Reaction Zones of Detonating Solid Explosives, CHEMIA I PIROTECHNIKA, Chemia i Pirotechnika

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Combustion, Explosion, and Shock Waves, Vol. 36, No. 6, 2000
Reaction Zones of Detonating Solid Explosives
B. G. Loboiko
1
and S. N. Lubyatinsky
1
UDC 534.222
Translated from Fizika Goreniya i Vzryva, Vol. 36, No. 6, pp. 45{64, November{December, 2000.
Original article submitted May 31, 2000.
The reaction zones of normal and overdriven detonation waves in a number of solid
HE were studied by recording the shock-wave luminosity in chloroform placed at the
end of a high-explosive (HE) charge. The data obtained have led to some conclusions
on the regularities of HE decomposition in a detonation wave. Thus, in a powerful
solid HE, the heterogeneity of the charge plays a decisive role in the formation of a
chemical spike. In this case, the time of reaction of heterogeneous HE correlates with
the Jouguet pressure rather than with the sensitivity of the HE. The experimental
parameters of the chemical spike are in good agreement with calculations on an ex-
trapolated shock adiabat of the HE. This, however, does not indicate that the fraction
of the HE decomposed directly at the detonation front is small but only shows that
it depends smoothly on the front parameters. In overdriven detonation waves, an in-
crease in the overcompression pressure is accompanied by an increase in the fraction
of the HE decomposed directly at the front, and with a relatively large increase in
pressure, the chemical spike completely disappears. In TATB and TATB-based HE,
this occurs at a pressure of 40 GPa.
INTRODUCTION
a magnetohydrodynamic consideration. This moti-
vates the importance of experimental studies of the
reaction zone.
The rst experimental proof of the validity of
the Zel'dovich{Neumann{Doring model for solid HE
was obtained by Du and Houston [4], who mea-
sured the velocity of the free surface of an aluminum
target (W) in contact with a detonating charge of
the explosive V (36/64 TNT/RDX) versus the thick-
ness of the target l. The dependence of W(l) they
obtained was in complete agreement with the deto-
According to the Zel'dovich{Neumann{Doring
detonation model [1{3], detonation transformation
of a high explosive (HE) occurs under the action of
a shock wave, which initiates an exothermic chemi-
cal reaction in the HE charge, whose energy is ex-
pended in sustaining the process (Fig. 1). It is as-
sumed that the detonation wave consists of a shock
wave propagating over the HE (point F), which is
followed by a reaction zone terminated by a Jouguet
plane (point J), where the sum of the mass velocity
and the velocity of sound is equal to the detonation
velocity. This condition, called the Jouguet condi-
tion, is satised at the point in the plane p{v where
the Michelson straight line issuing from the initial
state (point O) is tangent to the Hugoniot adiabat
of the explosion products. Due to the laws of con-
servation of mass and momentum, the sequence of
states occurring in the reaction zone is represented
by a straight line (FJ) in Fig. 1a. The structure of
the reaction zone is determined by the kinetics of
HE decomposition and cannot be determined from
1
Russian Federal Nuclear Center,
Institute of Technical Physics, Snezhinsk 454670.
Fig. 1. Structure of a stationary, plane detonation
wave in the planes p{v (a) and p{X (b) according
to the Zel'dovich{Neumann{Doring model.
716
0010-5082/00/3606-0716 $25.00
c
2000
Plenum Publishing Corporation
Reaction Zones of Detonating Solid Explosives
717
nation front structure in the Zel'dovich{Neumann{
Doring model. Using the known equation of state for
aluminum, they calculated the Jouguet pressure, the
pressure at the front, and the length of the reaction
zone: p
J
= 27:2 GPa, p
f
= 38:5 GPa, p
f
=p
J
= 1:42,
and X
J
= 0:13 mm.
The study of [4] became classical: not only did
it determine the most promising method for study-
ing the structure of the reaction zone (measurement
of parameters of the shock wave formed in a tar-
get upon detonation-wave reection) but it also re-
vealed the main source of errors | both in the reac-
tion zone of a detonation wave and behind it there
is a smooth decrease in the pressure gradient with-
out any discontinuities. In this case, determining the
target thickness corresponding to the Jouguet state is
rather dicult (especially in discrete measurements).
The length of the reaction zone obtained by Du and
Houston X
J
= 0:13 mm corresponded, in their opin-
ion, to the fast stage of HE decomposition, whereas
a severalfold larger value of X
J
could correspond to
complete decomposition of HE. This uncertainty in
the choice of the target thickness corresponding to
the Jouguet plane is apparently the main reason for
the wide spread (from 0.13 to 0.4 mm [5]) in val-
ues obtained afterward by various researchers for the
length of the detonation reaction zone for the com-
position V.
