a single step reaction mechanism with the products assumed to be in equilibrium. The model was applied to detonators containing PETN at various heating rates to evaluate detonator failure during cookoff. The model was also used to evaluate postignition photos of the SITI experiments. Experimental Observations. Figure 1 shows a differential thermal analysis (DTA) and a thermogravimetric analysis (TGA) for PETN from two separate experiments.11 The top of Figure 1 also shows a reaction sequence with PETN decomposing into equilibrium products, which were determined using the JCZS equation of state12 at a grid of various temperatures (27-227 °C or 300-500 K) and pressures (0.1-1 MPa or 1-10 atm). The equilibrium product concentrations over this temperature and pressure range were similar as long as the temperature was high enough for water products to be in the gas phase. At low temperature and high pressure, liquid water is favored over water vapor. The concentration of the gas phase decomposition products CO2, N2, H2O, and CH4 is 41.7, 20.0, 36.6, and 1.7 mol %, respectively, giving an average gas product molecular weight of 30.8 g/mol. The equilibrium reaction enthalpy (6.45 × 106 J/kg of PETN) was determined using Hess’s law with the heat of formation of PETN being 500 KJ/mol, which is the average of the formation enthalpies given in ref 8 and 11. Figure 2A shows 12 DSC tests consisting of 3 runs from each of 4 PETN lots numbered 17 086, 17 200, 17 668, and 18 715. The average sample mass was 2.1 mg with a standard

10.1021/jp1007329  2010 American Chemical Society Published on Web 04/02/2010

PETN Ignition Experiments and Models

Figure 1. DTA/TGA of PETN.11

deviation of 0.3 mg. One of the DSC samples was an outlier with a mass of 1.3 mg. (Heat flow was not normalized with sample mass since mass was not measured during the DSC experiments.) The average of the other 11 DSC runs was 2.2 mg with a standard deviation of 0.2 mg. The average of the baseline corrected heat flow (µ) associated with the endothermic processes is plotted in Figure 2B with the dispersion plotted as

J. Phys. Chem. A, Vol. 114, No. 16, 2010 5307 µ ( 1σ, with σ representing a single standard deviation calculated from the 12 DSC tests. The integral of the average baseline corrected heat flow divided by the average mass of the samples with respect to the temperature gives the enthalpy associated with the endothermic processes. The average mass during the endothermic process is assumed to be 6% less than the initial sample mass. The mass losses during the endothermic processes were estimated from the TGA data in Figure 1. The average mass during the endothermic processes is estimated to be about 2.0 mg. The latent enthalpy calculated in this manner is 177 ( 56 J/g as shown in Figure 2.B. This range is close to several literature values of latent enthalpy (128-156 J/g).2,9 The higher mean in the current work results from wider integration limits or result from uncertainties in sample mass. The latent enthalpy is modeled using an effective capacitance method as shown in Figure 2, panels C and D. A 73 point trapezoidal integration of the overall energy flow is separated into latent and caloric contributions to determine the effective heat capacitance as PETN changes phase and melts between 406 and 424 K with the maximum latent energy sink occurring at the melting point of 415 K. The effective heat capacity is given in Table 1. The uncertainty in the latent energy is approximated as a multiplier of the mean, which ranges between 0.8 and 1.2. Figure 3 shows the reaction of 450 mL of Semtex 1A and Semtex 10 in a beaker on a hot plate. Semtex 1A and Semtex 10 are composed of 87 and 82% PETN, respectively, with the remaining constituents being dye (e.g., Sudan I), antioxidant (e.g. n-phenyl-2-naphthalamine), plasticizer (e.g. n-octyl phthalate butyl citrate), and binder (e.g., styrene-butadiene rubber).13 The Semtex melts at the bottom of the beaker and forms

Figure 2. (A) Twelve DSC runs, (B) average and dispersion of the baseline corrected endotherms, (C) geometric derivation of effective capacitance during the endotherms, and (D) mean (solid orange line) and assumed dispersion (solid black lines) of effective capacitance.

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TABLE 1: Effective Heat Capacity for Endothermic Processes between 406 and 424 K T (K)

Ceff (J/kg · K)

T (K)

Ceff (J/kg · K)

T (K)

Ceff (J/kg · K)

T (K)

Ceff (J/kg · K)

T (K)

Ceff (J/kg · K)

406.00 406.25 406.50 406.75 407.00 407.25 407.50 407.75 408.00 408.25 408.50 408.75 409.00 409.25 409.50

1312.6 1317.7 1324.6 1333.7 1344.2 1354.9 1366.6 1378.7 1391.1 1406.3 1422.5 1441.6 1464.0 1489.9 1518.3

409.75 410.00 410.25 410.50 410.75 411.00 411.25 411.50 411.75 412.00 412.25 412.50 412.75 413.00 413.25

1550.5 1587.1 1627.9 1673.4 1728.7 1793.7 1869.2 1957.0 2061.8 2183.9 2330.5 2505.0 2718.1 2987.6 3339.0

413.50 413.75 414.00 414.25 414.50 414.75 415.00 415.25 415.50 415.75 416.00 416.25 416.50 416.75 417.00

3837.5 4707.5 7059.6 13 281.7 22 757.8 32 762.4 40 787.3 45 485.3 46 439.0 45 496.6 43 777.9 41 920.1 40 249.9 38 312.3 36 009.7

417.25 417.50 417.75 418.00 418.25 418.50 418.75 419.00 419.25 419.50 419.75 420.00 420.25 420.50 420.75

33 439.0 30 766.6 27 936.5 25 068.9 22 312.7 19 739.5 17 353.7 15 174.7 13 219.6 11 463.9 9909.7 8546.2 7352.6 6318.9 5434.4

421.00 421.25 421.50 421.75 422.00 422.25 422.50 422.75 423.00 423.25 423.50 423.75 424.00

4685.9 4055.9 3528.5 3089.0 2723.1 2420.2 2168.0 1961.1 1788.3 1646.1 1528.2 1430.9 1351.3

a black char along with decomposition gases that cause the pressure to increase at the bottom of the beaker. This pressure forces the Semtex to move like a solid plug. To prevent movement, holes were put in the Semtex to relieve the pressure caused by the decomposition gases accumulating at the bottom of the plate. The fuel-rich gases ignite when mixed with air. Figure 3 also shows that the solid Semtex ignites before it is melted. These observations are much different than TNT ignition since the TNT melts completely before decomposition begins.10 Model. Thermal ignition of PETN can be determined by solving the conductive energy equation using a volumetric source for chemical reactions. This approach is acceptable for PETN since ignition occurs before the PETN completely melts as shown in Figure 3. Flow of liquid PETN is assumed to be negligible since most of the PETN is still solid at ignition. However, the partially melted PETN contains bubbles filled with

decomposition gases. The thermal conductivity of this melt phase is assumed to approach the thermal conductivity of the decomposition gases. Low thermal conductivity of the melt enables the model to match ignition data for fast cookoff where boundary temperatures are high. Table 2 gives the PETN ignition model; Table 3 gives the PETN reaction mechanism with auxiliary equations; Table 4 gives the PETN material parameters; and Table 5 gives parameters specific to individual experiments. The PETN ignition model uses a single acceleratory rate14 obtained by normally distributing the activation energy with respect to the extent of reaction. Distributed activation energies have been used to describe decomposition of large molecules such as coal,19 polymers,20 and more recently, explosives.10 When the extent of reaction is small, the activation energy is high and reaction rates are low.

