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
THE BURNING RATE OF ALUMINIUM PARTICLES IN CYLINDER
TESTS.
David J. Evans1, Alec M. Milne1 and lan Softley2
1
Fluid Gravity Engineering Ltd, 83 Market Street, St. Andrews, Fife, KY16 9NX, U.K.
Defence Evaluation Research Agency, Porton Down, Salisbury, Wiltshire, SP4 OJQ, U.K.
2
Abstract. Aluminium is a common fuel component in propellants and explosives. There is a wealth
of literature on Aluminium combustion in gases at relatively low pressure but limited data on
combustion at high pressure (as in explosive detonation products). In this work we have carried out
and analysed cylinder tests with Aluminium loaded explosives with a view to assessing the
applicability of low pressure burning rates in this regime. The analysis makes use of detailed
numerical two phase flow modelling and a range of experiments used to validate other relevant
aspects of the physics, such as drag laws. We conclude that the burning rate is significantly faster than
that implied by extrapolating laws applicable at lower pressures.
The experimental data for this work was provided
from Standard Cylinder Tests. The experimental
arrangement for our cylinder tests is shown in Fig.
1. The cylinder is 300mm long with inner diameter
25mm and outer diameter 30mm. The Debrix pellet
is 25mm long and is centrally initiated by an RP80
detonator. The mixtures considered here are NitroMethane combined with Aluminium particles at
varied loading densities and particle sizes. The
standard diagnostic is to measure the radius of the
cylinder at 200mm from the point of initiation.
INTRODUCTION
Aluminium particles burning in a low pressure
environment, e.g. air, typically exhibit a
dependence of the burn time on particle size of the
form [1,2, 3],
(i)
where ^ is the burn time, d§ is the particle diameter
and a is a constant. Typically the value of a is
4xl06sm~2. In the course of studying propellants
and explosives it is of interest to study the burning
of such particles in a high pressure environment
such as occurs detonation. There is limited data
available on this subject so a coupled modelling
(FGE) and experimental (DERA) programme was
instigated. We have also made use of cylinder test
data published by Baudin et al. [4],
Cylinder
Debrix
Initiator
pellet
FIGURE 1. Standard Cylinder Test
These experiments have been modelled using a
two-dimensional,
axi-symmetric
hydrocode
1011
experiments is probably less reliable than Baudin's
VIS AR data in the early stages
previously used in two-phase modelling of
Aluminium Detonation [5]. The mixture is
modelled using two-phase flow where the NM uses
a "programmed burn" approach: the burn front
moves at a constant, pre-determined, speed
releasing energy as it moves through the explosive.
In order to infer the effects of particle burning rate
From cylinder tests it is important to ensure first
that the model accurately represents cylinder tests
with no particles and also with inert particles.
Nylon cylinder Test. NM + 1mm Steel balls
MODEL VERIFICATION
First, consider cylinder tests with no particles
present.
Data from Baudin and Softley are
available to compare with and Fig. 2 shows the
results obtained. The plots show the cylinder
radius at 200mm from the initiator.
The
programmed burn model for the NM uses
parameters obtained from the CHEETAH code [6].
The model fits the Baudin data better in the early
stages but later the match is better for the terminal
speed of the Softley data.
time (microsec)
FIGURE 3. 1mm steel particles (not burning) in NitroMethane: comparison of experimental and numerical data
BURNING PARTICLES
Baudin's paper presents results using 5|im and
lOOnm diameter particles at 20% and 40% loading
densities by weight. The experimental data shown
for the lOOnm AL at 40% loading indicates radial
motion much slower than the 5[im case. This is
difficult to understand in that all other work has
indicated that the smaller particles should burn
more quickly and yet this result moves more slowly
than even the simulation of inert particles.
Comparison with the 20% experimental data shows
that this is a unique result and so calls into question
the validity of this particular experiment and for t
this reason this case is neglected here.
Copper Cylinder Tests
In order to assess the particle burning it is
necessary for the the numerical model to
incorporate a burn law. Usually the EDEN code
uses a constant radial burn velocity law. Assuming
the particles are spherical and burning occurs all
over the surface simultaneously, the radius of the
particle reduces at a constant rate. The rate of mass
burnt per second is then proportional to the rate of
change of the particle volume:
FIGURE 2. Comparison of programmed burn model with
experimental data
To assess the dynamic effects of the particles an
experiment was carried out using 1mm diameter
steel particles, which do not burn, in the NitroMethane at a volume fraction of 62%. It can be
seen that the agreement is good though there is
some discrepancy in the early stages when the
radius variation is small.
