Burning Behavior of Composite Propellant Containing Fine Porous Ammonium Perchlorate, CHEMIA I PIROTECHNIKA, ...
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182
Propellants, Explosives, Pyrotechnics 23, 182±187 (1998)
Burning Behavior of Composite Propellant Containing Fine Porous
Ammonium Perchlorate
Makoto Kohga and Yutaka Hagihara
Department of Chemistry, The National Defense Academy, Hashirimizu 1±10±20, Yokosuka, Kanagawa, 239-8686 (Japan)
Abbrandverhalten von Komposit-Treibstoffen mit Gehalt an fein
por Èsem Ammoniumperchlorat
Fein por Èses Ammoniumperchlorat (FPAP) wurde hergestellt durch
SprÈ htrocknung. Das Abbrandverhalten eines Treibstoffs mit FPAP
wurde untersucht und verglichen mit einem Treibstoff mit feinem
nichtpor Èsem Ammoniumperchlorat (PAP), bei welchem die mittlere
Korngr Èûe fast dieselbe war wie bei FPAP. Die Ergebnisse sind wie
folgt: (1) Die Abbrandgeschwindigkeit des Treibstoffs mit FPAP
nimmt zu bei zunehmendem FPAP-Gehalt. (2) Wenn die Treibstoffe
mit FPAP oder PAP dieselbe Zusammensetzung haben, ist die
Abbrandgeschwindigkeit des Treibstoffs mit FPAP gr È ûer als dieje-
nige des Treibstoffs mit PAP bei unterschiedlichen DrÈ cken. (3) Die
Temperaturemp®ndlichkeit des Treibstoffs mit FPAP nimmt ab mit
zunehmendem Druck. (4) Es wurde gefunden, daû die Unterschiede im
Abbrandverhalten des Treibstoffs mit FPAP und des Treibstoffs mit
PAP ihre Ursache haben in der PorositÈt von FPAP.
Mode de combustion de propergols composites contenant un per-
chlorate d'ammonium microporeux
Du perchlorate d'ammonium microporeux (FPAP) a Ât synthÂtisÂ
par sÂchage par pulvÂrisation. Le mode de combustion d'un propergol
Á base de FPAP a Ât Âtudi et compar Á un propergol contenant du
perchlorate d'ammonium ®n sans porosit (FAP), dont la granulo-
m
Â
tric moyenne
Â
tait
Á
peu pr
Á
slam
Ã
me que celle du FPAP. Les
rÂsultats sont les suivants: (1) La vitesse de combustion du propergol Á
base de FPAP augmente avec la teneur de FPAP. (2) Lorsque les
propergols Á base de FPAP ou de FAP possÁdent la mÁme composi-
tion, la vitesse de combustion du propergol
Á
base de FPAP est
supÂrieure Á celle du propergol Á base de FAP pour des pressions
diff
Â
rentes. (3) La sensibilit
 Á
la temp
Â
rature du propergol
Á
base de
FAP est relativement constante sous des pressions diffÂrentes, mais Á
base de FPAP elle diminue lorsque la pression augmente. (4) On a
montr que les diffÂrences de modes de combustion du propergol Á
base de FPAP et du propergol Á base de FAP Âteient dues Á la porositÂ
du FPAP.
Summary
prepared by heating in temperature range of 500 K±560 K
and decomposing a part of AP particles.
It is reported that ®ne porous AP (FPAP) can be prepared
by the spray-drying method
(5)
, in which the droplets of an
AP solution atomized by pneumatic atomizer are dried by
the air stream of high temperature. The mean diameter and
the speci®c surface area of FPAP prepared by the spray-
drying method are about 3.5 mm and 2.1610
3
m
2
=kg,
respectively. Since FPAP has the particle characteristics
which combines that of a ®ne AP and that of a porous AP,
the burning behavior of the propellant containing FPAP is
particularly interesting.
The purpose of the present study is to study the burning
behavior of composite propellants containing FPAP as
oxidizer. When the propellant is prepared with only FPAP,
the maximum FPAP content in the propellant is 73 wt%.