Figure 3. Beaker tests of (A) Semtex 1A and (B) Semtex 10 on a hot plate.

TABLE 2: PETN Ignition Modela Showing Domain

a Cb, Cg, hi, ho, hr, k, m ˙ i, m ˙ o, Mg, Mwg, P, Q, r, F0c , R, S, t, T, Tb, V, x, y, z, Fb, Fg, φ, φc, φ0, and Λ represent bulk specific heat, gas specific heat, influx enthalpy, outflux enthalpy, reaction enthalpy, thermal conductivity, influx mass, outflux mass, mass of gas, molecular weight of gas, pressure, heat loss, reaction rate, initial density of condensed phase, gas constant, enclosure surface, time, temperature, bulk element temperature, volume, x-coordinate, y-coordinate, z-coordinate, bulk density, gas density, gas volume fraction, critical gas volume fraction, initial gas volume fraction, and permeable region, respectively.


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TABLE 3: PETN Reaction Mechanism and Auxiliary Equationsa mechanism reaction rate distribution parameter gas volume fraction bulk density thermal conductivity

mole basis : C5H8N4O12 f 4.17 CO2 + 2 N2 + 3.66 H2O + 0.17CH4 + 0.66C or mass basis : petn f 0.975gas + 0.025carbon d r ) (petn) ) ξA exp[-(E + zσE)/RT]petn, where petn(t ) 0) ) 1 dt z 1 -z2 1 - petn ) -∞ dz or Z ) norminv(1 - petn) exp 2 √2π φ ) 1 - [Sf(1 - φ0)F0c /Fc] where Sf ) petn + carbon Fb ) φFg + (1 - φ)Fc

∫

( )

2 16σT3 k ) φkg + (1 - φ)kc + 3 3[φRg + (1 - φ)Rc]

(5) (6) (7) (8) (9) (10)

a A, carbon, E, gas, k, kc, kg, norminv, petn, P, P0, r, R, T, z, Rc, Rg, φ, φ0, π, Fc, F0c ,Fb, Fg, σ, σE, and ξ represent prefactor, carbon mass fraction, activation energy, gas mass fraction, effective thermal conductivity, condensed conductivity, gas conductivity, inverse of the normal probability distribution function, PETN mass fraction, pressure, initial pressure, reaction rate, gas constant, temperature, cumulative distribution parameter, condensed absorption, gas absorption, gas volume fraction, initial gas volume fraction, pi, condensed density, initial condensed density, bulk density, gas density, Stephan Boltzmann constant, activation energy dispersion, and liquid rate multiplier, respectively. Bounds on z are 3.5 and -3.5.

TABLE 4: PETN Material Parameters parameter

description

Rc (m-1) Rg (m-1) β

condensed absorption coefficient15 gas absorption coefficient16 volumetric expansion coefficient9

C298 (J/kg · K) C623 (J/kg · K) E (J/kg · mol) hpc (J/kg) hr (J/kg) kc (W/mK) kg,300 (W/mK) kg,500 (W/mK) kL (W/mK) krate ks (W/mK) Ln A (Ln(s-1)) Mwg (g/mol) Mwgo (g/mol) Fc (kg/m3) Fco (kg/m3) σE/R (K) Tpc (K) wpc (K) ξ

bulk specific heat2 at 298 K bulk specific heat2 at 623 K activation energy17 latent enthalpy (Figure 2B) reaction enthalpyb condensed thermal conductivity gas (air) conductivity18 at 300 K gas (air) conductivity18 at 500 K liquid conductivity to match fast cookoff reaction rate uncertainty multiplier solid conductivity to match SITI data natural logarithm of A average gas molecular weight initial gas (air) molecular weight condensed PETN density initial solid PETN density normalized activation energy dispersion melting point (DSC data, see Figure 2B) melting point range liquid rate multiplier (see Figure 4)

value 50 000 ( 10% 100 ( 10% 22.05 × 10-5 + 4.38 × 10-7(T - 273) + 7.78 × 10-10(T - 273)2 + 4.71 × 10-12(T - 273)3 1090a 1760a 1.5 × 108 1.77 × 105 ( 20% (implemented via Ceff ( 20%) 6.45 × 106 kfac[δ × kL + (1δ)ks]c 0.0263d 0.0407d 0.035 ( 50% 1 ( 10% 0.35 ( 10% 39.0 30.8 28 Fco/[1 + β(T - To)] 1780 1260 415 ( 1% 2 ( 10% 4.0 ( 10% [implemented as ξ ) δ +(1 - δ)4]

a Bulk heat capacity varies linearly between 298 and 623 K with constant extrapolation. b Based on equilibrium: C5H8N4O12 f 4.17 CO2 + 2N2 + 3.66H2O + 0.17CH4 + 0.66C on a mole basis. c δ ) 0.5 × {1 + tanh[(T - Tpc)/wpc]} for the transition. d Gas thermal conductivity varies linearly between 300 and 500 K with linear extrapolation.

As the extent of reaction increases, the activation energy decreases, leading to acceleratory reaction rates. Decomposition of PETN occurs in the solid state, the liquid state, and the gas state. First-order decomposition rates in each of these phases are substantially different. For example, Manelis et al.21 postulate that decomposition rates in the gas phase can be 4-5 times greater than in the liquid phase (i.e., ξ ) 4). Several hypotheses can explain higher liquid decomposition rates than solid decomposition rates. For example, the crystal lattice may inhibit mobility of the decomposition products or polymorphic phase changes may slow reactions in the solid phase. Manelis et al.22 indicated that PETN decomposition in the liquid phase can be 360 times greater than in the solid phase (i.e., ξ ) 360). Moreover, Manelis et al.23 conflictingly stated that “for PETN, the transition from liquid to solid phase leads to the initial rate decreasing by a factor of 100.” This discrepancy was resolved by calculating ξ to be about 50 at the melting point of PETN (415 K) using Roth’s24 first-order liquid

rate kinetics and the initial decomposition step used by Tarver et al.2 The increase in reaction rate due to liquefaction was investigated in the current work by fitting pressure rise in SITI test No. 103 with ξ ) 50.7, Ln A ) 49.5, E ) 1.97 × 108 J/Kg · mol, and σE/R ) 1150 K, then using these constants to predict the ODTX results. As shown in Figure 4, these coefficients fit the SITI tests adequately, but were too fast for the ODTX test. Consequently, new coefficients (ξ ) 4, Ln A ) 39, E ) 1.5 × 108 J/Kg · mol, and σE/R ) 1260 K) were determined that fit both sets of data. Thus, the reactions in the liquid phase are assumed to be four times (4×) faster than in the solid phase, at least with the mechanism proposed in the current article. The model uses a low Mach flow assumption to determine the pressure in closed systems. The gas velocity is assumed to be much less than sound speeds and the pressure within the system is only a function of time, e.g. P(x,y,z,t) ) P(t). Pressure changes temporally due to increasing temperature and reaction.

