CP620, Shock Compression of Condensed Matter - 2001
edited by M. D. Furnish, N. N. Thadhani, and Y. Horie
© 2002 American Institute of Physics 0-7354-0068-7/02/$ 19.00
STEADY-STATE MODEL OF HETEROGENEOUS DETONATION
WITH INERT PARTICLES
Alexander Gonor1, Irene Hooton2' Shankar Narayan3
Applied Science & Engineering Consulting, 624-523 Finch Avenue West, Toronto, ON Canada M2R 1N4
2
Defence Research Establishment, PO 4000, Medicine Hat, AB Canada T1A 8K6
3
Adsorption Technology Consultant, 78 Stonemeadow Drive, Kanata, ON Canada K2M 2M3
Abstract. A comprehensive, 1-D model of steady-state detonation of a condensed explosive with inert
particles was developed. The interaction between the particles and leading shock wave front was
described by a novel approach accounting for the penetration of a single particle through the shock wave
and generalized jump conditions on the leading shock wave. Results for the detonation of RDX and
inert aluminum particles, 0.1 and 5 microns in diameter, with mass fractions in the range of 0 to 40%
were obtained. The theory predicts that the detonation velocity can increase or decrease with the
addition of 5-micron inert particles depending on the EOS of the explosive. The detonation velocity of
the mixture decreased with increasing 0.1-micron particle mass fraction.
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INTRODUCTION
The heterogeneous detonation of a condensed
explosive/inert particle mixture was studied to
improve understanding of the mechanical and thermal
interaction between the explosive, detonation
products and particles without considering particle
combustion. In addition, reactive particles behave as
inert material throughout most of the reaction zone.
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FIGURE 1. Schematic of reaction zone
parameters of a particle, it is necessary to consider
the process of particle penetration in this layer,
which will be conventionally, called the layer of
particle immersion. Thus, the structure of the
heterogeneous detonation wave becomes more
complicated and will consist of the shock wave for
the carrying phase, where the jumps in velocity,
temperature and density of a particle and, also
additional changes to parameters of the carrying
phase will take place. The shock wave and the
immersion layer in the full model are regarded as a
single surface of discontinuity.
The process of the combustion reaction of the
primary explosive, with the decomposition of the
condensed phase into a gaseous state, takes place in
area (3), the right boundary of which coincides with
the plane where the generalized C-J conditions are
DESCRIPTION OF THE GENERAL SCHEME
OF THE BASIC MODEL
The 1-D structure of the heterogeneous
detonation model is considered (Fig. 1). The front
part of the structure is the leading shock wave (1),
propagating in the condensed medium. Metallic
particles, which pass through the shock wave, obtain
new velocity and temperature values as a result of
compression and acceleration on the shock wave.
The processes of fast acceleration of the particles
and their heating in the shock wave actually takes
place in a layer approximately one particle diameter
in width (Fig. 1, (2)).
To determine new values of the characteristic
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fulfilled. Here, the combustion reaction of the
metallic particles also begins in the multi-component
flow of the detonation products. The combustion
zone of the metallic particles extends to the area of
low-velocity flow (4).
To describe the above-mentioned processes, a
three-phase, two-velocity, two temperature, multicomponent one-dimensional model for mixtures of
condensed explosives (nitromethane, RDX, etc) with
metallic particles was developed.
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INTERACTION OF METALLIC PARTICLES
WITH THE LEADING SHOCK WAVE
FIGURE 2. Dependence of Ti1 on D
on the dispersed phase, as the leading shock wave
passes through them, should be considered
significant for all parameters of the dispersed phase.
As shown in Fig. 3, the absolute particle velocity
(u2x) reduces significantly (25-35%) as the leading
shock wave passes through it.
The particle
temperature increases 2 to 5 times its original value
as the leading shock wave passes through it, and
reaches ~1500°K at high values of detonation
velocity (~8000 m/s). These results were obtained
for RDX using n=4 and n=7 in the Tait EOS.