The photographic
measurement technique employed in these
dV
—
dt
1012
dr
—
dt
(2)
An alternative law often used in these models is to
assume that the rate of change of the surface area
of the particle is a constant. In this case the rate of
change of volume is:
dt
dt
80-20 Al Smicron Cylinder Wall Radii
(3)
By varying the particle burn time until a best fit is
obtained with the 40%, 5|im Al data it is possible
to get an estimate of the burn time. For this case a
burn time of BOjus was found. The fit is good but
there is a discernible difference in the second
derivative with the simulation producing more
motion at late time. One possible solution to this is
to reduce the burn energy of the particles. This is
reasonable since the given energy release is only
valid if the Aluminium is completely burnt. It
seems plausible that this will not be the case since
an oxide layer will be present initially and
complete combustion requires carefully controlled
amounts of the fuel and oxidant. Therefore a
second fit was attempted with the particle burn
energy reduced from 1.33xl07J/kg to 1.0xl07J/kg.
The resulting fit is shown in Fig. 4 and was
achieved using a burn time of 24^us. This is a
better fit to the data than the full burn model.
FIGURE 5. Best fit of 5^um particle burn simulation with
reduced burn energy
The 20%, 5jUm particle case was simulated using
the same burn energy and time parameters derived
for the 40% Al runs, as would be expected if the dsquared law held. The resulting simulation shows
that in the early time the cylinder wall motion is
slower than with no particles for the first few /xs,
disagreeing with the experimental data as can be
seen in Fig. 5. Even with the burn energy returned
to the full value of 1.33xl07J/kg the radial motion
is still too slow as can be seen in Fig. 6. In this
case it seems that a more complex relationship
between burn time and particle size than the simple
square
law
discussed
earlier
may
apply.
60-40 Al Smicron Cylinder Wall R
80-20 Alex il Cylinder Wall Radii
Optimised Burning A) Smicron
Inert Al Smicron
Baudin, Smicron particles
Inert Alex II
0.07
Burning Alex II
Baudin, Alex II particles
0.06
0.05
0.04
0.03
3e-OS
Time(s)
FIGURE 4. Best fit of 5/im particle burn simulation to Baudin
data
3e-05
Time (s)
FIGURE 6. Summary of results for 20% by weight of 5jUm Al
particles
Using the ^-squared law and extrapolating from the
optimised case above (40%, 5mm) gives a burn
1013
time of 9.6ns for lOOnm particles. Using this in the
simulations gives a good fit to the experimental
data as can be seen in Fig 6.
possibly dependence on other factors such as
loading density.
Improved modelling capabilities for the NitroMethane and the particle elements have been
developed and these will be applied to this problem
in the near future so that a better understanding of
the burn laws may be developed.
These models used the constant radial burn
velocity law. To consider whether there is any
dependence on the form of burn law the first run
was repeated with the constant rate of area change
law. The optimisation procedure for the 40%, Sum
case was repeated using such a burn law and this
yielded a burn time of 25jns, very close to the
previous value.
There appears to be little
dependence on the nature of the law, only the
speed. If the burn times were much longer this
may not remain true.
REFERENCES
1 Khasainov, B. A. and Veyssiere, B., Archivium
Combustionis, 7, 333-352, 1987
2 Bouriannes, R., Ph.D. Thesis, Univ. of Poitiers,
1971
3 Marion, M., Chauveau, C. and Gokalp, L.,
"Studies on the Ignition and Burning of Levitated
Aluminium Particles", Combust Scl and Tech.,
1996,115, 369-390
4 Baudin, G. et al, "Combustion of Nanophase
Aluminium in the Detonation Products of Nitromethane, 11th Detonation Symposium,
Snowmass, 1998
5 Milne, A. M. and Evans, D. J., "Numerical
Modelling of Two-Phase Reactive Flow and
Aluminised Explosives", in Shock Wave
Processes in Condensed Media, I. G. Cameron
(Ed.), Hunting Brae, U.K., 1997
6 Fried, L. E., Cheetah 1.39 User Manual, 1996
CONCLUSIONS
With a limited set of experimental data available it
has been possible to begin testing the applicability
of relationships between particle burn time and
particle diameter in high pressure environments. In
all cases it has been found that the burn time is
significantly shorter than would be predicted by the
d-squared law with the a value appropriate for
combustion in low pressure environments. The
burn times are reduced by a factor of 4 in general.
However not all results are consistent with this
reduction: one result in particular showed an even
shorter burn time.
It seems likely that the dsquared law is still applicable in high pressure
environments but with different coefficients and
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