CP620, Shock Compression of Condensed Matter - 2001
edited by M. D. Furnish, N. N. Thadhani, and Y. Hone
© 2002 American Institute of Physics 0-7354-0068-7/02/$ 19.00
NUMERICAL SIMULATION ON LASER INITIATION
OF THIN EXPLOSIVE
Shiro Kubota1, Kunihito Nagayama2, Hideki Shimada1 and Kikuo Matsui1
1
Department of Earth Resources Engineering, Faculty of Engineering,
Kyushu University, Fukuoka, 812-8581, Japan
2
Department of Aeronautics and Astronautics, Faculty of Engineering,
Kyushu University, Fukuoka, 812-8581, Japan
Abstract The processes of the laser initiation of pentaerythritol tetranitrate (PETN: density l.Og/cc)
are calculated using one-dimensional hydrodynamic code to study the effects of the initiation methods
on the initiation process. The simplified assumptions for the initial condition are used to model the three
types of the initiation method, utilizing direct absorption of laser energy, impact of the laser driven-flyer
plate and ablation of the metal film. The governing equations are Lagrangian conservation equations and
are solved by a finite difference method. The reaction rate law is used the ignition and growth model.
servation equations and are solved by a finite difference
scheme. The reaction rate law of the high explosive used
is the ignition and growth model. For both the detonation
products and the unreacted solid explosive, the JWL equation of state is used.
INTRODUCTION
There are three types of the initiation methods of the explosive utilizing pulse laser energy. The first one is the
direct absorption of the laser beam to the explosive surface,
the second one is the impact of the laser-driven flyer plates
and the last one is the utilization of ablation of metal film
by laser irradiationlj 2. In this paper, the processes of the
laser initiation of pentaerythritol tetranitrate (PETN: density l.Og/cc) are calculated using a one-dimensional hydrodynamic code to study the effects of the initiation
methods on the initiation process. The simplified assumptions for the initial conditions of numerical simulations are
used in these calculations. Because the explosive instantaneously absorbs the laser energy without a density change,
the absorption process is ignored, and the initial energy
distribution of the high explosive is assumed to follow
Lamber's law. As the model for the ablation of aluminum
film, the extremely high energy is deposited in the calculation field of very thin aluminum film contacted with the
explosive. The governing equations are Lagrangian con-
NUMERICAL TECHNIQUE AND
INTIAL CONDITION
The processes of the laser initiation are calculated by
solving Lagrangian conservation equations together with
the reaction rate law which determines the reaction rate
1; A, =0 is the unreacted stale and A, =1 is the completely reacted state. The ignition and growth model proposed by Lee and Tarver (1980)3 is adopted for reaction
rate law. The explosive parameters of the reaction rate law
are determined so that the results from numerical simulation agree with the experimental data for shock initiation
of the explosive. In this calculation, to obtain these parameters the least square fit to experimental data4 for
PETN at a density of l.Og/cc was used The equations of
468
direct absorption are shown in Figure 1 and Figure 2, respectively. The contribution of the coefficient of absorption to initiation process of the explosive is explored
Although the acceleration process of the laser-driven
flyer plate includes many complicated phenomena, the
initial velocity is simply applied to the aluminum film
contacting the left end of PETN, as the initial condition for
the impact problem of the laser-driven flyer plate. This
velocity is set so that the sum of the energy of the film is
equal to that of the direct absorption case in the explosive.
In the case of the ablation of the metal film, very high
internal energy is set with the 500nm aluminum film between PMMA and the left end of PETN as the initial condition.
state for condensed and reacted phases of explosive are
necessary to describe the mixture in any rate of 1. For
both phases, the JWL equation of stale is used The values
of JWL parameters of PETN(1.0g/cc) for both solid and
gas phases are used the values in the reference 3.
Since the absorption of pulse laser energy to the explosive surface is assumed to be completed instantaneously,
Lamber's law is applied to obtain the initial energy distribution of the explosive layer immediately after the irradiation of pulse laser. The initial energy distribution for the
explosive layer that absorbs the energy of pulse laser is
expressed by
/(*) =
l-exp(jj L)
exp(jJ x)
NUMERICAL RESULTS AND DISCUSSION
where the I(x) is the internal energy per unit length at the
position x, ep is the pulse energy divided by the cross section of laser beam, and JLL =1/1 is the coefficient of absorption. In this calculation, we set the total energy, equal to the
output pulse energy of the laser of 3J, and the diameter of
focused beam is 2mm.
PETN1.0g/cc
3(J) l=2.5e-4 (mm)
Pcj= 8.5904(GPa)
O
x=0
Ax=0.01mm
PMMA
PETN
PMMA
0.5mm
0.5mm
0.5mm
Figure 1. Calculation field in the case of direct absorption
£.
8.4
Initial condition 3(J)
\
(0
\
Q.
i
^
\
n 1• i
i
(/>
v i
£
I (mm)
K n<*—A.
——— . 2.5e-4
_._._. i.Oe-4
1.2
1.6
2
Figure 3. The particle path on p-v plane along the three
particles in the case of direct absorption (H2.5e-4 mm)
The pressure P, specific volume v and mass fraction of
detonation product A are observed along three particles
that are located in the explosive. The first particle is initially 0.05 mm from the left end of the PETN, second one
is middle point, and third is 0.05 mm from the right end.
