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
NEAR-FIELD IMPULSE EFFECTS FROM DETONATION OF
HETEROGENEOUS EXPLOSIVES
David L. Frost1, Fan Zhang2, Susan McCahan3, Stephen B. Murray2,
Andrew J. Higgins1, Marta Slanik1, Marc Casas-Cordero1, and
Chayawat Ornthanalai1
1
McGill University, Department of Mechanical Engineering, 817 Sherbrooke St. W.,
Montreal, Quebec, Canada H3A 2K6
2
Defence Research Establishment Suffield, PO 4000, Stn Main, Medicine Hat, Alberta T1A 8K6 Canada
3
University of Toronto, Department ofMechanical and Industrial Engineering, 5 King's College Rd., Toronto,
Ontario M5S 3G8 Canada
Abstract. Particle momentum effects from the detonation of a spherical heterogeneous charge
consisting of a packed bed of inert particles saturated with a liquid explosive have been investigated
experimentally and numerically. When such a charge is detonated, an interesting feature of the
subsequent flow field is the interplay between the decaying air blast wave and the rapidly expanding
cloud of particles. Using a cantilever gauge, it is found that the particle momentum flux provides the
primary contribution of the multiphase flow to the near-field impulse applied to a nearby small
structure. To determine the impulse from the particle momentum flux on the structure, a novel
particle streak gauge was developed to measure the rate of particle impacts at various locations. The
trends of the experimental results are reproduced using an Eulerian two-fluid model for the gas-particle
flow and a finite-element model for the structural response of the cantilever gauge.
INTRODUCTION
rapid acceleration within the combustion products,
the particle velocity remains roughly constant due
to the inertia of the particles. In some cases, the
particles catch up to and penetrate the leading
shock wave, as predicted numerically by Lanovets
et al. (3) and confirmed experimentally by Zhang et
al. (4). In this case, the particles decelerate due to
aerodynamic drag until eventually the shock wave
overtakes the particles in the far field.
The
interchange of momentum and energy between the
particles and the surrounding flow field changes the
rate of decay of the blast wave pressure and
impulse in comparison with a homogeneous
explosive (5). In the near field, the impact of the
particles with nearby structures can make a
significant contribution to the overall structural
damage. In the present paper, experimental and
numerical results will be presented which
The addition of solid particles to a
homogeneous explosive introduces additional
length and time scales that influence both the
detonation propagation within the reactive twophase medium and the subsequent blast wave
propagation and particle dispersal in the
surrounding air.
The detonation propagation
within the heterogeneous explosive has a nonideal
nature due to nonequilibrium effects associated
with the acceleration, heating and fracture of the
particles (1,2). When the detonation wave reaches
the surface of a spherical charge, a shock wave is
transmitted into the surrounding air and the
particles are accelerated radially by the expansion of
the combustion product gases to supersonic speeds.
For large (e.g., millimeter-sized) particles, after the
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investigate the relative contribution of the particles
and the blast wave to the bending work done on a
nearby cantilevered structure. A particle streak
gauge was developed to record the time history of
particles arriving at a given location.
The
experimental results are used to validate the
predictions using a two-fluid multiphase model.
The model is then used to determine the dominant
mechanism responsible for the work done by the
multiphase flow on nearby structures.
particles. Strain gauges were also placed just
above the bend location.
RESULTS AND DISCUSSION
When particles are added to a homogeneous
liquid explosive, the peak blast wave overpressure
is reduced in comparison with a homogeneous
charge. For example, Frost et al. (5) showed that
for the heterogeneous charge described above, the
peak overpressures generated were smaller than
those for a homogeneous charge (with the same
amount of NM) by a factor of 2-3. In contrast, the
heterogeneous charge produced substantially more
bending of the cantilever gauge than a
homogeneous charge, as shown in Fig. 2.
EXPERIMENTAL
The experiments were carried out using
spherical charges consisting of packed beds of
spherical steel beads saturated with nitromethane
sensitized with 10% triethylamine.
The
heterogeneous charges tested had a diameter of
11.8 cm and contained about 10 million 463 (im
steel beads (4,300 g) together with 430 g of NM +
10% TEA. Details of the experimental procedure
can be found in Zhang et al. (4).
