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HIGH-IRRADIANCE LASER IGNITION OF EXPLOSIVES

A. N. Alia; S. F. Sona; B. W. Asaya; M. E. Decroixa; M. Q. Brewsterb a Los Alamos National Laboratory, Los Alamos, New Mexico, USA. b University of Illinois at Urbana/Champaign, Champaign, Illinois, USA.

To cite this Article Ali, A. N. , Son, S. F. , Asay, B. W. , Decroix, M. E. and Brewster, M. Q.(2003) 'HIGH-IRRADIANCE

LASER IGNITION OF EXPLOSIVES', Combustion Science and Technology, 175: 8, 1551 — 1571 To link to this Article: DOI: 10.1080/00102200302358 URL: http://dx.doi.org/10.1080/00102200302358

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Combust. Sci. andTech., 175: 1551^1571, 2003 Copyright # Taylor & Francis Inc. ISSN: 0010-2203 print / 1563-521X online DOI: 10.1080=00102200390219416

HIGH-IRRADIANCE LASER IGNITION OF EXPLOSIVES

Downloaded By: [Purdue University] At: 20:00 9 August 2010

A. N. ALI, S. F. SON*, B. W. ASAY, AND M. E. DECROIX Los Alamos National Laboratory, Los Alamos, New Mexico, USA M. Q. BREWSTER University of Illinois at Urbana=Champaign, Champaign, Illinois, USA

A current issue important to high explosive safety is deflagration-to-detonation transitions (DDTs) in accident scenarios. In order to better understand the reactive mechanisms involved in DDT and to begin to approach the fast ignition and heating rates seen in DDT, high-irradiance (800 W=cm2) CO2 laser ignition experiments were performed on the common high explosives octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) and 1,3,5-triamino2,4,6-trinitrobenzene (TATB). Reported data include time to ignition as a function of laser irradiance, energy, and ignition temperature. A simple dual ignition criteria model (DICM) was used to interpret the HMX results. The DICM requires two basic criteria for ignition: (1) a minimum surface temperature must be reached and (2) a minimum energy concentration must exist within the solid. The DICM sucessfully predicted the slope transition trend and the critical ignition energy for HMX to within 10% of the measured values. TATB had a single dependence on irradiance over the entire range of heating rates. Keywords: ignition, laser, explosives, HMX, TATB, DDT Received 1 October 2001; accepted 18 March 2003. We acknowledge the support of Los Alamos National Laboratory under contract W7405-ENG-36. In particular, we acknowledge the support of the Laboratory Directed Research and Development Program of Los Alamos National Laboratory. *Address correspondence to [email protected] 1551

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INTRODUCTION There is currently an interest in improving the safety of high explosives (HE) by studying deflagration-to-detonation transitions (DDTs). DDT is a mechanism that can cause an explosive to detonate by friction, heat, compaction, or other accident scenario. DDT models have traditionally used the temperature field within the energetic material to determine if and when ignition occurs (Baer et al., 1986; Powers et al., 1990). However, the work presented in this article provides insight into the relevance of the amount of deposited energy as well as surface temperature states. The precise deposition of energy can be studied by laser ignition experiments, which allow thermal ignition without having knowledge of the material’s mechanical properties. Laser ignition experiments also allow control over many variables: power, total energy input, heating depth, and spot size. Laser ignition has been successfully used by other researchers to study ignition of energetic materials. (Ali et al., 1999a, 1999b; Assovskii and Leipunskii, 1980; Boggs et al., 1981; Brannon, 1981; Cohen and Beyer, 1993; Dik et al., 1991; Dimitriou et al., 1989; Forch et al., 1994; Harrach, 1975; Hasue et al., 1993; Kashiwagi, 1974; Kunz and Salas, 1987; Kuo et al., 1993; Lengelle et al., 1991; Mutoh et al., 1984; Ostmark, 1985; Ostmark and Grans, 1990; Ostmark et al., 1992, 1994, 1996; Park and Tien, 1994; Price et al., 1991; Vilyunov and Zarko, 1989). The laser ignition experiments in this work were conducted with CO2 lasers using thermal and photodiagnostics. Rapid heating was achieved with laser irradiance levels approaching 800 W=cm2. EXPERIMENTAL SETUP The explosives used in these experiments were octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) and 1,3,5-triamino-2,4,6-trinitrobenzene (TATB). The explosives were pressed into pellets 1 cm in diameter and 6.4 mm thick and no binder was used. A diagram of the laser ignition setup is shown in Figure 1. A HeNe laser was colinear with the CO2 laser beam and used for alignment of the optics and samples. The main laser beam was directed downward to the pellet surface by three goldcoated mirrors. This configuration was chosen to eliminate any threedimensional buoyancy effects. Two CO2 lasers were used, Edinburgh Instruments Ltd. PL-6 (180 Watt) and PRC Corp. SL 1000 (1000 watt). An NaCl window reflected


