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European Journal of Applied Sciences – Vol. 11, No. 3
Publication Date: June 25, 2023
DOI:10.14738/aivp.113.14608.
Partom, Y. (2023). Diameter and Thickness Effects Scaling Deviations of High Explosives. European Journal of Applied Sciences,
Vol - 11(3). 155-159.
Services for Science and Education – United Kingdom
Diameter and Thickness Effects Scaling Deviations of High
Explosives
Y. Partom
18 HaBanim, Zikhron Ya'akov 3094017, Israel
ABSTRACT
One way to characterize the sensitivity (or the reaction rate) of explosives is
through size-effect tests. For explosive rods they are called diameter effect tests,
and for explosive plates, they are called thickness effect tests. With high reaction
rate explosives, different test configurations usually yield almost the same reaction
rate or detonation velocity. But with low reaction rate explosives, different test
configurations usually yield somewhat different detonation velocities. Following
one of our previous papers [1], we propose here that those different detonation
velocities result from the phenomenon of partially reacted boundary layers, that
form when a detonation wave is grazing along a free boundary. In what follows we
perform computer simulations to show how such a phenomenon comes about.
INTRODUCTION
One way to characterize the sensitivity of explosives (in the sense of reaction rate), is through
size effect tests. Using cylinders (rods) they are called diameter effect tests, and using wide
plates they are called thickness effect tests. From the steady state equations of motion for the
two configurations it can be deduced that these two test configurations scale as:
( ) ( )
( ) ( )
d D 2h D
or
r D h D
=
=
(1)
where d=rod diameter, r=rod radius. h=plate thickness and the scaling hold for the same
steady detonation velocity D,
But tests on various explosives show deviations from the above scaling. Those deviations are
quite small for so called ideal explosives that have very high reaction rates, or very short (of
the order of few nanoseconds) reaction times. But they can be substantial for less ideal or non- ideal explosives. Tests on various explosives show, that sometimes we may get r/h<1, and
other times r/h>1, and that deviations from perfect scaling may be as high as 10%. Searching
the literature, we haven’t seen any explanation of these scaling deviations. Here we attempt
such an explanation. Our explanation is based on previous work of ours [1], where we show
that a boundary layer of partial reaction usually forms when a detonation wave is grazing
along a free boundary.
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European Journal of Applied Sciences (EJAS) Vol. 11, Issue 3, June-2023
Denoting the equivalent thickness of such a boundary layer by r for a rod, and by h for a
plate, we have:
( )
( )
( )
( )
r r r 2 h r 1 1
h h h h
so that :
r D 1 for 2 h r
h D
r D 1 for 2 h r
h D
− −
= = −
−
(2)
On this basis we suggest that scaling deviations of the diameter effect from the thickness effect
are related to the partially reacted boundary layer phenomenon.
SIMULATIONS
To establish the above suggestion, we ran direct numerical simulations of the rod and plate
geometries, using our reactive flow code that we call TDRR (Temperature Dependent Reaction
Rate) [2]. As we’ve shown previously, by using our TDRR model we’re able to reproduce the
partially reacted boundary layer discussed above. It follows, that if TDRR is also able to
reproduce the above-mentioned scaling deviations as well, this would strengthen our
suggestion mentioned above for the origin of those scaling deviations.
The material parameters in our simulations are those of the explosive PBX9502, but without
the slow reaction component it usually exhibits. And this is probably why we’re not able to
reproduce diameter effect data exactly.
The rod radius in our simulations is between 5 and 10 mm, and the plate thickness is between
5 and 12 mm. We show the simulation results in Fig. 1.