Therefore, the propellant containing 80 wt% AP is prepared
by mixing FPAP and a ground commercial AP (GrAP). The
effect of FPAP content in the propellant on the burning rate
based on a bimodal oxdizer, which is different in the rela-
tive amounts of FPAP and GrAP in the propellant con-
taining 80 wt% AP, is examined. And the measurements of
the combustion wave structures at different initial pro-
pellant temperatures are done in order to determine the
mode of the temperature sensitivity of burning rate of the
propellant containing FPAP.
A ®ne porous ammonium perchlorate (FPAP) was prepared by the
spray-drying method. The burning behavior of a propellant containing
FPAP was investigated and compared with that of a propellant con-
taining a ®ne ammonium perchlorate without porosity (FAP), of which
the mean diameter was almost the same as that of FPAP. The results
are as follows: (1) The burning rate of the propellant containing FPAP
increases with increasing FPAP content. (2) When the propellants
containing FPAP or FAP have the same composition, the burning rate
of the propellant containing FPAP is larger than that of the propellant
containing FAP at various pressures. (3) The temperature sensitivity of
a propellant containing FAP is relatively constant at various pressures.
However the temperature sensitivity of the propellant containing FPAP
decreases with increasing pressure. (4) It was found that the differ-
ences in the burning behavior of the propellant containing FPAP and
the propellant containing FAP are caused by the porosity of FPAP.
1. Introduction
Ammonium perchlorate (AP) is the most widely used
oxidizer in composite propellants. The burning rate of AP
composite propellants can be controlled by the physical
properties of the combustion wave structure such as dif-
ferent sizes of AP particles. For example, it is generally
known that the burning rate of propellants increases with
decreasing the mean diameter of AP particles. And the
burning rate of propellants containing porous AP (PAP) has
been studied in some references
(1±3)
, where the positive
effect of PAP on the burning rate of propellants is proved.
PAP used in the earlier papers
(1,2,4)
was prepared by the
thermal decomposition of large AP particles, of which the
mean diameter was larger than 177 mm. Because PAP was
2. Experimental
In this study, three kinds of AP are used as oxidizer:
FPAP, ®ne AP(FAP), and GrAP. As mentioned above,
# WILEY-VCH Verlag GmbH, D-69451 Weinheim, 1998
0721-3115/98/0408±0182 $17.50:50=0
Propellants, Explosives, Pyrotechnics 23, 182±187 (1998)
Burning Behavior of Composite Propellant 183
Table 1. Propellant Compositions Tested in this Study
Ingredients
Propellant Composition (wt %)
A
B
C
D
E
F
G
H
GrAP
80
72
56
40
32
32
0
0
FPAP
0
8
24
40
48
0
73
0
FAP
0
48
0
73
HTPB
20
27
FPAP is prepared by the spray-drying method and the mean
particle diameter is about 3.5 mm. The mean particle dia-
meter of FAP is about 3 mm, which is almost the same as
that of FPAP. GrAP is prepared by grinding a commercial
AP for 5 minutes in a vibration ball mill, and the mean
particle diameter of GrAP is about 105 mm. HTPB
(hydroxy-terminated polybutadiene) is used as a binder. The
compositions of propellants tested in this study are shown in
Table 1. The propellant mixtures are then cured for 4 days
at 333 K. HTPB is cured with isophorone diisocyanate.
The size of each strand is 10 mm610 mm in cross sec-
tion and 40 mm in length. The side of each strand is
inhibited by silicon resin. The burning rate is measured in a
chimney-type strand burner which is pressurized with
nitrogen. The strand burner is set in a temperature condi-
tioner which is operated at a temperature of 2881.5 K or
3332 K. The temperature of the nitrogen is also condi-
tioned by a heat exchanger set in a temperature conditioner.
The ignition of each strand is conducted by an electrically
heated nichrome wire attached on the top of each strand.
The burning rate is measured in a pressure range of 0.7 MPa
to 7 MPa, and is calculated with the cutoff period of two
fuses which penetrate the strand at 25 mm distance.
Figure 1. Burning rate of Propellants A±E measured at 288 K.
Table 2. Burning Behavior of Experimental Propellants
Prop.