LASER IGNITION OF EXPLOSIVES

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Figure 1. Typical laser ignition setup showing the Molectron pyrometer, InSb IR detector with collecting lens and the photodiode.

approximately 8% of the beam into the pyrometer for monitoring the rise time of the laser power. The Edinburgh laser rise time was approximately 2 ms and the PRC laser rise time was 0.6 ms. The lasers were operated at a wavelength of 10.6 mm for all the experiments and the beam was TEMoo. The effect of the laser beam profile on ignition delay time was determined by comparing results from a clipped Gaussian beam profile (50% of the beam power) and a uniform, top-hat profile created using a beam integrator (Ali et al., 1999b). The ignition results for the two different beam profiles revealed no difference in the ignition delay in atmospheric conditions and for the irradiances less than 60 W=cm2. The Gaussian beam profile was used for these experiments due to the high optical losses associated with creating a top-hat profile. Diagnostics included photodiode, thermocouple, pyrometer, power meter, and video (high speed and 30 frames per second). A power meter fitted with 1-cm-diameter mask measured laser power incident on the pellet surface before each experiment. A photodiode (300 to 1100 nm, 10 ns) was positioned to collect emission above the pellet surface for ‘‘first light’’ measurement. A 25-mm type-S thermocouple measured the surface temperature during the ignition event. The thermocouple was centered on the energetic material pellet and secured to posts on either side of the pellet (Ali, 2000). The published rise time of thermocouple was 0.05 s in air and 0.002 s in water. The thermocouples were not expected to absorb appreciable amounts of laser energy. To confirm this, sample thermocouples were placed in a 180-W CO2 laser beam at 10.6 mm. No significant thermocouple response was observed.

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RESULTS AND ANALYSIS The purpose of this work was to provide experimental ignition data over a range of heating rates for high explosives using laser ignition. Figure 2 is an example of a laser ignition event for an HMX pellet (1-cm diameter) at an irradiance of 43 W=cm2. The sample surface is at the left of each image and the CO2 laser beam enters the image from the right. Ignition occurs off the sample surface in the pyrolized gas. The luminous flame kernel is visible in frame T ¼ 0 s. In subsequent frames, the flame ‘‘snaps back’’ to the surface and then establishes a steady flame off the surface. The gas-phase ignition by CO2 laser seen in the high-speed video is consistent with observed gas-phase ignition of HMX pellets heated by conductive and convective methods. Thermocouple traces from the low-power experiments allowed a comparison of the HMX and TATB surface heating. Figure 3(a) and 3(b) show that the ignition temperatures for HMX and TATB did not change significantly for the irradiances used in these experiments. HMX had an average ignition temperature of 377 C (650 K), which was lower than the average ignition temperature of TATB, 435 C (708 K). The lower ignition temperature of HMX is attributed to its lower decomposition temperature (HMX critical temperature is 253 C [526 K], compared to the critical temperature of TATB, 347 C [620 K, Gibbs and Popolato, 1980]). The micro-thermocouples did not respond fast enough to measure the surface temperature at high heating rates.