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TABLE 5: PETN Experiment Parametersa parameter

ODTXb

SITI (No. 102)c

SITId

h, W/m2K Fbo, kg/m3 Venc, cm3 Vpetn, cm3 Vtube, cm3

0 1720 ( 10 0 1.07 0

1 1101 7.05 7.05 0.2

1 1690 ( 10 1.51 12.9 0.2

SITI-small (No. 117)e detonatorf 1 1570 0.157 1.6 0.2

1 670 0.713 0.709 0

a ODTX, SITI, and detonator are described in subsequent sections. h, Fbo, Venc, Vpetn, and Vtube represent the convection coefficient, initial bulk density, enclosure volume, bulk PETN volume, and pressure tubing volume. b Half inch spheres exposed to constant temperature. c Test No. 102 used powdered PETN. This test was vented since PETN crystals on the transducer threads were a safety concern. Outside temperature ramped to 418 K in 550 s, and then ramped at 1 °C/min until ignition at 1546 s. d One inch diameter by one inch tall cylinders with the boundary temperature ramped to the set point temperature (Tsp) in 10 min and held at Tsp until ignition. Parameters describe tests 103 (Tsp ) 415.5 K), 104 (Tsp ) 413.5 K), 106 (Tsp ) 405.5 K then ramped to 423.5 after 5 h), 107 (Tsp ) 423.5 K), 114 (Tsp ) 415.5 K), 115 (Tsp ) 438.7 K), and 116 (Tsp ) 407.5 K). e Test No. 117 is a 0.5 in. diameter by 0.5 in. tall cylinder of PETN making the PETN volume one-eighth of the PETN used in the other SITI tests. The boundary temperature was ramped from room temperature to 419.6 K in 10 min. f Nonelectric detonators encased in copper cylinder with outside temperature exposed to constant temperature ramp.

Condensed and gas phase temperatures are also assumed to be equal, that is, Tc ) Tg ) T(x,y,z,t). The reaction rates are assumed to be pressure independent following Occam’s razor. (Occam’s razor implies that one should use the simpler of two competing theories. This assumption does not imply that the decomposition mechanism is pressure independent. Rather, the model matches available data without using a pressure dependency. Few unsealed vented experiments have been performed. More experiments with controlled pressure are needed to better characterize the effects of confinement and pressure.) A pressure dependent model with the rates multiplied by (P/P0)n did not fit the data any better than the pressure independent model. The inset drawing of the domain in Table 2 shows a more general open system with permeable and impermeable regions. In the current work, only closed, permeable systems are considered. The model equations were solved using Calore.25 The form of the effective thermal conductivity in eq 10 of Table 3 has been used by Glicksman26 for cellular materials. The factor 2/3 describes tortuosity. The absorption coefficients given in Table 4 were chosen based on the absorptivity of

polyurethane15 and air,16 which were used in a similar model for TNT decomposition.10 The solid and liquid thermal conductivity in Table 4 were determined using data from Sandia’s Instrumented Thermal Ignition (SITI) experiment. The transition from solid to liquid thermal conductivity was achieved by using a smooth hyperbolic tangent with the same transition width as the phase change width as shown in footnote c of Table 4. The gas thermal conductivity is assumed to be a linear function of temperature using the air thermal conductivity18 given in Table 4. The volumetric expansion coefficient (β in Table 4) is assumed to be the same for both solid PETN I and PETN II. The theoretical maximum density of PETN I at room temperature is 1.78 g/cm3. The density becomes 1.72 g/cm3 at 135 °C, which is the same density of PETN II.8 The density of liquid PETN has not been measured and is assumed to be the same as the solid PETN corrected for thermal expansion. The latent enthalpy is partitioned from 406 to 424 K using an effective capacitance method as discussed with Figure 2C. The specific heat is assumed to be linearly dependent on temperature using the two bulk specific heat given in Table 4. The specific heat is increased to the effective capacitance values given in Table 1 in the temperature range, 133 °C (406 K) < T < 151 °C (424 K), to account for latent enthalpy. Figure 5A shows the effective thermal conductivity as a function of temperature for PETN with an initial bulk density of 670 kg/m3, which is the density of the PETN in the detonators. Figure 5B shows the effective thermal conductivity as a function of temperature for PETN with the initial bulk density of 1760 kg/m3, which is the density of the PETN in the ODTX experiments. The thermal conductivity values were taken near the ignition point for both the detonator experiment with a 10 °C/min heating rate and the ODTX experiment with the anvils preheated to 500 K. The contributions due to condensed phase conduction (keff), gas phase conduction (kgas), and diffusive radiation (krad) are also shown in Figure 5. The gas volume fraction is shown as a dashed line in Figure 5. The gas volume fraction decreases as the condensed PETN thermally expands. The gas volume fraction increases when PETN starts to decompose prior to thermal ignition. The effective thermal conductivity is dominated by condensed phase conduction, especially for the ODTX case with a high initial density. The initial increase in the thermal conductivity is attributed to the increase in the solid volume fraction as the condensed phase thermally expands. The symbols in Figure 5B

Figure 4. Predictions of (A) SITI test No. 103 and (B) ODTX data. The predictions are made using two sets of kinetic parameters with the model described in Tables 2-5 showing the effect of liquid rate enhancement.



Figure 5. Thermal conductivity and the contributions due to condensed conduction, gas conduction, and diffusive radiation from (A) low density (670 kg/m3) and (B) high density (1720 kg/m3) PETN. The dashed line is the gas volume fraction calculated with the PETN response model. Symbols in B represent the thermal conductivity of PETN, solid intermediates, and gases used by Tarver et al.2

Figure 6. Schematic of ODTX experiment.

represent the thermal conductivities used by Tarver et al.2 for PETN, solid intermediates, and gases. Reference 11 gives a thermal conductivity of 0.143 W/mK for a composite explosive

that contains 80% PETN and 20% silicon rubber. The diffuse radiation contribution to the effective thermal conductivity is negligible for both the low density and high density PETN. One-Dimensional Time-to-Explosion (ODTX) Experiments. A schematic of the Catalano et al.27 ODTX experiment constructed in 1975 is shown in Figure 6, where preheated aluminum anvils were used to confine 1.27 cm diameter spheres of PETN to 1500 atm. Heaters controlled the temperature of the anvils to (0.2 K, and the primary measurement was the “time-to-explosion.” The PETN data was obtained in 1987 on a lot of PETN received in 1965.28 The aged PETN is assumed behave similar to fresh PETN used in the SITI experiments described subsequently. Sandia’s Instrument Thermal Ignition (SITI) Experiments. The SITI experiment,1 shown schematically in Figure 7, panels A and B, had type K 76 µm diameter thermocouples located at various radial positions in the center of a 2.54 cm

Figure 7. SITI (A) schematic, (B) cross-section, (C) picture, and (D) typical boundary temperatures, internal temperatures, and pressure measurement. Example is test No. 103.