Burning rate (mm=s)
Pressure
exponent
0.7 MPa
1 MPa
3 MPa
5 MPa
7 MPa
(ÿ)
A
3.58
4.05
5.92
7.06
7.93
0.35
B
3.96
4.21
6.27
7.55
8.52
0.36
C
4.00
4.57
7.09
8.69
9.94
0.40
D
5.32
6.22
10.09
12.64
14.66
0.44
E
5.70
6.74
11.34
14.44
16.93
0.47
F
4.81
5.61
9.03
11.26
13.03
0.44
Propellant E is almost the same as that of Propellant F. The
difference in the composition between Propellant E and
Propellant F depends on whether AP mixed in the pro-
pellants was FPAP or FAP. It indicates that the positive
effect of FPAP on the burning rate is attributed to the
porosity of FPAP, since the mean diameter of FPAP is
almost the same as that of FAP. In order to reveal the
combustion process of the propellant containing FPAP, the
following qualitative analysis was done. The ¯ame of AP
composite propellant is a so-called diffusion ¯ame, and the
model of Multiple Flames
(6)
3. Results and Discussion
3.1 Burning Rate Characteristics
is generally accepted as a
The burning rates of Propellants A±E measured at 288 K
are shown in Figure 1. Their burning rates increase linearly
in a plot of log r versus log P in the pressure range of
0.5 MPa±8 MPa. The measured burning rates and pressure
exponents are given in Table 2. In order to make more clear
the effect of FPAP content on the burning rate at various
pressures, the relationship between FPAP content and the
burning rate at various pressures is shown in Figure 2. It is
seen that the burning rate increases with increasing FPAP
content at various pressures, and especially the increments
of burning rate at high pressures are larger than those at low
pressures.
The burning rate of Propellant F measured at 288 K is
shown in Figure 3. The measured burning rates and pressure
exponent are also given in Table 2. It is seen that the
burning rate of Propellant E is larger than that of Propellant
F in the pressure range tested, and the pressure exponent of
Figure 2. The effect of FPAP content on the burning rate.
184 M. Kohga and Y. Hagihara
Propellants, Explosives, Pyrotechnics 23, 182±187 (1998)
Figure 3. Burning rates of Propellants E and F.
a lower pressure the AP particles protruded above the
exposed surface of the binder to a greater height and at a
higher pressure they recessed. In other words, at a low
pressure the regression rate of the AP particles is less than
that of the binder and vice versa at higher pressures
(7,8)
. As
mentioned above, the AP monopropellant ¯ame is formed
on AP particles exposed to the burning surface. It seems that
when the regression rate of the AP particles is larger than
that of the binder, the location of each ¯ame is brought
closer to the burning surface. This indicates that (dT=dx)
s
increases with increasing difference between the regression
rate of the AP particle and that of the binder. Consequently
the location of each ¯ame is dependent on the diffusion
distance to react with the oxidizer and binder decomposition
products and the difference between the regression rate of
the AP particle and that of the binder.
As given in Table 2, the burning rate of Propellant E is
larger than that of Propellant F. The reason is considered as
follows. The decomposition area of FPAP particles is wider
than that of FAP particle, because FPAP particles are por-
ous. At a constant pressure, namely when the diffusion
distance to react with the oxidizer and binder decomposition
products is constant, the regression rate of FPAP particles is
larger than that of FAP particles. And it suggests that the
location of each ¯ame of Propellant E is brought closer to
the burning surface, and (dT=dx)
s
of Propellant E is larger
than that of Propellant F. In order to con®rm this, the
burning surface of Propellants G and H extinguished was
observed under a scanning electron microscope (SEM). The
SEM photographs of the burning surface of both propellants
extinguished at atmospheric pressure are shown in Figure 4.
In Figure 4, holes exist at the burning surface of Propellant
G, and AP remains in the hole on the burning surface of
Propellant H. It is found that the regression rate of FPAP
particles is larger than that of FAP particles, even at a low
pressure. As mentioned above, at a lower pressure the AP
particles protruded above the exposed surface of the binder
to greater height and at a higher pressure they recessed.