Figure 2. Laser ignition of a 1-cm-diameter HMX pellet at 43 W=cm2 (from high-speed video).

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Figure 3. Temperature profiles for the ignition of (a) HMX and (b) TATB at various irradiances. The ignition temperatures do not change significantly within the tested irradiance range and have average values of 377 C for HMX and 435 C for TATB.


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Ignition delay times are shown in Figure 4. The TATB times can be approximated over the entire irradiance range by a power curve fit with a slope of 1.43. However, the HMX data had two distinct trends: lowirradiance data had a slope of 2 and the high-irradiance data had a slope of 1. There was a region of high scatter in the HMX data from 50 to 100 W=cm2, which appears to be a transition region between the two slopes. Pantoflicek and Lebr (1968) developed a dual ignition criteria model (DICM) to explain radiant ignition experiments of ammonium perchlorate (AP; Fishman, 1967). The AP data exhibited the same trend as the HMX data in this work. Pantoflicek and Lebr proposed two ignition criteria to explain the AP data; minimum surface temperature (Ts) and minimum energy deposited in the solid. Criterion one, Ts ¼ Tign, is a temperature threshold that must be achieved for gasification of the

Figure 4. Ignition data up to 800 W=cm2 for HMX and TATB. The power fit through the TATB data has a slope of 1.43.



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condensed phase material and acceleration of the surface reactions past their collective high activation energies. For the second criterion, they used the steady-state burning thermal profile to define a critical energy, or an energy threshold within the solid that must be reached to sustain stable burning. Both criteria must be met for successful ignition. Consequently, the two criteria create two distinct ignition regions: a fixed-temperature region for low irradiances (where surface temperature is limiting) and a fixed-energy region for high irradiances (where energy within the condensed phase is limiting). Pantoflicek and Lebr also proposed a critical irradiance that marks the transition between the two regions and where the two criteria are met simultaneously. This is illustrated in AP experiments by Fishman, 1967; Hermance, 1984). The ignition model uses steady-state heat conduction combined with the steady-state burning thermal profile. For a semiinfinite solid with a constant irradiance or heat flux, the analytical solution to the heat equation is 2qðat=pÞ1=2 x2 qx x Tðx; tÞ ¼ erfc pffiffiffiffiffi þ T exp k k 4at 2 at

ð1Þ

where x is the depth within the solid phase (Carslaw and Jaeger, 1959). Equation (1) evaluated at the surface, x ¼ 0, is

Ts ¼

2q at1=2 þT0 k p

ð2Þ

where Ts is the surface temperature, T0 is the initial surface temperature, t is the time, q is the heat flux, k is the thermal conductivity, and a is the thermal diffusivity (Carslaw and Jaeger, 1959). The thermal diffusivity and conductivity are assumed to be constant. Equation (2) is solved for the ignition time as follows:

tign

p ðTs T0 Þk 2 ¼ 4a q

ð3Þ

From Eq. (3), log(t) is 2, which is shown by the low-irradiance HMX data in the fixed-temperature region in Figure 4. Also, the thermocouple traces for low irradiances in Figure 3(a) illustrates the fixed-

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temperature criterion. Ignition in the fixed-temperature region occurred when the surface temperatures reached Tign for all irradiances except 11.8 W=cm2. In that case, the surface temperature held at the ignition temperature for almost a second before ignition occurred. These experiments were done at ambient conditions, not in a vacuum. Consequently, ignition times at very low heating rates were sensitive to many external stimuli, such as room air currents, and ignition was delayed until the appropriate conditions were present in the gas phase. A critical energy can be derived from the steady-state burning thermal profile (Kubota, 1984): TðxÞ ¼ ðTs T0 Þ exp

rx a

þ T0

ð4Þ

where Ts is now the surface temperature during steady-state burning. The critical energy, Qc, is the thermal energy (above ambient conditions) contained within the condensed phase during steady-state burning: Qc ¼ rC