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Figure 8. Pre- and post-test pictures of three SITI test with PETN.

Figure 9. Schematic of detonator.

diameter by 2.54 cm tall cylinder of TNT. The outside temperature of the confining aluminum cylinders was maintained at a controlled set point using a coil heater. For the PETN experiments, the outside temperature of the aluminum confinement was ramped from room temperature until the set point temperature was reached. The ramp rate was controlled so that each experiment reached the set point temperature in 10 min (600 s). The experiment also has a pressure tap to monitor the pressure during the experiment. Figure 7D shows data from test No. 103. The red line in Figure 7D represents the boundary temperature. The boundary was held at the set point temperature until the PETN ignited. Figure 8 shows pictures of three of the SITI experiments using PETN. In test No. 102, PETN powder stuck to the threads of the pressure transducer opening as PETN powder was being loaded. Because of safety concerns, the transducer was left off of this test and the decomposition products were vented. The total mass of PETN powder was 7.76 g for test No. 102. Tests No. 103 and No. 105 were performed with pressed pellets. Test No. 103 consisted of two pellets weighing 10.83 and 10.82 g for a total PETN mass of 21.65 g. The mass of each of the two pellets used in test No. 105 was 10.98 g for a total of 21.96 g of PETN.

Detonator. A detonator encased in copper is shown schematically in Figure 9. The copper was wrapped in electric heating tape, insulated, and heated between 9 and 20 °C/min.6 For one test, the boundary was ramped to 153 °C and held until ignition. The lead azide does not react until 220 °C,6 which is well above temperatures at which the PETN thermally ignites. Thus, the lead azide was considered nonreactive in the simulations. Typical properties were used for the lead azide, air, and rubber. Violence in detonator experiments was correlated with the maximum expansion of the copper confinement. Zucker et al.6 detonated the PETN in the copper confinement tube at room temperature with no preheating and found the expansion to be about 7.8 mm. The shapes of the copper confinement after ignition for the ramped experiments were teardrop shaped with the widest part near the bottom.6 The shape of the copper confinement after ignition for the “ramp and hold” experiment had the widest shape near the lead azide charge and was the least violent of all of the experiments. Zucker observed expansions of ∼8 mm when the heating rates were greater than 9.53 °C/min. For heating rates less than and equal to 9.53 °C/ min, the cylinders only expanded ∼3 mm. Subsequent experiments29 done without lead azide were nonviolent, for all heating rates. Apparently, lead azide provided shock initiation of the degraded PETN after thermal ignition. We postulate that for fast heating rates, the PETN would ignite at the location shown in Figure 9. The hot decomposition gases might then initiate the lead azide primer, sending a shock into the PETN, resulting in a violent response. For slower heating rates, much of the PETN would probably decompose and leak from the unsealed detonator. For these conditions, the lead azide shock with substantially less material, resulting in a nonviolent response. Finite Element Mesh and Solution Method. Figure 10 shows four meshes corresponding to the experiments described

Figure 10. Two-dimensional (2D) axisymmetric meshes with quadratic elements for (A) ODTX, (B) SITI with powdered PETN, (C) SITI with pressed PETN, (D) SITI with 1/8th of the PETN volume in C, and (E) the detonator encased in copper.



TABLE 6: Number of Simulations for Uncertainty Analysis simulation

1000/T range

No. of LHS runs

No. of temp. BC’s

No. of simulations

ODTX SITI (solid) total )

2.000-2.465 1.90-2.01

20 20

26 30

520 600 1,120

in Table 5sone ODTX mesh, three SITI meshes, and one detonator mesh. The three SITI meshes were necessary since the experiments with the powdered, solid, and small PETN sample were all different sizes with different expansion gaps. The equations listed in Tables 2 and 3 were solved using a preconditioned conjugate gradient solver with the finite element code Calore.25 The endotherm associated with melting was included by using the effective thermal capacitance given in Table 1. The PETN material parameters were taken from Table 4. Parameters that are specific to each experiment, such as density, were taken from Table 5. Uncertainties in the calculated results for the ODTX and SITI simulations were determined using a Latin hypercube sampling (LHS) technique. The LHS technique is an efficient, constrained

sampling technique developed by McKay et al.30 and is used to propagate uncertainty into the predicted results. Ten parameterssRc, Rg, Ceff, kL, krate, ks, Tpc, ωpc, ξ, and Fboslisted in Tables 4 and 5 were assumed to vary uniformly about their nominal values. Uncertainty in the enclosure volume and tube volume was found to be insignificant in previous work with TNT10 and was not considered in the current article. In the current work, 2n samples were run for each LHS analysis with n being the number of parameters with uncertainty. Thus, 20 LHS runs were made for each boundary temperature for the ODTX and SITI simulations. The dispersion in 10 uncertain parameters was accounted for by selecting 20 different values for each of the 10 parameters. The range of each input parameter was divided into 20 nonoverlapping intervals based on equal probability. One random value from each interval was selected according to the probability density function in the interval. The 20 values thus obtained for the first parameter were then paired in a random manner with the 20 values obtained for the second parameter. These 20 pairs were then combined in a random manner with the 20 values of third parameter to form 20 triplets, and so on,

Figure 11. Ignition and selected scatter plots for ODTX and SITI simulations of PETN.

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TABLE 7: LHS Parameter Multipliers and Correlations Coefficients for Four LHS Runsa time-to-ignition (s) LHS parameter multipliers with uncertainty run 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 1000/T 20 ODTX 2.200 2.415 SITI

2.200 2.415

a

r) r2 ) r) r2 ) r) r2 ) r) r2 )

ks

kL

krate

Tpc

ξ

wpc

ODTX, 1000/T SITI, 1000/T

Rc

Rg

Fbo

Ceff

1.098 1.041 0.925 1.077 0.958 1.050 0.905 0.965 0.982 1.001 0.973 0.950 1.070 1.040 0.935 1.086 1.028 0.997 1.014 0.914

1.099 0.903 0.955 1.038 0.920 0.991 1.018 1.062 1.070 1.058 1.025 1.008 0.976 0.941 0.984 1.045 0.969 0.923 0.931 1.085

1.060 0.970 1.089 1.072 1.012 0.918 0.981 0.921 1.057 1.005 0.932 0.993 0.944 1.025 1.040 1.047 0.903 1.090 0.955 0.974

0.994 0.993 1.009 1.002 0.996 1.003 0.991 1.004 0.990 1.006 1.009 0.994 1.005 0.996 0.998 1.000 0.998 1.008 1.000 1.002