In succeeding years, a large number of papers
devoted to the reaction zone of detonating HE have
been published [6{10, etc]. The 1980s were the most
fruitful years, during which a number of experimental
methods possessing high time resolution evolved:
| An electromagnetic method with a time resolu-
tion of 10 nsec [23].
A detailed analysis of results of these studies is given
in [24]. In most of these studies, in complete accor-
dance with the Zel'dovich{Neumann{Doring model,
a zone of elevated pressures | a chemical spike |
was recorded at the detonation front. At the same
time, the following deviations from this classical
model were also detected: the absence of a chemi-
cal spike in agated HE (pressed in the presence of a
solvent to attain a relative HE density of 99% and
semitranslucent appearance) [11, 14], the presence of
an induction zone 0:1 mm thick [15] inside a chemi-
cal spike, stationary underdriven detonation of some
HE with an inert binder [11], and partial decompo-
sition of HE at the detonation front [24]. Thus, in
1988, when such studies began, there was no con-
dence in the validity of the Zel'dovich{Neumann{
Doring model for all solid HE. It was necessary to
answer the following questions:
| Does the zone of elevated pressure (chemical
spike) corresponding to the reaction zone exist
at the detonation front for all solid HE?
| What is the origin of the elevated pressure zone
(chemical spike)?
| What are the dimensions of the reaction zone?
| Does shock compression of the unreacted HE oc-
cur at the detonation front, as is assumed in the
Zel'dovich{Neumann{Doring model?
| Of what order is the HE decomposition reaction
and is there a reaction delay due to the induction
time, initiation of the sites, etc.?
| The method of ashing gaps [11, 12] and the
method of laser measurement of wave velocities
[11{14], which allow one to record the shock-
wave distribution in transparent layered targets
with micron-size gaps between the layers which
are in contact with HE charges;
The results of these studies, published in part earlier
[25{30], are discussed in the present paper.
STRUCTURE OF THE REACTION ZONE
OF NORMAL DETONATION
| The method of closed contacts [15], which al-
low one to record shock-wave propagation in sen-
sors | packets of aluminum foils in contact with
HE charges | from the decrease in their electri-
cal resistance;
The detonation reaction zone was studied by
recording the radiation intensity of a shock-wave
front in an indicator liquid placed at the end of a det-
onating HE using the photoelectric procedure, also
known as the indication procedure [31]. This method,
based on the electron-optical method of temperature
measurements [32], was developed in 1977 [33] after
detection of appropriate indicator liquids (CCl
4
, etc.)
that become transparent in shock waves and deter-
mination for them of the temperature of shock com-
pression as a function of pressure [34]. In 1984, the
photoelectric procedure was used for the rst time to
| A laser interferometric method for measuring the
velocity of thin metal foils located on the bound-
ary of HE charges with transparent windows [16{
21];
| A photoelectric method for recording shock-
wave parameters in a transparent medium in
contact with a HE charge from the radiation in-
tensity of the shock-wave front [22];
718
Loboiko and Lubyatinsky
Fig. 2. Setup for studying the detonation reaction
zone.
Fig. 4. Typical FEM signal (experiment with
TNT pressed with slight melting).
ber of HE based on them. Initial processing was con-
ducted as follows [30]. Beyond the reaction zone, the
signal I(t
f
) from the photoelectron multiplier (FEM)
(Fig. 4) was approximated by the expression
I = I
0
+ I
1
t
f
+ I
2
t
f
:
The parameters u
p
0
corresponding to I
0
for the shock
wave produced in chloroform by the explosion prod-
ucts expanding from the Jouguet state were calcu-
lated under the assumption of a polytropic approxi-
mation for the explosion products by solving the sys-
tem
p
0
=
0;x
(c
0;x
+ S
1;x
u
p
0
)u
p
0
;
Fig. 3. X{t-diagram of interaction of the reaction
zone with chloroform.
p
0
= p
J
1
n 1
2n
u
u
J
1
2n=(n1)
;
examine the detonation reaction zones for some solid
HE [22]. The procedure of [22] had a time resolution
of 30 nsec, which is not sucient to study the reac-
tion zones of HMX, RDX, and most of the HE based
on them, and was improved in [25{30]. The latest
version of the experimental setup is shown in Fig. 2.
A HE charge is initiated by a at waveguide lens.