For a homogeneous charge, the load applied to
the cantilever gauge will consist of the sum of i)
the short-duration force applied as the blast wave
diffracts around the gauge and ii) the drag force
from the flow behind the blast wave.
Tims
A "particle streak" gauge was developed to
determine the rate of particle collisions with a
surface at a given location from the charge. It
consisted of an aluminum cylinder (7.5 cm dia)
attached axially to the shaft of an AC motor which
was operated at a speed of 3685 rpm. A thin sheet
of aluminum was wrapped around the cylinder and
attached with double stick tape.
The
motor/cylinder assembly was placed inside a steel
cylinder which contained a vertical slot (5.08 cm x
0.64 cm) to allow the particles to strike the
cylinder as it rotated. After a trial the steel
cylinder was removed, and the aluminum foil was
recovered to obtain a direct temporal history of the
impact of particles with the cylinder.
A
photograph of a foil sample is shown in Fig. 1.
The distance between the lines drawn on the foil
corresponds to the width of the slot. The time for
the foil to move a distance of one slot width is
about 0.45 ms.
The cantilever gauges consisted of a 38.1 cm
long aluminum rod (with a diameter of either 0.95
cm or 0.635 cm) with 10.16 cm of the rod clamped
in a tripod stand. A steel plate (20.3 cm x 5.1 cm
x 0.48 cm) was fixed to the top portion of the rod
with an aluminum bracket, to serve as a witness
plate for the impact of the blast wave and the
FIGURE 1. Foil recovered from particle streak gauge
showing history of steel particle impacts at a distance of
90 cm from the charge. Note that some particles remain
embedded in foil. Particle diameter is 463 (im.
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arriving at a given location, as a function of time,
can be made. However, considering the reasonable
prediction of the particle dynamics by the twophase model (Fig. 3), the model has been used to
estimate the particle and gas velocity behind the
blast wave at various distances from the charge.
For example, at 90 cm from the charge, the blast
wave arrives just before the particles, but the peak
gas velocity behind the blast wave (about 500 m/s)
is smaller by a factor of 2 than the peak particle
velocity. The particle velocity also decays more
slowly than the gas velocity due to the high inertia
of the particles.
For a heterogeneous charge, a third force is
present due to the particle collisions with the
cantilever gauge.
To determine the relative
magnitudes of the three forcing functions
mentioned above, it is necessary to use the data
obtained with the particle streak gauge together
with overpressure data.
Experiments were carried out with the particle
streak gauge located at distances of 60, 90, 156,
and 200 cm away from the center of the charges.
By counting the number of particle impacts in each
segment of the foil (see Fig. 1), the cumulative
number of impacts was determined as a function of
time, and is shown in Fig. 3 for a distance of 90
cm. Note that from the particle streak gauge data
alone, we cannot determine the absolute arrival
time of the first particle at the gauge. This arrival
time was obtained from earlier flash X-ray data of
the expanding particle cloud (see Ref. 4). Also
shown in Fig. 3 are the results of the Eulerian twofluid model described in Zhang et al. (4). The
model predicts that the particles will arrive at a
given location slightly earlier than measured,
although the arrival time profile is similar. The
actual number of particle "hits" recorded on the foil
was 345, which is quite close to the predicted
value of 358, assuming that the particles are
distributed in a spherically symmetric fashion.
100
4
50
1.5
2
8
10
The work done on the cantilever gauge
depends on the momentum fluxes pV2 associated
with the gas and particles, which are shown in Fig.
4. From this figure it is apparent that the impulse
to the cantilever gauge due to the particle collisions
(which equals (1 + e) jppFp2d£ where 0 < e < 1 is
the coefficient of restitution) is considerably larger
than the impulse due to aerodynamic drag
(CD/2 lpBVB2dt). The reflected blast wave pressure
provides the third contribution to the impulse
which is generally larger than the drag force but
smaller than the particle force. At a distance of 90
cm, the particle collisions provide the majority
(about 70%) of the total impulse applied to the
cantilever. The particle force is applied over a time
of about 2 ms whereas the force due to the reflected
blast wave occurs over the relatively short time
(~ 200 jus) for pressure relief as the blast wave
diffracts around the cantilevered plate (see Kinney
& Graham, 6).
