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
CONVECTIVE DETONATIONS
Raafat H. Guirguisa and Alexandra M. Landsberg
Research and Technology Department and Weapons Department
Naval Surface Warfare Center
Indian Head, MD 20640
Abstract. Convective detonations are introduced, a novel concept whereby in some regions of the
reaction zone, instead of solely depending on the shock-induced hot spots, convection significantly contributes to igniting the unreacted materials coming through the shock front. Radiallygraded explosives is an application in which these detonations are likely to occur. Highly curved
detonations can be sustained in these explosives, resulting in transverse pressure gradients that
drive the decomposition products upstream, where these hot gases can ignite the surface of unreacted particles that crossed the shock front at a relatively weak section.
STRUCTURE OF REACTION ZONE IN
TRADITIONAL DETONATIONS
INTRODUCTION
In deflagration-to-detonation transitions (DDT)
often observed in porous propellants and explosives,
convective burning plays a dominant role in the
transition. Specifically, the convection of the hot
gas products through the pores drastically increases
the flame speed beyond that of laminar propagation.
However, a compression phase in which the flamegenerated pressure waves coalesce ahead of the
deflagration front always precedes the final stages
of transition to detonation. In traditional detonations
convective burning participates in the surface decomposition stage of the reaction, but it does not
contribute to igniting the unreacted materials coming through the leading shock front.
This paper argues the feasibility of convective
detonations in radially-graded explosives, a new
type of explosives manufactured with a built-in
gradual change in composition. Highly curved detonations resulting in transverse pressure gradients in
the proper direction for driving the gas decomposition products upstream can be sustained in these
explosives (1). Where the shock is relatively weak,
instead of the hot spots, these hot products can ignite the surface of yet unreacted particles.
In traditional detonations ignition is propagated
by the leading shock. Figure 1 illustrates the different stages of reaction in a heterogeneous explosive
composed of energetic crystals and a binder. Two
different pressure gradients develop in the reaction
zone - macroscopic, from one control volume to the
next, and microscopic, describing changes in pressure within the same control volume over length
scales comparable to the particle size. Each pressure
gradient drives the decomposition gas products in a
different manner.
Upon crossing the shock, the bed is compacted.
As illustrated in Fig. la, the dissipated work is localized in a number of hot spots where ignition occurs. The resulting bulk chemical decomposition
locally raises the pressure at the hot spots, thus introducing within the same control volume a large
number of microscopic pressure gradients, each
pointing in a different direction. At each of these
points, the difference in pressure forces the hot gas
products to burn channels around and between particles, as illustrated in Fig. Ib. These channels eventually connect the isolated pockets of decomposition
gas products together, forming a network through
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which gases can travel macroscopic distances uninterrupted, and partially deconsolidating the bed. As
the control volume moves downstream to lower
pressures, the resulting dilatation also help expand
the pores created at the hot spots and the channels
erosively bored into the bed. When the decomposition products completely engulf the remaining solid
fragments, the bed is fluidized, as illustrated in Fig.
Ic, and surface decomposition becomes the dominant reaction mechanism.
All the components within the control volume
are subjected to the same macroscopic pressure
gradient, but being lighter, the gas products acquire
a higher velocity. They infiltrate through the network of open channels and through the interstitial
spaces in the fluidized bed into neighboring control
volumes having lower pressures, as illustrated in
Fig. Ic, same as convective burning in DDT. However, unlike this macroscopic flow, the microscopic
flows described above, driven in different directions
by the different microscopic pressure gradients
within the control volume, do not add up to a flow
with a net velocity component.
Eventually, due to the drag between the two
phases, the remaining smaller fragments reach the
same velocity as the gas products, and all 2-phase
energetic crystals
flow aspects cease. As illustrated in Fig. Id, laminar
surface decomposition then completes the reaction
process, which in 1-D detonations and in detonations with slightly curved fronts has to end at the
Chapman-Jouguet (CJ) surface.