An aluminum foil, screening the detonation radia-
tion, is attached to the charge end by epoxy resin.
Diaphragms bound the 3-mm-diameter visible part
of the shock front in chloroform. The radiation of
the shock front is transmitted by 1.5-mm double-
component plastic optical ber to an SNFT-3 pho-
tomultiplier connected to an SUR-1 oscillograph. By
the method of characteristics, it is possible to show
that the pressure prole at the shock front in chlo-
roform reects the detonation wave pressure prole
(Fig. 3).
This method was used to study cast and pressed
TNT, RDX, HMX, PETN, TATB, and also a num-
where p
J
,
J
, u
J
, and n are, respectively, the pres-
sure, density, mass velocity, and polytropic exponent
of the explosion products at the Jouguet point (de-
termined under the assumption of zero length of the
reaction zone),
0;x
= 1:483 g/cm
3
is the initial den-
sity, c
0;x
= 1:774 km/sec and S
1;x
= 1:367 are the
coecients of the (u
s
{u
p
) relation for chloroform,
and u
s
and u
p
are the shock and mass velocities.
This approach completely corresponds to the conven-
tional method of determining the Jouguet parameters
under the assumption of zero length of the reaction
zone. Next, we determined the velocity of the HE{
chloroform interface u
p
(t):
u
p
= (u
b
p
0
A ln(I=I
0
))
1=b
;
(1)
t = Zt
f
: (2)
Here A = 0:0390:001, b = 1:17, and Z = 0:520:02.
We note that the design of the experimental facility
allows one to implement calibration by the average
shock-wave velocity in chloroform on the base from
the HE{chloroform interface to the glass plate [29].
Reaction Zones of Detonating Solid Explosives
719
Fig. 5. Typical velocity proles of the HE{
chloroform interface versus time (two experiments
with TNT pressed with slight melting).
Fig. 6. Derivative of the velocity of the HE{
chloroform interface versus time for TNT pressed
with slight melting: the prole of u
p
(t) is averaged
beforehand over two experiments and smoothed.
For all tested HE, except for agated ones, which
are considered below, a chemical spike was recorded
with a rise time of 5 nsec (time resolution of the
method) (Fig. 5). The absence of a distinct interface
between the reaction zone and the Taylor rarefac-
tion wave made it dicult to distinguish a point on
the prole of u
p
(t) that corresponded to the Jouguet
state. In addition, this was indirect evidence for the
incompleteness of the reaction in the Jouguet plane.
Nevertheless, for deniteness, it was assumed that
the reaction zone terminated in the Jouguet plane,
which separated subsonic and hypersonic ow regions
(reaction zone and Taylor wave), in which the atten-
uation of the shock wave in chloroform obeyed dif-
ferent laws. With allowance for the experimental
error, the dependence of du
p
=dt on t in semilog-
arithmic coordinates is represented as two straight
lines, and the second line has practically zero slope
(du
p
=dt = const) [25]. The point of intersection of
these lines, which corresponds to the Jouguet plane,
determines the reaction time t
J
(the time of passage
of the HE element from the front to the Jouguet
plane) (Fig. 6).
To eliminate the occurrence of negative values
of du
p
=dt due to FEM noise, the experimental pro-
les of u
p
(t) must be smoothed before dierentiation.
The degree of smoothing depends on the dimensions
of the reaction zone, the FEM noise level, etc., and
was determined individually for each HE [25{30]. A
unied processing technique was based on the follow-
ing expedient. The linear dependence of du
p
=dt on
t in semilogarithmic coordinates in the reaction zone
implies an exponential dependence of u
p
(t) for t < t
J
:
u
p
= u
11
+ u
12
exp(t=); (3)
where is the characteristic time of reaction, which
approximately corresponds to a decrease in the
amount of the unreacted HE by a factor of e. The
constancy of du
p
=dt behind the reaction zone points
to a linear relation u
p
(t) for t > t
J
:
u
p
= u
p
0
+ u
0
t: (4)
Here u
p
0
corresponds to the calculated parameters
of the shock wave produced in chloroform by the ex-
plosion products expanding from the Jouguet state,
and u
11
, u
12
, u
0
, and are approximation parame-
ters, which are not completely independent because
at the point t
J
, the two branches [(3) and (4)] have
both equal values and rst derivatives. Since rela-
tion (4) guarantees the equality u
p
= u
p
0
for t = 0, it
becomes unnecessary to preliminarily determine the
region with no eect of the reaction zone and to nd
the value of I
0
by the method described above, and I
0
is treated as an independent approximation parame-
ter.