Heterogeneous
NM/Fe charges
1
6
Time (ms)
FIGURE 3. Cumulative impacts on the particle streak gauge as
a function of time at a distance of 90 cm from the charge:
experimental results and model predictions.
2.5
Distance (m)
FIGURE 2. Cantilever bend angle as a function of distance
from the charge for heterogeneous charges (containing 430 g
of sensitized NM with 4,300 g of 463 urn steel beads) and
homogeneous charges (with the same amount of NM).
Cantilevers at 0.6 m had diameters of 9.5 mm whereas other
cantilevers had diameters of 6.4 mm.
Using the particle streak gauge data at the four
locations, an estimate of the velocities for particles
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3)
Lanovets, V. S., Levin, V. A., Rogov, N. K., Tunik,
Yu.-V., and Shamshev, K. N., Fizika Goreniya i
Vzryva29, 88-92(1991).
4) Zhang, F., Frost, D. L., Thibault, P. A., and Murray,
S. B., Shock Waves 10, 431-443 (2001).
5) Frost, D. L., Kleine, R, Slanik, M., Higgins, A J.,
A finite element model was developed using
the code ABAQUS to model the response of the
cantilever to a dynamic load.
The loading
functions were determined assuming that the
particles collide elastically with the cantilever plate
and the peak reflected pressure was estimated using
measured side-on pressure data and reflected
pressure data from Baker (7). The calculated
dynamic displacement of the end of the cantilever
gauge is shown in Fig. 5 for the heterogeneous and
homogeneous charges. The final bend angles agree
well with the experimental results (Fig. 2)
considering that the collisions are not perfectly
elastic. Note that if only the drag and reflected
blast wave forces for the heterogeneous charge are
applied to the cantilever gauge (i.e., neglecting the
particle force), then negligible bending work is
done on the cantilever.
6)
7)
McCahan, S., Zhang, F., and Murray, S. B., "Blast
Waves from
Heterogeneous
Explosives,"
Proceedings of 22nd International Symposium on
Shock Waves, paper 0560, CDROM (1999).
Kinney, G. F. and Graham, K. J. Explosive Shocks
in Air, 2nd Ed., Springer-Verlag, New York, (1985).
Baker, W. E., Explosions in Air, University of
Texas Press (1973).
, Particle momentum flux p v
In summary, it has been found that adding
inert particles to a homogeneous explosive reduces
the peak overpressure in the near field (within 10
charge diameters).
However, the integrated
momentum flux of the particles in the near field is
larger (by a factor of 3-4) than the gas momentum
flux. The dynamic response (strain and final bend
angle) of a cantilevered target is greater for a
heterogeneous charge than for a homogeneous
charge with the same energy.
Further
Gas momentum flux pgv*
0
1
2
3
4
5
Time (ms)
FIGURE 4. Numerical particle and gas momentum flux at a
distance of 90 cm from heterogeneous charge.
improvements to the modelling of the near-field
heterogeneous blast and particle dispersion
dynamics will require the development of
appropriate equations of state for the dense solidgas system, including a treatment of a large
number of high-speed inelastic collisions.
- Heterogeneous charge
- - - Homogeneous charge
- - - - - Heterogeneous charge:
drag & blast wave force only
(no particle force)
ACKNOWLEDGMENTS
The authors wish to acknowledge the
assistance of K. Gerrard, A. Nickel, D. Boechler
and S. Trebble during the field trials. Useful
information regarding cantilever gauges was also
provided by Dr. A. van Netten.
REFERENCES
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Time (s)
1)
2)
Lee, J. J., Frost, D. L., Lee, J. H. S., and Dremin, A.,
Shock Waves 5, 115-119 (1995).
Lee, J. J., Brouillette, M., Frost, D. L., Lee, and J. R
S., Combustion and Flame 100, 292-300 (1995).
FIGURE 5. Calculated dynamic displacement of top of
cantilever gauge subject to loading from heterogeneous and
homogeneous charges at a distance of 90 cm from charge.
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