Z

0

ðTs T0 Þ exp

1

k Qc ¼ ðTs T0 Þ r

rCrx dx k

ð5Þ

ð6Þ

The ignition time in the fixed-energy region is the time required for the critical energy to be deposited in the solid at a given irradiance: tign ¼

Qc k ¼ ðTs T0 Þ qr q

ð7Þ

Therefore, in the fixed-energy region the slope of the ignition delay time versus irradiance is 1 on a log-log plot. This is consistent with the experimental data at high irradiances from this work shown in Figure 4. It is also consistent with Fishman’s AP data (Fishman, 1967). Combining Eq. (3) and (7) provides a method of calculating the critical irradiance, qc, which is the intersection point of the two irradiance lines: qc ¼

prk ðTs T0 Þ 4a

ð8Þ



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It should be noted that qc is a function of the burning rate. As the ambient pressure increases, the burning rate r, will also increase. This will cause the critical irradiance qc to increase and the critical energy Qc to decrease with increasing pressure as shown in Figure 5. This will make the ignition times within the fixed-energy region faster, but will move the boundary of the fixed-energy region to a higher critical irradiance, as seen in Fishman’s AP data (Fishman, 1967). This fixed energy can be easily seen in Figure 6, where the experimental ignition delay times are shown as a function of energy: laser irradiance multiplied by the ignition delay time. Figure 6 shows two distinct regions in the HMX data. The average energy in the fixed-energy region is 6.5 J=cm2.

Figure 5. Pressure trends from the model by Pantoflicek and Lebr (1968) to explain the radiant ignition results by Fishman (1967). The pressure increases such that P1 < P2 < P3 (Hermance, 1984).


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Using T0 ¼ 300 K, r ¼ 1.8 g=cm3, and values of 1.38 J=gK, 0.002 W=cm K, and 0.12 cm=s for C, k, and r, respectively, the predicted critical irradiance, qc, is 82 W=cm2. The calculated critical energy is 5.8 J=cm2, which is 10% less than the average measurement of 6.5 J=cm2. However, the experimental data were not corrected for reflection of the CO2 laser by the HMX surface. Isbell and Brewster (1998) measured a reflectivity of HMX at 10.6 mm of approximately 15%. The measured average energy corrected for reflectance would be 5.5 J=cm2. The predicted and measured values are in good agreement, but other possible sources of error may exist. Those may include the energy required for the phase transitions that are not included in the analysis but are believed to be significant, variable thermal properties (conductivity and diffusivity),

Figure 6. Ignition energies shown with the average ignition energy of 6.5 J=cm2 and the calculated energy of 5.8 J=cm2 from the dual ignition criteria model.


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and variable optical properties (emissivity, reflectivity, and absorption depth). Figure 7 illustrates the DICM regions with numerical solutions of the heat equation at three irradiances. Figure 7(a) shows transient temperature profiles from the start of heating to ignition at 650 K for an irradiance in the fixed-temperature region (low irradiance). By the time the

Figure 7. (a) Condensed-phase transient temperature profiles within the fixed-temperature region such that when the surface temperature reached Tign ¼ 650 K, the energy criteria were already met; (b) condensed-phase transient temperature profiles for the critical irradiance of 82 W=cm2 and the corresponding ignition time of 0.071 seconds. Note that the area under the heat equation curve and the steady-state burning profile are equal while the ignition temperature is still 650 K; (c) condensed-phase transient temperature profiles within the fixedenergy region. Surface heat-up continued past 650 K until the energy introduced to the condensed phase was equal to the area under the steady-state burning profile.