The problem of unsteady-state penetration of a
spherical particle into a liquid (solid) half-space
bounded by a shock wave is a separate, complicated
problem of the numerical integration of twodimensional unsteady-state equations of fluid
dynamics. Our task was to find a simple approach
connecting the final velocity of the particle and its
temperature behind the shock wave with the
characteristic parameters of the whole problem:
detonation velocity, characteristics of the condensed
medium, etc. Therefore to estimate the parameters
of the particle and the flow behind the leading shock
wave, a 1-D method based on the break-up of
arbitrary discontinuity and mass, momentum and
energy balance equations on the shock wave was
used. This approach involved writing the five
balance equations on the leading shock wave, two
Tait equations of state (EOS) for the carrier and the
dispersed phases, and the equations, describing the
penetration of the particle through the shock wave.
Overall, nine equations were obtained for nine
unknown parameters («/, «2> P-> TI, T2, pi, p2, n^ and
a/) to determine their dependence on the detonation
velocity, D, and the particle mass fraction, m2.
To start with, the influence of the interaction of
the particle with the shock wave on the parameters
of the carrier phase is considered. An increase in
the particle mass fraction (m2) results in a small
increase in flow velocity (ui1) and pressure (p).
However, the addition of particles increases the flow
temperature (Ti1) significantly, as shown in Fig. 2,
where the sonic velocities C 10=2000 and 2300
correspond to RDX densities p = 1.0 and 1.4 g/cm3,
respectively.
On the other hand, the effect of the carrier phase
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FIGURE 3. Dependence of u2* on D
ON SYSTEM OF GOVERNING EQUATIONS
OF MULTI-PHASED FLUID DYNAMICS
The 1-D steady-state motion of a mixture,
containing liquid (condensed), gaseous and solid
phases, is considered. Using the basic assumptions
of the dynamics of multi-phase reaction media1'2,
the equations of mass, momentum and energy
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balance were written in the system of coordinates
with a fixed shock wave. As a result, the system of
equations was reduced to an ODE-system with
respect to independent variable x (Fig. 1), that was
completed by the Tait EOS and the detonation
products EOS3. To obtain the numerical solution,
the "shooting" method, for different values of
detonation velocity, was used.
particles. The pressure, as a result of the interaction
of the particles with the flow, seems to exceed the
Neumann spike substantially.
The most unexpected result from the model is the
apparent increase in the detonation velocity with an
increase in the concentration of 5-um diameter inert
particles (Fig. 4). The distribution of (carrier phase)
flow-temperature, as shown in Fig. 5, can be used to
explain this unexpected behavior.
MODEL RESULTS FOR MIXTURES OF RDX
CONTAINING MICRON- AND SUBMICRONSIZED INERT PARTICLES
Calculations were carried out for the detonation
of RDX (p = 1.0 and 1.4 g/cm3) containing 5-um
and 0.1-um diameter Al particles with mass
fractions, m2, of 0.1, 0.2, 0.3 and 0.4. Comparison
of the distributions of the flow field for detonations
without particles (m2 = 0.0) and with particles (m2 =
0.1 - 0.4), shows that the addition of inert particles
increases the flow velocity (ui) in the front part of
the reaction zone, and significantly reduces the
width of the reaction zone. The distribution for the
particle velocity (u2) seems to indicate that the
particle velocity approaches the flow velocity (u^.
However, the velocity difference, particularly for
high particle concentrations (m2 > 0.2), remains
noticeably significant up to the C-J plane.
As can be seen in Fig. 4, instead of the usual
monotonic reduction of pressure behind the leading
shock wave seen for pure explosives (Neumann
spike), there is an increase in pressure in the front
part of the reaction zone for mixtures with
!