Therefore, the burning surface of Propellant G extinguished
at atmospheric pressure was similar to the burning surface
of the propellant extinguished at a high pressure. The result
supports the above consideration.
model of the ¯ame structure. According to the model of
Multiple Flames, the ¯ame structure of AP composite pro-
pellant consists of the AP monopropellant ¯ame, the pri-
mary ¯ame, and the ®nal diffusion ¯ame. The AP
monopropellant ¯ame, which is composed of AP decom-
position products, is not considered to occur at the pro-
pellant surface, but to extend from the surface. The primary
¯ame is a premixed ¯ame with the oxdizer and binder
decomposition products mixing completely before reaction
occurs. And the ®nal diffusion ¯ame follows the primary
¯ame. On the other hand, the burning rate is given by the
heat balance equation at the burning surface as follows:
r
l
g
dT=dx
s
c
p
r
p
T
s
ÿ T
o
ÿ Q
s
=c
p
1
where r is burning rate, l is thermal conductivity, (dT=dx) is
temperature gradient in the vicinity of the burning surface, c
is speci®c heat, r is density, T
s
is temperature at the burning
surface, T
o
is initial temperature of propellant, and Q
s
is
heat per unit mass generated at the burning surface. Sub-
scripts g, p, and s mean gas phase, propellant, and gas
phase at the burning surface, respectively. When the com-
positions of propellant are constant, it can be assumed that
l
g
, c
p
, r
p
, and T
s
of the propellants are almost the same
values, respectively, at the same pressure. When T
o
is
constant, Eq. (1) indicates that the burning rate increases
with increasing (dT=dx)
s
. Consequently (dT=dx)
s
is a
dominant factor on the burning rate. It can be considered
that (dT=dx)
s
is dependent on the location of each ¯ame;
and when the location of each ¯ame is brought close to the
burning surface, (dT=dx)
s
increases. In general, the burn-
ing rate increases with increasing pressure. This can be
explained as follows. The diffusion distance to react with
the oxidizer and binder decomposition products decreases
with increasing pressure, and the location of each ¯ame is
brought closer to the burning surface. This implies that
(dT=dx)
s
increases with increasing pressure. On the other
hand, when the burning surface of a propellant extinguished
by rapid depressurization was observed, it was found that at
Figure 4. SEM micrographs of the burning surface of Propellants G
and H extinguished.
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182
Propellants, Explosives, Pyrotechnics 23, 182±187 (1998)
Burning Behavior of Composite Propellant Containing Fine Porous
Ammonium Perchlorate
Makoto Kohga and Yutaka Hagihara
Department of Chemistry, The National Defense Academy, Hashirimizu 1±10±20, Yokosuka, Kanagawa, 239-8686 (Japan)
Abbrandverhalten von Komposit-Treibstoffen mit Gehalt an fein
por Èsem Ammoniumperchlorat
Fein por Èses Ammoniumperchlorat (FPAP) wurde hergestellt durch
SprÈ htrocknung. Das Abbrandverhalten eines Treibstoffs mit FPAP
wurde untersucht und verglichen mit einem Treibstoff mit feinem
nichtpor Èsem Ammoniumperchlorat (PAP), bei welchem die mittlere
Korngr Èûe fast dieselbe war wie bei FPAP. Die Ergebnisse sind wie
folgt: (1) Die Abbrandgeschwindigkeit des Treibstoffs mit FPAP
nimmt zu bei zunehmendem FPAP-Gehalt. (2) Wenn die Treibstoffe
mit FPAP oder PAP dieselbe Zusammensetzung haben, ist die
Abbrandgeschwindigkeit des Treibstoffs mit FPAP gr È ûer als dieje-
nige des Treibstoffs mit PAP bei unterschiedlichen DrÈ cken. (3) Die
Temperaturemp®ndlichkeit des Treibstoffs mit FPAP nimmt ab mit
zunehmendem Druck. (4) Es wurde gefunden, daû die Unterschiede im
Abbrandverhalten des Treibstoffs mit FPAP und des Treibstoffs mit
PAP ihre Ursache haben in der PorositÈt von FPAP.