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Figure 7. (Continued)

surface temperature reached 650 K, the energy in the solid (area under the curve) had already exceeded the energy required for stable burning. Therefore, at low irradiance, the time required to meet the temperature threshold was the limiting factor for ignition. Figure 7(b) shows numerical results for the critical irradiance, qc, where the two criteria are met simultaneously. As the surface temperature reached the critical ignition temperature of 650 K, the energy deposited into the condensed phase simultaneously reached the threshold energy. Figure 7(c) shows results for irradiances in the fixed-energy region. For these high heating rates, insufficient energy was deposited to the solid in the time it took the surface temperature to reach 650 K. By the time the energy threshold was met, the HE surface temperature was predicted to



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Figure 7. (Continued)

be 1071 K. Therefore, the time to deposit sufficient energy for stable burning was the limiting factor for ignition at high irradiances. In reality, the surface temperature in the fixed-energy region would not be expected to rise nearly as high as predicted. The model does not account for phase transitions, pyrolysis, and other energy-removal mechanisms that would act to lower the surface temperature. However, due to the extremely fast nature of the ignition at high irradiances, it would be expected to see a slight increase in ignition temperature. More experiments need to be performed to confirm this effect. Figure 8 more concisely summarizes the dual ignition criteria using the model results for irradiances within the fixed-temperature region, at the critical irradiance, and within the fixed-energy region. It is seen that at


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Figure 8. Calculations of the surface temperature rise and energy rise at three irradiances, 50 W=cm2 (fixed temperature region), 82 W=cm2 (critical irradiance, qc), and 150 W=cm2 (fixed-energy region). Each line ends at the calculated ignition time. It is seen that at ignition in the fixed-temperature region the energy is greater than critical, at the critical irradiance the surface temperature and energy meet at the critical temperature and critical energy, and in the fixed-energy region the surface temperature is greater than critical.

only the critical irradiance do the temperature and energy reach their respective thresholds simultaneously. In the fixed-temperature region, the surface temperature is limiting, and in the fixed-energy region, the energy contained within the solid is limiting. Shown in Figure 9 is the DICM fit using the measured ignition temperature of 650 K for the fixed-temperature region, which is just the heat equation with surface absorption. It is seen that the heat equation predicts ignition times longer than the actual data. There are a few possible explanations for this discrepancy. Since the HMX is igniting



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Figure 9. The ignition delay vs. irradiance data are shown with the corresponding fit from the measured Qc of 6.5 J=cm2 and the calculated Qc of 5.8 J=cm2 from the dual ignition criteria model. The irradiance fits are created from the two critical energies by Eq. (7). The fixed-temperature region is fit by the heat equation.

faster than predicted, a possible assumption is that there is additional energy being introduced into the condensed or gas phase. This additional energy may come from exothermic reactions within the condensed phase or from the CO2 laser itself. The condensed-phase chemistry is not fully understood at this point, but it has been widely assumed that the condensed phase processes, such as phase transitions, are mostly endothermic. However, a recent numerical model by Liau and Lyman (1999) suggest that small amounts of lesser energy are absorbed by the gas phase. They found that the ignition delay is shorter when this gas-phase


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absorption is included than when it is not (Liau and Lyman, 1999). A second explanation may be that the shorter ignition delays are due to the fact that the experiments were performed in air. Kuo et al. (1993) showed that, for RDX-based propellants, the laser ignition delays of experiments occuring in a high-oxygen-concentration atmosphere (21%) are significantly shorter than those in a low-oxygen-concentration atmosphere (1%). A third explanation may be simply that there is some change in the material properties (thermal conductivity, heat capacity, burning rate, etc.) upon heating that is significant enough to offset the ignition delays predicted by the heat equation model from the actual data. However, this model is clearly useful in interpreting the given data. In addition to this model, another physical phenomenon, that of indepth absorption, was previously explored to explain the observed slope change in the data (Ali et al., 1999a). The heat equation was combined with Beer’s law describing in-depth absorption. It was numerically determined that an absorptivity coefficient of approximately 500 cm 1 seemed to best match our data, which was consistent with previously published measurements of 5672 cm 1 (Isbell and Brewster, 1998) and 180 cm 1 (Vilyunov and Zarko, 1989) for HMX irradiated by a 10.6-mm CO2 laser. While the in-depth absorption model did have a marked slope change at higher irradiances, it did not fit the overall 1 slope at higher irradiances or the slope transition, as well as the model presented in this article. However, it is clear that both of these phenomena play an important role in the ignition of HMX and perhaps the best model would be one that combined the two effects. An issue in applying this model to the experiments presented in this article is the fact that the model assumes a go=no-go ignition criteria, while the experiments presented in this article measured first light and the laser flux was not removed after ignition. However, when the data are compared to past experiments by Boggs et al. (1981; see Figure 10) where they conducted both first light and go=no-go experiments, it is seen that our data compare well with the go=no-go Boggs et al. data rather than the first light data. This may be due to differences in the sensitivity of the first light detector used. Our experiments used a photodiode sensitive to the visible spectrum that was only activated when a significant amount of visible-wavelength light was present. Therefore, the photodiode was only activated when strong, sustained burning was present (secondary flame reactions were present) such that a large amount of light was generated. This would seem to correlate better with a go=no-go ignition criteria.



