Chemistry Reference
In-Depth Information
that of the sample-block contact). This systematic inaccuracy does not cause any
significant errors when estimating the kinetic parameters.
When analyzing experimental data, one should also evaluate the limits of the ap-
plicability of the homogeneous model for ignition in real heterogeneous composite
solid propellants at
T
0
= const. The model is believed to be valid if the reaction layer
thickness exceeds the maximum characteristic size of the AP crystal. For most of
the ignition delay period, the temperature field in the composite solid propellant can
be described using
=
er f
x
,
T
−
T
∞
2
√
a
s
t
ign
(5.3)
−
T
0
T
∞
where
a
s
is the temperature diffusivity of the sample.
The upper limit of
t
ign
is important for homogeneous systems, since it deter-
mines the applicability of the semi-infinite continuum preheating and ignition model
to samples of a finite length
l
0
(for composite solid propellants and powders at
l
0
= 1 cm the upper limit of
t
ign
is in the range of 150-200 s). Assuming that the
temperature change in the reaction layer is equal to one Semenov interval R
T
0
/
E
(with an accuracy that is acceptable for approximate estimation), one obtains for the
reaction layer thickness at the moment of ignition,
Δ
ign
,
Δ
ign
2
√
a
s
t
ign
.
R
T
0
E
(
T
0
−
T
∞
)
=
Φ
(5.4)
For standard composite solid propellants with high contents of fine-grained AP, one
can suppose that
10
−
4
cm. Thus, for example, for a typical polyurethane
composite solid propellant (with the thermophysical characteristics given above and
E
Δ
ign
≥
165 kJ mol
−
1
), the homogeneous model is valid for
t
ign
≥
3
.
5s.
An expression obtained by Averson, Barzykin and Merzhanov [11] (who studied
ignition at
T
0
= const for a first-order reaction) in order to analyze the experimental
data is
≈
2
0∞
3
/
2
)(1 +
τ
ign
=(1 + 1
.
6
Θ
0∞
+ 0
.
2
Θ
)(1 + 8
Θ
0∞
γ
β
)
,
(5.5)
where
exp
.
R
T
0
E
E
R
T
0
c
Q
=
R
T
0
E
τ
ign
=
t
ign
Qk
0
E
c
R
T
0
E
R
T
0
Θ
0∞
=
(
T
0
−
T
∞
);
γ
=
;
β
;
−
Equation (5.5) was obtained by the approximation of a numerical solution for a com-
plete set of thermal conductivity and kinetic equations. An analytical expression for
the
) dependence cannot be obtained by the ignition methods. However, for a
wide range of non-self-catalyzed reactions occurring at
T
= const, the inaccuracy
caused by the a priori assignment of
ϕ
(
η
) does not result in serious errors when de-
termining
Qk
0
and especially
E
, due to the low degree of conversion (
ϕ
(
η
η
ign
) attained
for
t
ign
.
The determination of kinetic constants by the ignition method is considered in
Sect. 5.4.