FIGURE 5. Flow temperature distribution within
reaction zone
First of all, it is important to notice the
significantly higher initial (at x = 0) values of the
flow temperature with increasing mass fraction of
inert particles compared with the value for a
detonation without particles. It was determined that
an increase of even 150-200°K in the initial flow
temperature resulted in multiple order-of-magnitude
increases in the reaction rate of the primary
explosive and a significant decrease in the width of
the reaction zone. These features contribute to the
increase in detonation velocity. Also, because of
extremely small width of the reaction zone, the
temperature of the particles (Fig.6) does not increase
to a level where rapid combustion reactions could
occur. Therefore, particles of a diameter equal to or
greater than 5 um are expected to behave as inert in
the reaction zone of the primary explosive. Keeping
in mind the importance of the effect of T^ on the
detonation velocity, a run was done using a slightly
lower value of Ti1 (ATi1 - -150°K), corresponding
to an intermediate value for n between 4 and 7 in the
Tait EOS, 5-um diameter particles and m2 = 0.1. It
was found that the detonation velocity reduces from
J^SlSvlt
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FIGURE 4. Pressure distribution within reaction zone
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5808 m/s for pure RDX to 5750.5 m/s for RDX with
5-um diameter Al particles and m2 = 0.1.
t
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FIGURE 7. Pressure distribution for 0.1-um
particles
FIGURE 6. Particle temperature distribution within
reaction zone
ACKNOWLEDGEMENTS
A number of researchers [4-10] have
experimentally obtained intensification of the
detonation wave and an increase in the detonation
velocity with the addition of inert particles (W and
SiC) or coarser Al particles which behave as inert in
the reaction zone.
Distributions of flow-velocity and pressure for
detonations with the inert ultradispersed (0.1 um)
particles show that, in the vicinity of the leading
shock wave, the velocity and pressure increase
significantly due to interaction between the particles
and the carrier phase flow as shown for pressure in
Fig.7. The overall distribution of the particle
temperature (T2) is similar to the distribution of the
carrier phase flow temperature and the particle
temperature approaches the flow temperature fairly
quickly. The detonation velocity of the mixtures
decreases with increase of 0.1 jim particle mass
fraction (Fig. 7).
This work was supported under the auspices of
the DND contract W7708-8-R718.
REFERENCES
1.
Mader C. L., Numerical Modeling of Detonation,
University of California, Berkeley, CA, 1979, Ch. I.
2. Nigmatulin R. L, Dynamics of Multiphase Media,
Part I, Hemisphere Publishing, NY 1991, Ch. I-III.
3. Kuznetsov N. M. et al., Combustion, Explosion and
Shock Waves, 18, No. 1, 98, (1982).
4. Apin A. Ya., "Vzryvnoe Delo", (USSR), No.52/9,
167, (1963).
5. Cook, M. A. et al., /. of Physical Chemistry, 61, 189,
(1957).
6. Sosnova, L S., Combustion and Detonation, in 3rd
All-Union Symposium on Combustion and
Detonation, (USSR), p. 355, 1972.
7. Shvedov K. K., Dremin A. N., et al., Combustion,
Explosion and Shock Waves, 18, No.l, 12, (1982).
8. Gonor A. L., Heterogeneous Detonation of
Condensed Explosives with Metallic Particles,
Global Consultants, Inc., Alexandria, VA, 1994, pp.
73-74.
9. Tao W.C. et al., The Role of Metallic Additives, in
14th Symposium on Explosives and Pyrotechnics,
Burlingame, CA, 1990, p. (5) 1 - (5) 9.
10. Tao W. C. et al., Understanding Composite Explosive
Energetics: IV, in 10th Symp. (Int) on Detonation,
ONR, Boston, 1993, pp. 628-636
CONCLUSIONS
The increase in flow temperature and pressure,
caused by the interaction between the particles and
the leading shock wave and viscous interaction of
the particles with the flow, have a crucial effect on
the detonation velocity and the profiles of the
detonation wave in the reaction zone.
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