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Figure 10. Comparison of HMX ignition data with previous ignition data from Vilynov and Zarko’s book Ignition of Solids (Vilyunov and Zarko, 1989) citing Strakovskii et al. (1977) and Boggs et al. (1981). Both the Edinburgh and PRC data match up with this previous data. It is interesting to note that there is little difference between the Boggs first light data and the Boggs go=no-go data except that the go=no-go data begins to deviate from the rest of the data at high irradiances.

The data presented in this article are also shown with CO2 laser ignition data taken by Strakovskii et al. (1977) and cited by Vilynov and Zarko (1989; see Figure 10). The Strakovskii et al. data points compare well overall, but they do not display the slope change seen in experiments reported in this article. However, the specific experimental conditions present during the Strakovskii et al. tests are not clear and so it is not possible to draw any further conclusions concerning the comparison of


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the different data sets. Furthermore, there are only two data points in the low-irradiance region. Ostmark (1985) had also observed the phenomenon of a fixed energy in his laser ignition experiments using a pyrotechnic mixture containing Mg and NaNO3. His data showed a logarithmic decrease in the energy with a decrease in pulse width until a critical energy was reached. For pulse widths less than that at the critical energy, the ignition energy is a fixed 2.1 J=cm2. This is similar to our observation of a fixed energy for irradiances greater than the critical irradiance (or resulting ignition times less than the ignition time at the critical irradiance). Ostmark creates a model based on the heat flow equation such that the critical energy is a function of the absorption depth of the laser, the heat capacity, the density, and a fixed ignition temperature. His model does not account for any change in the critical energy with the pressure even though his data in a subsequent paper (Ostmark and Grans, 1990) show that the ignition energy is strongly dependent on pressure. Our model will account for the decrease in the critical energy with increasing pressure through an increase in the burn rate with pressure. The ignition energies for TATB, shown in Figure 4, do not appear to undergo any transition. Model results for TATB are a calculated critical irradiance of 5.3 W=cm2. For these calculations burn rates were extrapolated from high-pressure burn rate data and values of 1.86 g=cm3, 2 J=gK, and 0.0046 cm=s were used for r, C, and r, respectively (Son et al., 1999). Thus, the data range tested in this work lies within the energy threshold region and the slope of the data should be 1 on the ignition time versus irradiance plot. The best fit for the TATB data in Figure 4 had a slope of 1.43. It is not clear why TATB does not match the predicted slope of 1 like HMX and AP. However, this difference may derive from the significant differences in combustion properties (burning stability at atmospheric pressures, layer of solid decomposition products on surface, etc.) of TATB compared to other energetic materials. It may be expected that any material that does not burn stable under testing conditions will not follow the predictions of this model due to an unsteady burning thermal profile. SUMMARY AND CONCLUSIONS Laser ignition experiments with CO2 laser irradiances of up to 800 W=cm2 were performed on the high explosives HMX and TATB.