1.084 1.037 1.074 0.909 0.926 1.094 1.028 0.949 1.053 0.972 0.998 0.960 0.967 0.985 0.933 0.912 1.048 1.068 1.002 1.017

1.042 0.987 1.064 0.919 0.998 0.958 1.037 0.962 0.907 1.015 0.973 1.085 1.059 0.925 0.943 1.096 1.026 0.931 1.080 1.001

0.980 1.020 1.010 0.994 0.902 0.973 1.079 0.921 0.919 0.964 0.956 0.944 1.045 1.093 1.082 1.031 1.058 0.939 1.004 1.062

1.004 0.999 0.999 0.997 1.001 0.995 1.001 1.002 1.000 0.998 1.003 0.997 1.000 0.996 1.005 0.998 1.004 1.003 1.002 0.996

0.981 1.003 1.079 1.051 0.964 0.917 0.950 1.091 1.022 0.923 0.905 0.957 1.017 0.979 0.936 0.999 1.083 1.031 1.047 1.064

1.079 1.170 1.054 0.808 1.024 0.897 0.834 1.156 0.999 1.198 0.953 0.858 0.864 1.123 1.082 1.118 0.921 0.910 0.977 1.004

0.017 3 × 10-4 -0.037 0.001 0.244 0.060 -0.049 0.002

-0.172 0.029 0.072 0.005 -0.326 0.106 0.078 0.006

-0.52 0.271 -0.168 0.028 -0.347 0.120 -0.175 0.031

-0.37 0.135 0.950 0.903 0.015 0.000 0.961 0.924

-0.004 1 × 10-5 0.033 0.001 0.098 0.010 0.012 0.000

-0.567 0.322 -0.098 0.010 -0.534 0.285 -0.084 0.007

0.015 2 × 10-4 -0.230 0.053 -0.125 0.016 -0.203 0.041

0.106 0.011 -0.027 7 × 10-4 -0.176 0.031 -0.037 0.001

0.091 0.008 0.029 8 × 10-4 0.056 0.003 0.067 0.004

0.136 0.018 -0.005 2 × 10-5 -0.243 0.059 0.023 0.001

2.200 48 57 43 51 53 53 50 57 54 48 51 48 49 55 52 45 56 49 51 52

2.415 2.200 2.415 1690 1830 5190 3560 1940 4460 1650 5110 1800 5400 6300 1650 5190 2170 2460 2670 2380 4970 2740 3480

590 597 590 599 598 600 595 595 597 595 596 590 595 598 589 591 599 597 595 594

2510 2700 6140 4490 2830 5340 2490 6150 2580 6310 7010 2470 5900 3080 3510 3770 3410 5780 3860 4640

Significant parameters contributing the to uncertainty are highlighted in bold.

until 20 sets of the 10 input variables were formed. The ignition times were then calculated 20 times with the 20 different sets of input parameters. The mean and standard deviation of the ignition times were then calculated from the 20 sets of responses. A distinct LHS analysis was made for each new boundary temperature. Table 6 indicates that 1120 simulations were run in order to determine the mean ignition time as a function of the applied boundary condition for the ODTX and SITI experiments using LHS. The dispersion in the ignition times are presented using the range of the LHS runs. To measure the correlation strength or sensitivity of the ignition time, the standard linear correlation coefficient was computed for each of the uncertain input parameters, n

r)

∑

1 (t - µt)(yi - µy) n - 1 i)1 i σt × σy

(11)

where µt represents the mean or average computed ignition time in the n LHS runs; µy is the mean of the corresponding LHS input values for the uncertain variable y; σt and σy are the standard deviations of the response ignition time and input values. A perfect positive or negative linear correlation is |r| ) 1. A linear correlation strength is assumed significant when |r| > 0.5 or r2 > 0.25. Such judgments of r values depend on whether a linear model is a good fit of the simulation results. Examination of scatter plots of response versus parameter values is a good way to judge strongly organized linear or nonlinear relationship between the model parameters and the model response. Mean parameter values were used for individual SITI

runs. The LHS analysis was performed with a 10 min ramp to 30 different set point temperatures to evaluate uncertainty in the SITI predictions. ODTX and SITI Simulations. Figure 11 shows comparisons between predicted and measured ignition times for the ODTX and SITI experiments, respectively. For each experiment, three prediction lines are shown. The middle line represents the mean of 20 LHS samples for the ODTX and SITI simulations. The upper and lower lines represent the range of the 20 LHS simulations as discussed in the previous section. The measurements represent individual runs. The ODTX temperature is the temperature of the anvils. The SITI temperature is the set point temperature of the outer confinement. The temperature of the outer confinement was made to reach the set point temperature from room temperature in 10 min. The semilogarithmic plot of ignition time for the ODTX simulations versus the inverse temperature is fairly straight as observed by other researchers.2 However, the 10 min ramp causes the semilogarithmic plot of ignition time for the SITI simulations versus inverse temperature to be nonlinear. This happens since the boundary temperature is not hot enough to cause ignition until after the sample reaches the set point. The scatter plots show the correlation strength of the phase change temperature and liquid thermal conductivity to the ignition time when 1000/T is 2.415 and 2.2. Specific values of the input parameter multipliers used in the LHS analysis and the ignition time response for these two boundary conditions are given in Table 7. Clearly, the uncertainty in the phase change temperature affects the uncertainty when the boundary temperature is between 1000/T values of 2.35 to 2.45. This corresponds to temperatures ranging from 408 to 425 K, which is where the endotherm energy changes occur as shown in Figure 2D. The uncertainty is not with the values



TABLE 8: Percent Error in Predicted Ignition Time for SITI Experimentsa,b test No.

102

103

104

106

107

114

115

116

117

measured time, tm (s) calculated time, tc (s) error, 100(tc - tm)/tm

1546 1260 -18%

2760 2730 -1%

4064 4259 +5%

18964 18722 -1%

1705 1249 -27%

2735 2790 +2%

895 701 -22%

10717 11639 +9%

1831 1600 -13%

a n Root mean square deviation (rmsd) ) [(∑i)1 (tc - tm)2/n)]1/2 ) 384.6s. b Normalized root mean squared deviation (NRMSD) ) 100(RMSD/ (tmmax - tmmin)) ) 2.1%.

of the latent enthalpy, but is related to the reaction rate change as it increases due to liquefaction. The reaction rate multiplier correlates with the uncertainty for the ODTX simulations at 1000/T ) 2.20 but does not correlate with the uncertainty for the SITI simulations as shown by the correlation values in Table 7. SITI Internal Temperature and Pressure Predictions. Table 8 gives measured and calculated time-to-ignition as well

as the percent error for all of the SITI runs. The range of errors is from -26 to +9% with an average error of about -7%. The root mean squared deviation (rmsd) is 385 s, and the percent normalized rmsd is 2.1%. The small inset plot in Table 8 shows the measured ignition time plotted against the calculated ignition time with a linear correlation coefficient close to unity. Figure 12 shows the difference between the predicted and measured ignition times and internal temperatures for each of the nine

Figure 12. Predicted (black lines) and measured (green lines) internal temperatures at locations specified in Figure 7B for the SITI experiments. The red line is the control temperature. Predicted (cyan lines) and measured (blue lines) pressure for each SITI experiment also shown on each plot. The ignition time is indicated on each plot.