Mode de combustion de propergols composites contenant un per-
chlorate d'ammonium microporeux
Du perchlorate d'ammonium microporeux (FPAP) a Ât synthÂtisÂ
par sÂchage par pulvÂrisation. Le mode de combustion d'un propergol
Á base de FPAP a Ât Âtudi et compar Á un propergol contenant du
perchlorate d'ammonium ®n sans porosit (FAP), dont la granulo-
m
Â
tric moyenne
Â
tait
Á
peu pr
Á
slam
Ã
me que celle du FPAP. Les
rÂsultats sont les suivants: (1) La vitesse de combustion du propergol Á
base de FPAP augmente avec la teneur de FPAP. (2) Lorsque les
propergols Á base de FPAP ou de FAP possÁdent la mÁme composi-
tion, la vitesse de combustion du propergol
Á
base de FPAP est
supÂrieure Á celle du propergol Á base de FAP pour des pressions
diff
Â
rentes. (3) La sensibilit
 Á
la temp
Â
rature du propergol
Á
base de
FAP est relativement constante sous des pressions diffÂrentes, mais Á
base de FPAP elle diminue lorsque la pression augmente. (4) On a
montr que les diffÂrences de modes de combustion du propergol Á
base de FPAP et du propergol Á base de FAP Âteient dues Á la porositÂ
du FPAP.
Summary
prepared by heating in temperature range of 500 K±560 K
and decomposing a part of AP particles.
It is reported that ®ne porous AP (FPAP) can be prepared
by the spray-drying method
(5)
, in which the droplets of an
AP solution atomized by pneumatic atomizer are dried by
the air stream of high temperature. The mean diameter and
the speci®c surface area of FPAP prepared by the spray-
drying method are about 3.5 mm and 2.1610
3
m
2
=kg,
respectively. Since FPAP has the particle characteristics
which combines that of a ®ne AP and that of a porous AP,
the burning behavior of the propellant containing FPAP is
particularly interesting.
The purpose of the present study is to study the burning
behavior of composite propellants containing FPAP as
oxidizer. When the propellant is prepared with only FPAP,
the maximum FPAP content in the propellant is 73 wt%.
Therefore, the propellant containing 80 wt% AP is prepared
by mixing FPAP and a ground commercial AP (GrAP). The
effect of FPAP content in the propellant on the burning rate
based on a bimodal oxdizer, which is different in the rela-
tive amounts of FPAP and GrAP in the propellant con-
taining 80 wt% AP, is examined. And the measurements of
the combustion wave structures at different initial pro-
pellant temperatures are done in order to determine the
mode of the temperature sensitivity of burning rate of the
propellant containing FPAP.
A ®ne porous ammonium perchlorate (FPAP) was prepared by the
spray-drying method. The burning behavior of a propellant containing
FPAP was investigated and compared with that of a propellant con-
taining a ®ne ammonium perchlorate without porosity (FAP), of which
the mean diameter was almost the same as that of FPAP. The results
are as follows: (1) The burning rate of the propellant containing FPAP
increases with increasing FPAP content. (2) When the propellants
containing FPAP or FAP have the same composition, the burning rate
of the propellant containing FPAP is larger than that of the propellant
containing FAP at various pressures. (3) The temperature sensitivity of
a propellant containing FAP is relatively constant at various pressures.
However the temperature sensitivity of the propellant containing FPAP
decreases with increasing pressure. (4) It was found that the differ-
ences in the burning behavior of the propellant containing FPAP and
the propellant containing FAP are caused by the porosity of FPAP.
1. Introduction
Ammonium perchlorate (AP) is the most widely used
oxidizer in composite propellants. The burning rate of AP
composite propellants can be controlled by the physical
properties of the combustion wave structure such as dif-
ferent sizes of AP particles. For example, it is generally
known that the burning rate of propellants increases with
decreasing the mean diameter of AP particles. And the
burning rate of propellants containing porous AP (PAP) has
been studied in some references
(1±3)
, where the positive
effect of PAP on the burning rate of propellants is proved.