The loci of the P-v relation along the three different particles in the case of l=2.5e-4 mm are shown in Figure 3. In
this figure, the dotted line corresponds to the particle path
near the left end, the dashed line is the middle particle and
dot dashed line is the particle near the right end of PETN.
The two solid lines are the Hugoniot curve of unreacted
PETN and isentropic curve of completely reacted PETN.
•\\
CL
0.8
Specific volume (cc/g)
n
0.05
0.1
Position (mm)
0.15
Figure 2. Initial pressure distribution near the left end of
PETN in the case of direct absorption
The calculated field and initial pressure distribution near
the end of the initiation surface of PETN in the case of
469
3(J) l=2.5e-4 (mm)
PETN1.0g/cc
3(J) l=1.0e-4(mm)
Si
o
Pcj= 8.5904(GPa)
I
0.5
8.4
Time (p s)
^
(a) Particle near the left end of PETN
1.2
1.6
2
Figure 5. The particle path on p-v plane along the three
particles in the case of direct absorption (1=1 .Oe^4 mm)
3(J) l=2.5e-4(mm)
At the position in which the steady detonation occurs, the
locus of P-v relation trace the simple path, the pressure
rises along the Hugoniot line up to the spike point, and
then falls along the Rayleigh line to the C-J point In contrast, at the point where the reaction mode is deflagration,
the particle path is relatively complicated on the P-v plane.
Furthermore, when the both ends of the explosive have
boundaries as this calculation of thin explosive initiation,
the particle path becomes more complicated Figure
4(a)-(c) indicate the pressure and mass fraction profiles at
these three different particles. The pressure of the particle
near the left end of PETN increased the instant PETN
absorbed the laser energy, however, the reaction at this
particle has not progressed yet (Figure 4(a)). After about
50ns, the pressure wave from the left end of PETN
reaches the particle and, the reaction of this particle starts.
Because of the lack of the energy in the DDT process, the
reaction progress is relatively slow. When the reaction
wave reaches the particle near the right end of PETN
(Figure 4(c)), the pressure is higher than initial maximum
pressure in PETN due to effect of decomposition of PETN.
Immediately after, the pressure at this particle raises again
due to arrival of the reflected wave from the right hand
side PMMA. After this reflected wave, which is accompanied by the growth of reaction arrival at the intermediate
particle(Figure 4(b)), the reaction rate at this particle becomes higher and almost the same as that in the region of
the right end particle.
In the case of a higher coefficient of absorption,
l=1.0e-4 mm, the particle path on the P-v plane is shown
in Figure 5. The particle path near the right end can not
Time QJ s)
Intermediate particle
3(J) l=2.5e-4(mm)
Si
o
0.5
0.8
Specific volume (cc/g)
1
Time (p s)
(c) Particle near the right end of PETN
Figure 4. Pressure and mass fraction profiles in the case of
the direct absorption (l=2.5e-4 mm)
470
trace the path for steady detonation, but the path becomes
close to it From the comparison of Figs 3 and 5, the absorption rate gives the contribution for the energy release
rate of the explosive, and a high absorption rate causes
rapid initiation. Figure 6 (a) and (b) show the results of
impact problems with flyer thickness 200 y. m and 15 y. m,
respectively. Because the impact velocity increases as the
flyer thickness decreases, the local pressure in the explosive becomes higher as the thickness decreases. As in the
case of 15 p. m thickness flyer, the particle path approaches
steady detonation on each particle.
At the right end particle, both particle paths become that of
steady detonation, and another particles completely
decomposed without the effect of reflected wave from left
hand side PMMA. Although in both cases, the impact
velocity is greater than the particle velocity at C-J point
(about 1.5km/s), the path of the intermediate point does
not trace the path for the steady detonation. Moreover, in
the 15 fj. m case, the locus of shock front on the x-t diagram indicates the formation of an overdriven detonation.
Figure 7 corresponds to the ablation cases. Although the
initial pressure in aluminum is extremely high, after
0.05mm propagation of shock wave, the pressure at the
shock front falls to 4GPa. During propagation to the
intermediate particle, the decomposition of PETN can not
affect the shock front, so the degradation of pressure continues. In this case, the effects of the reflected wave from
the PMMA boundary are observed on each particle.
200p m Al impact with u=0.185 cmf\i s
PETN1.0g/cc
Pcj= 8.5904(GPa)
CO
4
0.8
1.2
1.6
o_
O
2
Specific volume (cc/g)
(a) 200/zmAl
15p m Al impact with u=0.676 cm^j s
0.8
PETN 1.0g/cc
Pcj= 8.5904(GPa)
1.2
1.6
2
Specific volume (cc/g)
Figure 7. The particle path on p-v plane along the three
particles in the case of ablation of aluminum
REFERENCES
0.8
1.2
1.6
1. Watson, S., Gifford, M. J., and Field, J. E., Journal of
Applied Physics, 88,65-69(2000)
2. Paisley, D. L., 9th Symposium (International) on
Detonation, Office of Naval Research, Portland, OR,
1989, pp. 1110-1117
3. Lee, E. L., andTarver, C. M., Physics of Fluids 23,
2362-2372(1980)
4. Cooper, P. W., 1 Oth Symposium (International) on
Detonation, Office of Naval Research, Boston, MA,
1993,pp.690-695
2
Specific volume (cc/g)
(b) 15/zmAl
Figure 6. The particle path on p-v plane along the three
particles in the case of impact problem of aluminum
471