Whether discussing DDT or convective detonations, in this paper the term "convection" specifically refers to the flow of gas products through the
interstitial spaces between solid fragments. The
interstitial spaces are either pre-existing, such as in
porous explosive beds, or could be generated by
chemical decomposition. The term "convective
detonation" means that in some regions of the reaction zone, instead of solely depending on the shockinduced hot spots to start the reaction, hot gases
from a partially decomposed region downstream
infiltrate back and ignite some of the unreacted material upstream. In traditional detonations, the macroscopic pressure gradient is pointed in the wrong
direction. However, as explained next, in detonations with highly curved fronts the transverse pressure gradient is positive (Vp • n > 0; n = unit vector
normal to streamline), i.e., in the proper direction
for driving the lighter gas decomposition products
upstream.
MACROSCOPIC PRESSURE GRADIENT
IN THE TRANSVERSE DIRECTION
decomposition
products
Figure 2 illustrates the details of the reaction
zone for three detonation waves with progressively
curved fronts. A planar front is an idealization of
practical detonation waves that is only applicable in
the asymptotic limit, when the charge is rigidly confined or is infinitely large. In finite charges, the
detonation front becomes curved in order to accommodate the divergence resulting from the lateral
expansion of the high-pressure decomposition products and at the same time, satisfy the CJ condition
of unit Mach number at some location within the
reaction zone (2). The curvature of the streamlines,
on the other hand, depends on the sign of the pressure gradient in the transverse direction (orthogonal
to streamlines), the resultant of two competing factors, both tending to decrease the pressure, but one
faster than the other.
In general, after crossing the shock the pressure
decreases along the streamline due to the heat liberated by the exothermic chemical reactions, i.e., p3 <
pr Due to the wave curvature, the pressure also
binder
FIGURE 1. Different stages of reaction: (a) formation of hot
spots in shock-compacted bed; (b) ignition of the hot spots
creates a network of connected porosity; (c) convective surface
decomposition in fluidized bed; (d) laminar surface decomposition of solid fragments of explosive floating in the gas products.
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decreases along the detonation front and along the
constant reaction-progress contours behind it, i.e., p2
< pp but for planar detonations, p2 = p3.
If the front is slightly curved, the pressure drops
along the streamline faster than it does along the
detonation front, yielding p3 < p2. The inclination of
the streamlines to the axis continuously decreases
after the shock, but more importantly, the gas decomposition products tend to infiltrate inwards and
downstream, from cooler regions closer to the front,
to hotter points where the reaction has progressed
further.
If the detonation front is highly curved, however, the pressure drop along the detonation front
becomes larger than that along the streamline,
hence p3 > p2. The gas products tend to infiltrate
outwards and upstream, from regions where the
reaction has progressed further and the gas products
are hotter, to cooler locations. At a minimum, this
convection should accelerate surface decomposition
upstream. If, however, the shock is too weak to
quickly ignite the incoming materials, or if the explosive is insensitive to shock initiation, these hot
products may start surface decomposition first, or at
least dominate the reaction process by igniting more
of the unreacted particles than the shock-induced
hot spots do.
However, as explained above, ignition of these
hot spots also plays a significant role in creating a
network of open channels through which the gas
products can travel. If ignition at the hot spots is
completely eliminated, the convection of the hot gas
products forced by the pressure gradient in the
transverse direction will be the only remaining
mechanism for boring travel channels through the
bed. The shock may introduce microscopic cracks
in the compacted bed, but to open such channels the
hot gas products will have to push through these
cracks and widen them by burning the walls.
HIGHLY CURVED DETONATIONS
IN RADIALLY-GRADED EXPLOSIVES
In ideal explosive charges, the detonation front
is slightly curved, but as the size of the charge approaches the critical diameter, the radius of curvature decreases. Detonation waves with significantly
curved fronts are also observed in non-ideal explosives containing a considerable fraction of slowreacting components, but in all these detonations the
resulting front is not curved enough to create a
strong positive pressure gradients in the transverse
direction. Such highly curved detonation fronts can
be created, however, in radially-graded charges.
Figure 3 compares the structure of the detonation waves resulting in two explosive charges 4 cm
Planar
p2 < p! , p3
transverse direction
(orthogonal to streamlines)
slightly-curved
P2<Pi>P3<Pi
streamlines
P3<Pl
f = 0.2 0.1 0
reaction-progress
constant contours
(a)
highly-curved
(b)
FIGURE 3. Density contours in pressed cylindrical explosive
charges detonated underwater (reproduced from reference 1).
Charge (a) is radially-graded - PETN at the axis, gradually
changing to TNT at the outer radius, resulting in a highly
curved detonation front. Charge (b) is pure TNT. The curvature
of the front is imperceptible.