PAP used in the earlier papers
(1,2,4)
was prepared by the
thermal decomposition of large AP particles, of which the
mean diameter was larger than 177 mm. Because PAP was
2. Experimental
In this study, three kinds of AP are used as oxidizer:
FPAP, ®ne AP(FAP), and GrAP. As mentioned above,
# WILEY-VCH Verlag GmbH, D-69451 Weinheim, 1998
0721-3115/98/0408±0182 $17.50:50=0
Propellants, Explosives, Pyrotechnics 23, 182±187 (1998)
Burning Behavior of Composite Propellant 183
Table 1. Propellant Compositions Tested in this Study
Ingredients
Propellant Composition (wt %)
A
B
C
D
E
F
G
H
GrAP
80
72
56
40
32
32
0
0
FPAP
0
8
24
40
48
0
73
0
FAP
0
48
0
73
HTPB
20
27
FPAP is prepared by the spray-drying method and the mean
particle diameter is about 3.5 mm. The mean particle dia-
meter of FAP is about 3 mm, which is almost the same as
that of FPAP. GrAP is prepared by grinding a commercial
AP for 5 minutes in a vibration ball mill, and the mean
particle diameter of GrAP is about 105 mm. HTPB
(hydroxy-terminated polybutadiene) is used as a binder. The
compositions of propellants tested in this study are shown in
Table 1. The propellant mixtures are then cured for 4 days
at 333 K. HTPB is cured with isophorone diisocyanate.
The size of each strand is 10 mm610 mm in cross sec-
tion and 40 mm in length. The side of each strand is
inhibited by silicon resin. The burning rate is measured in a
chimney-type strand burner which is pressurized with
nitrogen. The strand burner is set in a temperature condi-
tioner which is operated at a temperature of 2881.5 K or
3332 K. The temperature of the nitrogen is also condi-
tioned by a heat exchanger set in a temperature conditioner.
The ignition of each strand is conducted by an electrically
heated nichrome wire attached on the top of each strand.
The burning rate is measured in a pressure range of 0.7 MPa
to 7 MPa, and is calculated with the cutoff period of two
fuses which penetrate the strand at 25 mm distance.
Figure 1. Burning rate of Propellants A±E measured at 288 K.
Table 2. Burning Behavior of Experimental Propellants
Prop.
Burning rate (mm=s)
Pressure
exponent
0.7 MPa
1 MPa
3 MPa
5 MPa
7 MPa
(ÿ)
A
3.58
4.05
5.92
7.06
7.93
0.35
B
3.96
4.21
6.27
7.55
8.52
0.36
C
4.00
4.57
7.09
8.69
9.94
0.40
D
5.32
6.22
10.09
12.64
14.66
0.44
E
5.70
6.74
11.34
14.44
16.93
0.47
F
4.81
5.61
9.03
11.26
13.03
0.44
Propellant E is almost the same as that of Propellant F. The
difference in the composition between Propellant E and
Propellant F depends on whether AP mixed in the pro-
pellants was FPAP or FAP. It indicates that the positive
effect of FPAP on the burning rate is attributed to the
porosity of FPAP, since the mean diameter of FPAP is
almost the same as that of FAP. In order to reveal the
combustion process of the propellant containing FPAP, the
following qualitative analysis was done. The ¯ame of AP
composite propellant is a so-called diffusion ¯ame, and the
model of Multiple Flames
(6)
3. Results and Discussion
3.1 Burning Rate Characteristics
is generally accepted as a
The burning rates of Propellants A±E measured at 288 K
are shown in Figure 1. Their burning rates increase linearly
in a plot of log r versus log P in the pressure range of
0.5 MPa±8 MPa. The measured burning rates and pressure
exponents are given in Table 2. In order to make more clear
the effect of FPAP content on the burning rate at various
pressures, the relationship between FPAP content and the
burning rate at various pressures is shown in Figure 2. It is
seen that the burning rate increases with increasing FPAP
content at various pressures, and especially the increments
of burning rate at high pressures are larger than those at low
pressures.
The burning rate of Propellant F measured at 288 K is
shown in Figure 3. The measured burning rates and pressure
exponent are also given in Table 2. It is seen that the
burning rate of Propellant E is larger than that of Propellant
F in the pressure range tested, and the pressure exponent of
Figure 2. The effect of FPAP content on the burning rate.