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Figure 13. (A) Maximum predicted conductive (Da,c) and storage (Da,s) Damko¨hler numbers in the detonator heated at various rates with ∂T/∂t being a field variable. (B) Maximum predicted Da,s and Da,c in the detonator with the boundary ramped to 155 °C and held. The red and green curves were calculated with ∂T/∂t being a field variable. The cyan and black curves were calculated with ∂T/∂t being unity. (C) Maximum predicted Da,s with ∂T/∂t being unity for various heating rates. (D) Reacted gas mass predicted when the boundary is ramped at various rates. The magenta symbol marks the time when the maximum storage Damko¨hler number (∂T/∂t ) 1) exceeds 20.

SITI runs. The time to ignition, set point temperatures, and initial bulk densities are indicated on the plots. The control thermocouple was on the outside boundary of the SITI apparatus. Test No. 103 was used to obtain the thermal conductivity parameters and the pre-exponential factor (Ln A). The light gray lines span the range of the endothermic processes occurring between 406 and 424 K. Most of the set point temperatures were within this range. Detonator Effectiveness. The detonator experiments are shown schematically in Figure 9. Violence was correlated with the maximum expansion of the copper confinement. Zucker et al.6 detonated the PETN in the copper confinement tube at room temperature with no preheating and found the expansion to be about 7.8 mm. The shapes of the copper confinement after ignition for the ramped experiments were teardrop shaped with the widest part near the bottom.6 This is in agreement with the predicted location of the ignition shown in Figure 9. The shape of the copper confinement after ignition for the “ramp and hold” experiment had the widest shape near the lead azide charge and was the least violent of all of the experiments. Zucker observed expansions of ∼8 mm when the heating rates were greater than 9.53 °C/min. For heating rates less than and equal to 9.53 °C/min, the cylinders only expanded ∼3 mm. A method was developed to predict the effectiveness of the detonators following ignition by computing dimensionless Damko¨hler numbers. The Damko¨hler number has been used traditionally to relate reaction time scales to other phenomena

occurring in a system. In the current work, a conductive and storage Damko¨hler number are defined as follows:

Da,c ) DaIV )

Fbhrr reaction time scale ) ) conduction time scale ∇(k∇T) hrr ∂T Cb - hrr ∂t

Da,s )

hrr reaction time scale ) storage time scale ∂T Cb ∂t

(12)

(13)

The conductive Damko¨hler number (Da,c) is traditionally referred to as the Damko¨hler Group IV (DaIV) number.31 The storage Damko¨hler number (Da,s) is useful to determine when the PETN reactions runaway. The conductive Damko¨hler number becomes unstable when ignition is approached. However, the storage Damko¨hler number is smooth up to the ignition point and is a better indicator of the onset of ignition. However, both the conductive and storage Damko¨hler numbers are unstable for boundary conditions where the boundary temperature is held at a set point temperature as shown by the red and green lines in Figure 13B. The excessive noise in the predicted maximum Damko¨hler numbers in Figure 13B is caused by small temporal temperature gradients. To avoid such noise, the conductive and storage Damko¨hler numbers were calculated with the temporal tem-



Figure 14. Contour plots of various Damko¨hler numbers at the onset of ignition for various heating rates.

perature gradients set to a constant value of 1 K/s and plotted in Figure 13B as cyan and black lines, respectively. Figure 13B shows that the storage Damko¨hler number was smooth, even at ignition when temporal gradient was set to 1 K/s. The conductive Damko¨hler number was still unstable near ignition. Figure 13C shows the calculated maximum storage Damko¨hler number when the temporal temperature gradient is set to 1 K/s for all of the ramped boundary conditions (colored lines) as well as the ramp and hold boundary conditions (gray line). All of the curves are smooth leading into ignition. The time when the maximum storage Damko¨hler number exceeds 20 can be used to predict the onset of ignition as shown in Figure 13C. Figure 13D shows the predicted reacted gas mass within the detonator when the boundary temperature was heated at rates of 5, 6, 7, 8, 10, 12, 14, 16, 18, and 20 °C/min. The reacted gas mass is the sum of the decomposition mass generated via reaction:

reacted gas mass ) mg ) F0c

∫Λ (1 - Sf)(1 - φ0)dΛ (13)

The reacted gas mass for the experiment with the boundary temperature ramped to 153 °C and held at 153 °C is also shown in Figure 13D. The magenta circles on each of the reacted gas mass plots represent the time that the maximum Damko¨hler number exceeds 20 as discussed previously. The reacted gas mass can be used to evaluate the overall extent of reaction as the detonator starts to ignite. Other metrics such as pressure rise can also be used to evaluate the extent of reaction at ignition. If the extent of reaction is low at ignition, such as below 2.5 mg in Figure 13D, then the reaction will be similar to an intentional detonation with full output of the detonator. If the extent of reaction is large at ignition (i.e., reacted gas mass is greater than 2.5 mg), then the detonator will have an output significantly less than the unheated intentionally initiated detonator. Another method to evaluate post ignition violence is to plot the Damko¨hler number at the onset of ignition. Figure 14 shows contour plots of the storage and conductive Damko¨hler numbers when the external boundary temperature is ramped at 5, 6, 7, 8, 10, 12, 14, 16, 18, and 20 °C/min. Although the Damko¨hler numbers calculated with ∂T∂t ) 1 are useful for predicting the onset of ignition, the Damko¨hler numbers determined with ∂T∂t determined as a field variable are more useful to determine the propensity to burn at ignition.

Figure 15. Color contour plots of temperature with elevated surface proportional to liquid reaction rates. The blue surfaces are at the onset of liquefaction and the red surfaces are liquid.