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Surface temperature measurements for irradiances less than 55 W=cm2 revealed that HMX ignited at a fixed surface temperature of 377 C (650 K), while TATB ignited at a fixed surface temperature of 435 C (708 K). The difference between the ignition temperatures is attributed to the lower decomposition temperature of HMX. Two different ignition delay trends were observed over the range of irradiances. On a log-log plot, the slope of the data was 2 at low irradiances and at high irradiances the slope was 1. The transition between the two slopes was sharp and occurred somewhere between 50 and 120 W=cm2. The slope of 1 corresponded to a fixed energy of 6.5 J=cm2. The HMX ignition data reported in this work compare well with previous ignition work. The DICM described by Pantoflicek and Lebr defines the slopes of both the fixed-temperature and fixed-energy regions and defines the irradiance transition point, qc, between the two regions. The DICM predicted a critical energy of 5.8 J=cm2 in the energy threshold region, which is only a 10% deviation from the measured energy of 6.5 J=cm2. When reflectivity is accounted for in the energy measurements, the DICM error for the calculation of the critical energy is further reduced. The DICM model predicts high surface temperatures within the fixed-energy region. This problem may possibly be corrected by including a burn rate that is a function of irradiance and accounting for energy loss through gasification of the condensed phase during the ignition event. These results are significant because they call into question the traditional solid modeling assumption of using only a surface-temperature ignition criteria at high heating rates. Future work should include investigating the use of an energy-based criteria in DDT modeling, since this would be appropriate for the typical heating rates in compaction waves. Further experimental conditions will involve high pressures and large dissipative heating rates at irradiances greater than 100 W=cm2.

REFERENCES Ali, A.N. (2000) High explosive ignition dynamics. In Mechanical Engineering. University of Illinois at Urbana=Champaign, Champaign, IL, p. 151. Ali, A.N., Son, S.F., Asay, B.W., Sander, R.K., and Brewster, M.Q. (1999a) Laser Ignition of High Explosives. JANNAF, Cocoa Beach, FL. Ali, A.N., Son, S.F., Asay, B.W., Sander, R.K., and Brewster, M.Q. (1999b) Ignition Dynamics of High Explosives. 37th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV.


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Assovskii, I.G. and Leipunskii, O.I. (1980) Theory of ignition of fuels by light pulses. Fiz. Goren. Vzryva, 16, 3–10. Baer, M.R., Gross, R.J., Nunziato, J.W., and Igel, E.A. (1986) An experimental and theoretical study of deflagration-to-detonation transition (DDT) in the granular explosive, CP. Combust. Flame, 65, 15–30. Boggs, T.L., Price, C.F., et al. (1981) The Role of Gas Phase Reactions in the Deflagration-to-Detonation Transition of High Energy Propellants. 7th Symposium on Detonation, Annapolis, MD. Brannon, P.J. (1981) CO2-Laser Ignition of Dapp Targets. Sandia National Laboratory report SAND81-1403. Carslaw, H.S. and Jaeger, J.C. (1959) Conduction of Heat in Solids, Clarendon Press, Oxford. Cohen A. and Beyer, R.A. (1993) Laser Ignition of Solid Propellents: Ignition Delays. Army Research Laboratory report ARL-TR-162. Dik, I.G., Sazhenova, E.A., Selikhovkin A.M. (1991) Role of the gas phase in the transition of condensed material to combustion on ignition by a radiation flux. Fiz. Goren. Vzryva, 27, 7–12. Dimitriou, P., Hlavacek, B., Valone, S.M., Behrens, G.P., Hansen, J., and Margrave L. (1989) Laser-induced ignition in solid-state combustion. AIChE J., 35, 1085–1096. Fishman, N. (1967) Surface exotherm during ignition of ammonium perchlorate propellants. AIAA J., 5, 1500–1501. Forch, B.E., Barrows, A.W., et al. (1994) Trends Observed in the Laser Ignition of Black Powder and JA2 Propellant. Army Research Laboratory. Gibbs, T.R. and Popolato, A. (1980) LASL Explosive Property Data. University of California Press. Harrach, R.J. (1975) Estimates on the Ignition of High-Explosives by Laser Pulses. Lawrence Livermore Laboratory report UCRL-77125. Hasue, K., Khono, H., et al. (1993) Initiation of Some Explosives by Irradiation of CO2 Laser. Japanese National Defense Academy. Hermance, C.E. (1984) Solid-propellant ignition theories and experiments. In K.K. Kuo, (Ed.) Fundamentals of Solid-Propellant Combustion, American Institute of Aeronautics and Astronautics. New York, Vol. 90, pp. 247–250. Isbell, R.A. and Brewster, M.Q. (1998) Optical properties of energetic materials: RDX, HMX, AP, NC=NG and HTPB. Propell. Explos. Pyrot., 23, 218–224. Kashiwagi, T. (1974) A radiative ignition model of a solid fuel. Combust. Sci. Technol., 8, 225–236. Kubota, N. (1984) Survey of rocket propellants and their combustion characteristics. In K.K. Kuo (Ed.) Fundamentals of Solid-Propellant Combustion, American Institute of Aeronautics and Astronautics, New York, Vol. 90. Kunz, S.C. and Salas, F.J. (1987) Diode Laser Ignition of High Explosives and Pyrotechnics. Sandia National Laboratories.