184 M. Kohga and Y. Hagihara
Propellants, Explosives, Pyrotechnics 23, 182±187 (1998)
Figure 3. Burning rates of Propellants E and F.
a lower pressure the AP particles protruded above the
exposed surface of the binder to a greater height and at a
higher pressure they recessed. In other words, at a low
pressure the regression rate of the AP particles is less than
that of the binder and vice versa at higher pressures
(7,8)
. As
mentioned above, the AP monopropellant ¯ame is formed
on AP particles exposed to the burning surface. It seems that
when the regression rate of the AP particles is larger than
that of the binder, the location of each ¯ame is brought
closer to the burning surface. This indicates that (dT=dx)
s
increases with increasing difference between the regression
rate of the AP particle and that of the binder. Consequently
the location of each ¯ame is dependent on the diffusion
distance to react with the oxidizer and binder decomposition
products and the difference between the regression rate of
the AP particle and that of the binder.
As given in Table 2, the burning rate of Propellant E is
larger than that of Propellant F. The reason is considered as
follows. The decomposition area of FPAP particles is wider
than that of FAP particle, because FPAP particles are por-
ous. At a constant pressure, namely when the diffusion
distance to react with the oxidizer and binder decomposition
products is constant, the regression rate of FPAP particles is
larger than that of FAP particles. And it suggests that the
location of each ¯ame of Propellant E is brought closer to
the burning surface, and (dT=dx)
s
of Propellant E is larger
than that of Propellant F. In order to con®rm this, the
burning surface of Propellants G and H extinguished was
observed under a scanning electron microscope (SEM). The
SEM photographs of the burning surface of both propellants
extinguished at atmospheric pressure are shown in Figure 4.
In Figure 4, holes exist at the burning surface of Propellant
G, and AP remains in the hole on the burning surface of
Propellant H. It is found that the regression rate of FPAP
particles is larger than that of FAP particles, even at a low
pressure. As mentioned above, at a lower pressure the AP
particles protruded above the exposed surface of the binder
to greater height and at a higher pressure they recessed.
Therefore, the burning surface of Propellant G extinguished
at atmospheric pressure was similar to the burning surface
of the propellant extinguished at a high pressure. The result
supports the above consideration.
model of the ¯ame structure. According to the model of
Multiple Flames, the ¯ame structure of AP composite pro-
pellant consists of the AP monopropellant ¯ame, the pri-
mary ¯ame, and the ®nal diffusion ¯ame. The AP
monopropellant ¯ame, which is composed of AP decom-
position products, is not considered to occur at the pro-
pellant surface, but to extend from the surface. The primary
¯ame is a premixed ¯ame with the oxdizer and binder
decomposition products mixing completely before reaction
occurs. And the ®nal diffusion ¯ame follows the primary
¯ame. On the other hand, the burning rate is given by the
heat balance equation at the burning surface as follows:
r
l
g
dT=dx
s
c
p
r
p
T
s
ÿ T
o
ÿ Q
s
=c
p
1
where r is burning rate, l is thermal conductivity, (dT=dx) is
temperature gradient in the vicinity of the burning surface, c
is speci®c heat, r is density, T
s
is temperature at the burning
surface, T
o
is initial temperature of propellant, and Q
s
is
heat per unit mass generated at the burning surface. Sub-
scripts g, p, and s mean gas phase, propellant, and gas
phase at the burning surface, respectively. When the com-
positions of propellant are constant, it can be assumed that
l
g
, c
p
, r
p
, and T
s
of the propellants are almost the same
values, respectively, at the same pressure. When T
o
is
constant, Eq. (1) indicates that the burning rate increases
with increasing (dT=dx)
s
. Consequently (dT=dx)
s
is a
dominant factor on the burning rate. It can be considered
that (dT=dx)
s
is dependent on the location of each ¯ame;
and when the location of each ¯ame is brought close to the
burning surface, (dT=dx)
s
increases. In general, the burn-
ing rate increases with increasing pressure. This can be
explained as follows. The diffusion distance to react with
the oxidizer and binder decomposition products decreases
with increasing pressure, and the location of each ¯ame is
brought closer to the burning surface. This implies that
(dT=dx)
s
increases with increasing pressure. On the other
hand, when the burning surface of a propellant extinguished
by rapid depressurization was observed, it was found that at
Figure 4. SEM micrographs of the burning surface of Propellants G
and H extinguished.
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