In Figure 14, the time of each contour plot corresponds with the time that the maximum storage Damko¨hler number exceeded 20. These are the times that are marked in Figure 13D with magenta circles. The contour plots of the Damko¨hler numbers with ∂T∂t ) 1 all look similar since the ignition takes place in the bottom corners of the detonator. However, for nonviolent detonator response, the conductiVe Damko¨hler number for most of the PETN is greater than unity, signifying that the reactive time scales are larger than the conductive time scales. The opposite trend is observed for the violent responses, where the conductive Damko¨hler number is primarily less than one at the time of ignition. The conductive Damko¨hler number may be useful to access the propensity of PETN to burn quickly once it ignites. Combustion events following ignition should be more violent when the propensity to burn is high at the time of ignition than if the propensity were small. The extent of decomposition at the time that the storage Damko¨hler number exceeds 20 should also give an indication of how close the state of the PETN is to the pristine PETN. For example, Figure 15 shows color contour plots of temperature with elevated surface proportional to liquid reaction rates. The violent responses occur when most of the PETN is solid. More experiments are needed to correlate reaction violence at the onset of ignition. Many hypotheses can be constructed based on predictions such as those in Figure 15. For example, liquid PETN may have leaked around the lead azide primer as the confinement metal expanded faster than the lead azide. Depletion of PETN from the detonator would result in less energy available for the post ignition burn. Depletion could also cause nonuniform combustion paths causing the detonator to dud. Careful experimentation in conjunction with detailed models is needed for better correlation of violence to thermal boundary conditions of interest. Correlating SITI Cookoff Violence with Preignition Damage. The violence of the SITI experiments should also correlate with the calculated state of the PETN at the time of ignition. In the previous section, the reacted gas mass was used to correlate the effectiveness of a PETN-based detonator. The threshold value of the reacted gas mass for the detonator was 0.25 mg. The threshold used for the detonator was developed for a specific geometry and confinement level, and is not applicable to other geometries using PETN. However, the approach used for the detonators should be applicable to other geometries if used with corresponding test data. Figure 16 show a plot of the reacted gas mass history for the SITI experiments. The plot in Figure 16 is similar to the plot in

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Hobbs et al.

Figure 16. Cookoff violence in SITI experiments correlated with the extent of reaction at the onset of ignition.

Figure 13.D, except the critical mass loss is 150 mg instead of 0.25 mg, reflecting the differences in mass between the SITI experiments and the detonators. In Figure 16, each colored line represents a different test. A picture of the post-test debris for each run is also shown in Figure 16. The colored circles represent calculated time when the storage Damko¨hler number (with the temporal temperature gradients set to unity, ∂T∂t ) 1 K/s) exceeds 20. The calculated state of the PETN in SITI test No. 104 and test No. 105 are also shown to the right of the plot in Figure 16 at the time of ignition. The purple surface indicates that for the nonviolent result, most of the PETN was in the liquid state. For the violent test, most of the PETN was in the solid state. The SITI experiments with reacted gas mass above 150 mg at the onset of ignition were not as violent as the experiments with reacted gas mass below 150 mg at ignition. The pictures of postignition debris show the nonviolent SITI experiments were broken in a few large pieces due to bolt failure. The violent SITI experiments resulted in the apparatus being broken in many small pieces. All of the SITI tests shown in Figure 16 were self-ignited via thermal runaway except for test No. 105, which was intentionally ignited. In test No. 105, the test was run near the end of the day and the boundary temperatures were manually increased to force the PETN to ignite early. Given more time for self-ignition, test No. 104 would have been nonviolent. But since it was intentionally ignited, the resulting debris indicates a violent response. Thus, the violence associated with both self-ignited PETN (as in the detonator simulations and most of the SITI simulations except for test No. 105) and intentionally ignited PETN (SITI test No. 105) can be correlated with the reacted gas mass. Summary and Conclusions Ignition of PETN was modeled using data based on observations from various experiments. PETN starts to decompose at relatively low temperatures (75 °C) before melting begins. PETN has two solid phase polymorphs (PETN I and PETN II) and melts (142 °C) at relatively low temperatures when compared to RDX (205 °C) or HMX (285 °C) but not as low as TNT (81 °C). The early onset of decomposition occurs before melting begins, and the frothy liquid is composed of bubbles filled with decomposition gases. Simultaneous decomposition with melting produced a two-phase frothy material with a gas-like thermal conductivity. DSC experiments show multiple endothermic processes occurring near the

melting point of PETN, which are modeled in the current work using an effective capacitance method. Decomposition of PETN was modeled with a single-step mechanism using a modified Arrhenius reaction rate. The reaction rate was assumed to be independent of pressure, and the activation energy was assumed to be normally distributed with respect to the reaction progress. The decomposition products were assumed to be in chemical equilibrium. The mean activation energy was taken to be the same as the activation energy used by Makashir and Kurian.17 The reaction rate in the liquid was assumed to be four times the reaction rate in the solid PETN. The melting point was used to transition the rates from solid-phase reaction rates to liquid-phase reaction rates. Reaction rate coefficients were fit using data from both the ODTX and SITI experiments. Initially, the coefficients were fit using a pressure dependent reaction mechanism using a (P/P0)n dependency. The pressure dependent rate expression did not fit the known ignition data any better than a pressure independent mechanism with (P/P0)n ) 1. Thus, the mechanism in the current work is assumed to be pressure independent. This is convenient since pressure does not need to be calculated to perform ignition calculations with the PETN mechanism described in the current work. This does not imply that PETN decomposition is pressure independent. Indeed, Lee et al.32 have shown PETN ignition to be pressure dependent in diamond anvils with static pressures between 10-50 kbars, which are much larger than the pressures measured in the current work. These pressures are also larger than critical pressures of decomposition products. Future work should determine if PETN decomposition is affected by confinement and pressure. Thermal conductivity at temperatures below reaction thresholds were obtained from the SITI experiments. Thermal conductivities at higher temperatures were determined using an effective thermal conductivity model that separates conductive heat transfer into three parts: conduction through the condensed PETN, conduction through the gas decomposition products, and radiation through the decomposing PETN. The optically thick radiation contribution to the conductivity was shown to be negligible since the PETN ignites just after melting when the temperatures are relatively low. Evolving gas volume fraction and bulk densities were calculated as field variables. Pressures were determined as an integral quantity by assuming the gas velocities were significantly less than sound speeds. Thus, pressure was assumed to be spatially constant but varies in time as the PETN decomposes.

PETN Ignition Experiments and Models Uncertainty in the decomposition model was determined using an LHS analysis of both the SITI and ODTX experiments. The parameter that affected the uncertainty in the ignition time the most was the melting point temperature. The melting point temperature was used to transition the reaction rates between solid and liquid reaction rates, which differed by a factor of 4. The uncertainty in the reaction rates also affected the ignition times for the ODTX experiments at high boundary temperatures. All of the ODTX and SITI data were within the range of the predictions using 20 LHS runs. The SITI data also included time-to-ignition data for vented powdered PETN, confined pressed PETN, and confined pressed PETN pellets that were one-eighth the volume of the typical SITI samples. Spatially and temporally resolved temperatures and thermodynamic pressure were also predicted and compared to data. The time to ignition varied between -27 and +9% with a normalized rmsd of 2.1%. The shape and magnitude of the pressure predictions matched the measured pressure data. The PETN model was validated by simulating thermal ignition of a detonator. The data for the detonator and estimate of reaction violence was presented by Zucker et al.6 The measured and predicted ignition times were extremely close. For example, the predicted and measured ignition time for the detonator ramped at 20 °C/min was 447 and 446 s, respectively. The model predicted the time-of-ignition and the location of ignition adequately. A method was presented to assess whether or not the detonator would function as designed (violent response) after thermal ignition or to function below design (dud). The method was to compare the extent of reaction, at the time that the calculated maximum storage Damko¨hler number exceeded 20, to a threshold value of 2.5 mg of reacted gas. If the reacted gas mass was below the threshold value at the onset of ignition, the detonator was predicted to have the same metal deforming output as the design mode expansion. If the reacted gas mass was above the threshold value at the onset of ignition, the detonator was predicted to be a dud. This simple empirical method may be useful to determine whether or not reactive components that contain PETN would fail to function during abnormal thermal events such as fire or would give the same metal deforming output as an intentionally ignited detonator. The estimate of violence worked well for the detonator described in the current work because the mass was small and the spatial temperature was fairly uniform. However, the specific reasons for violence were only speculated without experimental evidence. More work is needed to see if this technique could be applied to larger systems. A second method to evaluate violence was also investigated. The propensity of the PETN to burn violently at ignition was determined by calculating the conductive and storage Damko¨hler number at ignition as a field variable. If the conductive Damko¨hler number in most of the PETN was greater than unity at ignition then the resulting burn would be nonviolent. The PETN model does not predict violence. The PETN model predicts ignition based on thermal runaway. A modified storage Damko¨hler number with the temporal temperature gradient set to 1 K/s was used as a consistent method to predict the onset of ignition. When the maximum value of the storage Damko¨hler number exceeded 20, the calculation was near the ignition point. This criterion was shown to be valid for both ramped experiments and isothermal experiments. The state of the PETN at the onset of ignition gives the degraded state of the material which may be used to consistently compare ignition states to help determine if the subsequent burn will be violent or benign.