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Kuo, K.K., Kim, J.U., Fetherolf, B.L., and Torikai, T. (1993) Preignition dynamics of RDX-based energetic materials under CO2 laser heating. Combust. Flame, 95, 351–361. Lengelle, G., Bizot, A., Duterque, J., and Amiot, J.-C. (1991) Ignition of solid propellants. Rech. Aerosp., 2, 1–20. Liau, Y.-C. and Lyman, J.L. (1999) Modeling Laser-Induced Ignition of Nitramine Propellants with Condensed and Gas-Phase Absorption. 37th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV. Mutoh, N., Hirano, T., and Akita, K. (1984) Experimental Study on Radiative Ignition of Polymethylmethacrylate. University of Tokyo. Ostmark, H. (1985) Laser as a Tool in Sensitivity Testing of Explosives. 8th Det. Symp., Albuquerque, NM. Ostmark, H. and Grans, R. (1990) Laser ignition of explosives: Effects of gas pressure on the threshold ignition energy. J. Energ. Mat., 8, 308–322. Ostmark, H., Bergman, H., and Ekvall, K. (1992) Laser pyrolysis of explosives combined with mass spectral studies of the ignition zone. J. Anal. Appl. Pyrol., 24, 163–178. Ostmark, H., Carlson, M., and Ekvall, K. (1994) Laser ignition of explosives: Effects of laser wavelength on the threshold ignition energy. J. Energ. Mat., 12, 63–83. Ostmark, H., Carlson, M., and Ekvall, K. (1996) Concentration and temperature measurements in a laser-induced high explosive ignition zone. Part I: LIF spectroscopy measurements. Combust. Flame, 105, 381–390. Pantoflicek, J. and Lebr, F. (1968) Comments on ‘‘Surface exotherm reaction during ignition of ammonium perchlorate propellants’’. AIAA J., 6, 1435– 1436. Park, S.H. and Tien, C.L. (1994) Radiation induced ignition of porous solid fuels. Combust. Sci. Technol., 95, 173–192. Powers, J.M., Stewart, D.S., and Krier, H. (1990) Theory of two-phase detonation — Part I: Modeling & Part 2: Structure. Combust. Flame, 80, 264–279. Price, C.F., Atwood, A.I., and Parr, T.P. (1991) The role of external radiation in the NWC combustion model. JANNAF Combust. Son, S.F., Berghout, H.L., et al. (1999) Burn Rate Measurements of HMX, PBX 9501, TATB, PBX 9502, DHT, DAAF and BTATz. JANNAF, Cocoa Beach, FL. Strakovskii, L.G., Ulyakov, P.I., et al. (1977). Combustion of Condensed Systems (in Russian). Chernogolovka, Division of the Institute of Chemical Physics. Vilyunov, V.N. and Zarko, V.E. (1989) Ignition of Solids, Elsevier Science, New York.