P2<Pl,P3<Pl
P3>Pi
FIGURE 2. Effect of detonation front curvature on pressure
gradient in the transverse direction. For slightly curved fronts,
convection is pointed downstream, whereas for highly curved
fronts, it is pointed upstream.
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causing a concomitant decrease in the rate apn. That
is what happens if a detonation wave is forcibly
initiated by a strong booster in an explosive charge
smaller than the critical diameter. However, as explained below, radially grading the explosive allows
us to build into the charge a core that can autonomously support the high pressure near the axis, as
well as enhance the lateral transfer of surface decomposition by seeding the outer layers with more
energetic materials.
Let us assume that the cylindrical charge in Fig.
3a is replaced with one that is constructed of only
two layers - a core of pressed PETN, 10 mm in diameter, and an outer layer 15 mm thick of a less
energetic powder. Since the critical diameter of
unconfined PETN is about 1 mm, a steady detonation can be obviously maintained in the core, independently of the outer layer. However, if the volumetric rate of gas generation in the outer layer is not
large enough to keep up with the wave front propagating as fast as the detonation in the core, a nonreactive oblique shock similar to that induced in the
water in Fig. 3b will result in the outer layer.
Now let us radially stratify the charge. If some
of the less energetic powder is mixed in the core,
the detonation will slow down. If some small fraction of PETN is mixed in the outer layer, its volumetric rate of gas generation is increased. If a significant fraction of PETN is mixed in, however, the
outer layer will become similar to the core and will
sustain a traditional detonation. By properly grading
the fraction of PETN mixed in, it is possible to
reach a condition whereby surface decomposition in
the outer layer keeps up with the front, and convection, not compression, transfers ignition laterally.
Thus, convective detonations are more likely to
occur in radially-graded charges.
in diameter, both pressed to a constant uniform density = 1.63 g/cc and detonated underwater. However, charge (a) is radially-graded - PETN at the
axis, gradually changing to TNT on the outer radius,
whereas charge (b) is pure TNT. Because PETN has
a higher detonation velocity (at 1.63 g/cc, D = 7.79
km/s) than TNT (D = 6.93 km/s), the detonation
propagating axially in charge (a) has a highly
curved front. Although charge (b) is not graded, the
detonation front is still curved because both the
charge diameter and acoustic impedance of the confining water are finite, but the curvature of the front
is imperceptible.
DISCUSSION AND CONCLUSIONS
Convective detonations are introduced. They are
defined in this paper as detonations in which the
convection of hot decomposition products significantly contributes to igniting the unreacted materials coming through the shock front. Radially-graded
explosives is an application in which these detonations are likely to occur because detonations with
highly curved fronts can steadily propagate in these
explosives, resulting in transverse pressure gradients in the proper direction for driving these products upstream. However, one has to wonder whether
the laminar surface decomposition that starts after
the gas products reach their destination is fast
enough to contribute to the propagation of the front.
At the high pressures generated by detonations,
the rate of surface regression driven by heat diffusion (conduction) and radiation, usually expressed
as apn, obviously can be quite large, but a quantitative estimate is nevertheless calculated next. As
explained above, even in detonation waves, laminar
surface decomposition is ultimately responsible for
burning the solid particles. In ideal explosives, the
reaction zone is usually 0.5-1 mm thick, which
takes about 50-100 ns to cross. Assuming the average particle size is 100 um, surface regression must
be proceeding at velocities at least of the order of 12 mm/us (km/s) in these detonations.
In uniform explosives, if the volumetric rate of
gas generation, which mainly depends on the composition, is not large enough to preserve a core of
high pressure near the axis against the action of the
rarefaction waves that originate at the surface of the
charge, these waves will eventually kill the detonation wave by decreasing the pressure in the core,
REFERENCES
1.
2.
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Guirguis, R., and Landsberg, A., "Structure of Detonation Waves in Stratified/Spatially-Graded Explosives," Proceedings of the 2000 JANNAF PSHS
meeting, 2000, CPIA, Columbia, MD.
Guirguis, R. H., "Streamlines Dynamics Method for
Highly-Curved Detonation Waves," Proceedings of
the Tenth Symposium (International) on Detonation,
pp. 27-36, 1993, ONR, Arlington, VA.