J. Phys. Chem. A, Vol. 114, No. 16, 2010 5319 Acknowledgment. Work was performed at Sandia National Laboratories (SNL). Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under Contract DE-AC04-94AL85000. I would like to thank Mel Baer for suggesting using Damko¨hler numbers to evaluate reaction violence; Craig Tarver and Tri Tran at Lawrence Livermore National Laboratory for supplying the ODTX data; Bob Patton (SNL) for the DSC data; Don W. Gilbert (SNL) for the SEMTEX beaker photographs; Bertha Montoya for the SEMTEX analysis; Bill Erikson and Dean Dobranich (SNL) for reviewing the article; and Terry Aselage and Imane Khalil (SNL) for management support. References and Notes (1) Kaneshige, M. J.; Renlund, A. M.; Schmitt, R. G.; Erikson, W. W. Twelfth International Detonation Symposium; ONR 333-05-2; Office of NaVal Research: San Diego, CA 2002, p 821. (2) Tarver, C. M.; Tran, T. D.; Whipple, R. T. Propellants, Explos., Pyrotech. 2003, 28, 189. (3) Zinn, J.; Mader, C. L. J. Appl. Phys. 1960, 31, 323. (4) Zinn, J.; Rogers, R. N. J. Phys. Chem. 1962, 66, 2646. (5) Merzhanov, A. G.; Abramov, V. G. Propellants, Explos., Pyrotech. 1981, 6, 130. (6) Zucker, J. M.; Dickson, P.; Sanders, V. E. Propellants, Explos., Pyrotech. 2009, 34, 142. (7) Ng, W. L.; Field, J. E.; Hauser, H. M. J. C. S. Perkin II 1976, 637. (8) Cady, H. H.; Larson, A. C. Acta Crystallogr. 1975, B31, 1864. (9) Gibbs, T. R.; Popolato, A.; Eds. LASL ExplosiVe Property Data; University of California Press: Los Angeles, CA, 1980; p 134. (10) Hobbs, M. L.; Kaneshige, M. J.; Gilbert, D. W.; Marley, S. K.; Todd, S. N. J. Phys. Chem. A 2009, 113 (39), 10474. (11) Dobratz, B. M., LLNL ExplosiVes Handbook Properties of Chemical ExplosiVes and ExplosiVe Simulants, Report DE85-01591; Lawrence Livermore National Laboratory: 1981; pp 19-126. (12) Hobbs, M. L.; Baer, M. R.; McGee, B. C. Propellants, Explos., Pyrotech. 1999, 24, 269. (13) Yinon, J.; Ed. AdVances in Analysis and Detection of ExplosiVes; Kluwer Academic Publishers: Netherlands, 1993; pp 409-427. (14) Erikson, W. W. Thirteenth International Detonation Symposium, Office of Naval Research ONR 351-07-01, Norfolk, VA, 2006; p 629. (15) Gibson, L. J.; Ashby, M. F. Cellular Solids Structure and Properties, 2nd ed.; Cambridge University Press: Cambridge, U.K., 1997; p 289. (16) Siegel, R.; Howell, J. R. Thermal Radiation Heat Transfer, 3rd ed.; Taylor & Francis: Washington DC, 1992; p 527. (17) Makashir, P. S.; Kurian, E. M. Propellants, Explos., Pyrotech. 1999, 24, 260. (18) Incropera, F. P.; DeWitt, D. P. Fundamentals of Heat and Mass Transfer, 5th ed.; John Wiley & Sons: New York, 2002; p 917. (19) Pitt, G. J. Fuel 1962, 41, 267. (20) Hobbs, M. L. Polym. Degrad. Stab. 2005, 89, 353. (21) Manelis, G. B.; Nazin, G. M.; Rubtsov, Y. I.; Strunin, V. A. Thermal Decomposition and Combustion of ExplosiVes and Propellants; Taylor & Francis: New York, 2003; p 12. (22) Manelis, et al., op.cit., p 24. (23) Manelis, et al., op.cit., p 129. (24) Roth, J. Pentaerythritol Tetranitrate, in Encyclopedia of ExplosiVes and Related Items, PATR 2700 8; Kaye, S. M., Ed.; US Army Research and Development Command, TACOM, ARDEC: 1978; p 111. (25) Bova, S. W.; Copps, K. D.; Newman, C. K. Calore: A Computational Heat Transfer Program; Sandia National Laboratories Report SAND2006-6083P; 2006; p 1. (26) Glicksman, L. R. Heat Transfer in Foams. In Low Density Cellular Plastics; Hilyard, N. C., Cunningham, A., Eds.; Chapman and Hall: London, U.K., 1994; Ch 5, p 104. (27) Catalano, E.; McGuire, R.; Lee, E.; Wrenn, E.; Ornellas, D.; Walton, J. Sixth Symposium (International) on Detonation; ONR ACR-221; Office of Naval Research: Coronado, CA, 1976; p 214. (28) Tran, T. D., Lawrence Livermore National Laboratory, private communication, 2008. (29) Zucker,J.M.,LosAlamosNationalLaboratory,privatecommunication,2009. (30) McKay, M. D.; Conover, W. J.; Beckman, R. J. Technometrics 1979, 21, 239. (31) Catchpole, J. P.; Fulford, G. Ind. Eng. Chem. 1966, 58 (3), 48. (32) Lee, E. L.; Sanborn, R. H.; Stromberg, H. D. Fifth Symposium (International) on Detonation, Report ACR-184; Office of Naval Research: Pasadena, CA, 1970; p 331.

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PETN Ignition Experiments and Models - The Journal of Physical

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