For each experiment, the prole of I(t
f
) was con-
verted to I(t) using (2), and the Nellis method was
used to obtain the values of the parameters , u
0
, t
J
,
and I
0
that correspond to the minimum of S
u
p
|
the standard deviation of the experimental velocity
prole calculated from (4) from the approximation
dependence calculated from (3) and (4). In this case,
the corresponding values of u
11
and u
12
were deter-
mined from the condition that the two branches of
the function join at the point t
J
. The reaction zone
length was calculated from the following formula, ob-
tained by analysis of the corresponding X{t-diagram
(see Fig. 3):
Z
t
J
X
J
=
(Du
p
) dt
(5)
0
(D is the HE detonation velocity). The mean values
of , t
J
, and X
J
are given in Table 1.
720
Loboiko and Lubyatinsky
TABLE 1
Parameters of the Reaction Zones of Detonating HE
HE
0
=
0;cryst
, % Dimensions of HE, mm , nsec t
J
, sec X
J
, mm
TNT (pressed
with slight melting)
97.9
?60 100
91 14
0:33 0:05
1:54 0:22
TNT (cast)
94.3
?60 100
80 12
0:29 0:04
1:36 0:19
TNT (pressed)
91.9
?60 100
62 13
0:19 0:04
0:87 0:17
TATB
95.4
?60 10
103 15
0:31 0:04
1:56 0:22
TATB
94.8
?40 80
109 16
0:24 0:03
1:18 0:17
TATB/inert
99.1
?120 120
99 21
0:26 0:05
1:24 0:25
TATB/inert
99.1
?60 150
94 14
0:21 0:03
1:03 0:14
50/50 RDX/TNT
97.6
?60 100
33 7
0:13 0:03
0:64 0:13
70/30 RDX/TNT
99.5
?60 150
19 4
0:08 0:02
0:44 0:09
90/10 HMX/TNT
99.1
?60 150
11 2
0:07 0:01
0:37 0:07
HMX/inert
99.2
?60 150
11 2
0:06 0:01
0:36 0:05
HMX/inert
69.1
?60 50
71 11
0:19 0:03
0:80 0:11
RDX (agated)
98.6
?40 80
|
<0:005
<0:03
RDX
92.4
?40 80
15 3
0:07 0:01
0:36 0:07
RDX
92.4
?40 40
12 3
0:05 0:01
0:28 0:06
PETN (agated)
98.3
?40 80
|
<0:005
<0:03
PETN
97.8
?40 40
32 7
0:08 0:02
0:42 0:08
PETN
91.5
?40 40
27 6
0:11 0:02
0:52 0:10
HMX
97.1
?40 80
10 2
0:04 0:01
0:25 0:04
HMX
94.7
?40 80
15 2
0:06 0:01
0:33 0:05
94/6 RDX/inert
99.4
?40 80
12 2
0:05 0:01
0:28 0:04
Note. Asterisk indicates that the HE was initiated by a charge of 70/30 RDX/TNT (?60150);
0
=
0;cryst
is the relative
density.
TABLE 2
Parameters of the Shock Adiabats of HE in the Form u
s
= c
0
+ S
1
u
p
+ S
2
u
p
HE
c
0
, km/sec
S
1
S
2
, (km/sec)
1
Source
TNT
2.485
1.835
|
Processing of the data of [35{38]
TATB
2.462
2.116
|
Processing of the data of [35{37]
RDX
2.78
1.9
|
[37]
PETN
2.87
1.69
|
[37]
HMX
2.901
2.058
|
[37]
RDX/TNT
2.868
1.670
|
Processing of the data of [35{37]
PBX-9404
2.494
2.093
|
[37]
TATB/inert
2.5101
2.4346 0:1983
[39]
The errors in the reaction zone parameters were
estimated under the assumption that the relative er-
rors of a single measurement of the reaction zone
parameters are equal for all HE. For each series of
experiments in the same arrangement, we calculated
the mean values of and t
J
, and for each experi-
ment in the series, we obtained the ratio of the mea-
sured quantities to the corresponding mean values:
= and t
J
=t
J
. Thus, for each of these parameters,
are estimated to be 0:20=
p
n, where n is the number
of experiments in the series.
The experimental data on the initial velocities
of the HE{chloroform interface u
p
f
made it possible
to check the course of the shock adiabat of the HE
we obtained 31 values, which were well described by
a normal distribution with center at 1 and a vari-
ance of 0.10. For a condence probability of 0.95,
the relative errors of the mean quantities and t
J
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