49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition
4 - 7 January 2011, Orlando, Florida
AIAA 2011-271
Modeling the Energy Release and Burn Rate Characteristics
of ZPP Based Initiators
Branden L. Poulsen1 and Karl K. Rink2
University of Idaho, Moscow, Idaho, 83844-0902
Abstract
Bridge-wire initiators using zirconium potassium perchlorate (ZPP) as pyrotechnic are
commonly found in the aerospace, defense, and automotive industries. To measure
pyrotechnic output, it is common practice to discharge initiators into small isochoric test
vessels and monitor the transient pressure response. The maximum pressures obtained in
these tests are usually compared to values determined theoretically based upon a thermochemical analysis. However, an analytical prediction for the rate of pressure increase is
problematic because a complete kinetic description of ZPP combustion is impractical;
furthermore, the burn rate parameters for ZPP are not reported in the literature. In this
research, a previous analytical model describing the energy release characteristic for THPP
based initiators is applied to ZPP initiators. ZPP based initiators are discharged into 100 cm3
test vessels filled with argon at initial pressures ranging between 1.72 and 22.4 MPa. From
these experiments the total energy content of the ZPP formulation used in this work is
determined to be 5600 J/g. Estimates for the burn rate parameters for ZPP are based upon
an earlier model, termed the TPPM, originally developed to describe the transient pressure
response of high pressure argon gas environments heated by burning THPP particles. To
estimate the burn rate parameters for ZPP a quasi-analytical approach using the TPPM is
presented. This approach assumes the initial pressure rise determined from experimental
data is proportional to the initial burn frequency which is defined based upon Vielle’s Law.
Results from this analysis yield a burn rate exponent (n) and burn rate parameter (A) of
approximately 0.47 and 1.94 x 10-3 cm/ms/MPan, respectively. These values for the burn rate
parameters are used as input in a previously developed model, termed the MTPPM,
describing the transient pressure response of argon gas heated by burning pyrotechnic over
a wide range of initial pressures. Predictions from the MTPPM using the burn rate
parameters of ZPP determined in this research are shown to accurately replicate the
measured transient pressures over all initial densities tested. Therefore, the method for
predicting burn rate parameters developed in this work can potentially be applied to other
pyrotechnic formulations.
Nomenclature
MwZPP
Mwi
∆Hrxn
Yi
Ec
Eg
Ei
t
dt
ao
1
2
=
=
=
=
=
=
=
=
=
=
molecular weight of ZPP (g/mol)
molecular weight of the ith species (g/mol)
enthalpy of reaction (kJ/mol)
mol fraction of the ith species (mol species/ mol total)
Energy content of ZPP (kJ/g)
amount of energy transferred from ZPP to surrounding gas (kJ)
energy deposition of ZPP (kJ)
time (ms)
time step (ms)
initial burn rate frequency (ms-1)
Graduate Student, Department of Chemical Engineering, [email protected], Student Member AIAA.
Associate Professor, Department of Mechanical Engineering, [email protected], Associate Fellow AIAA.
1
American Institute of Aeronautics and Astronautics
Copyright © 2011 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
b
A
P
n
d
L
R
T
V
NAr
CpAr
=
=
=
=
=
=
=
=
=
=
=
extinction coefficient (MPa-1/cm)
burn rate parameter (cm/ms/MPan)
pressure inside test vessel (MPa)
burn rate exponent
diameter of test vessel (cm)
characteristic length (cm)
universal gas constant (J/mol/K)
temperature inside reactor (K)
volume of test vessel (cm3)
mol of Argon
constant pressure heat capacity of Argon (J/mol/K)
I. Introduction
P
yrotechnic devices and energetic components are found throughout the aerospace, defense and automotive
industries. A specific type of pyrotechnic initiation device used extensively in the automotive industry is the
bridge-wire initiator. Two common pyrotechnic formulations for bridge-wire initiators commonly used in the
automotive industry are Titanium Hydride Potassium Perchlorate (THPP) and Zirconium Potassium Perchlorate
(ZPP) 1-4. When designing airbag inflation systems analytical predictions of the transient temperatures and pressures
generated by burning initiator pyrotechnic are useful, but they are generally difficult to formulate.
A complete analytical description for the heat transfer from burning pyrotechnic to a surrounding medium
requires the coupling of gas dynamics, chemical kinetics and complex mass and energy balances. Alternatively,
previous work by Poulsen and Rink provides a semi-empirical model capable of predicting the transient pressure
response of argon gas heated by burning THPP particles over a wide range of initial densities5.This model is termed
the modified transient pressure predictive model (MTPPM) and is a function of both the initial pressure of argon gas
and test vessel size. In order to apply the MTPPM to this work the burn rate parameters for ZPP must be first be
determined. Although burn rate parameters for most pyrotechnic formulations can be found in the literature,
parameters for ZPP are not reported. Therefore, a technique to estimate the burn rate parameters of ZPP is presented
in this work.
The objective of this research is to predict the transient pressure response of argon gas heated by burning ZPP
particles. The following list of methods is employed to accomplish this goal. First, the energy content of ZPP
formulation used in this research is determined from a thermo-chemical analysis. Second, the burn rate parameters
are estimated using a quasi-analytical approach in which the initial pressure rise rate determined from experimental
data is proportional to the initial burn frequency based upon Vielle’s Law6. Finally, the estimated burn rate
parameters for ZPP are used as input into the MTPPM. The validity of the MTPPM applied to argon gas heated by
burning ZPP particles is established through a comparison between model results and experimental data.
II. Experimental Apparatus and Methodology
A detailed description of the design and construction of the experimental test vessel used in this work can be
found in the literature7-9. However, some general design features are reviewed for clarity. First, the spherical test
vessel has an internal volume of approximately 100 cm3. This specific test vessel is designed for repetitive use and
will maintain structural integrity under pressures in excess of 690 MPa and transient temperatures typically
generated in isochoric testing of pyrotechnic initiators. Second, the test vessel used in this work has individual
attachment ports containing a static pressure transducer, dynamic pressure transducer, pyrotechnic initiator and fill
valve.
The experimental data collection method used in this work is identical to that described in the work of Poulsen
and Rink5. Dynamic pressures are recorded using Piezotronics® model 119B piezoelectric pressure transducers. An
Agilent 54624A digital oscilloscope is used to record 50 pressure transducer signals every microsecond for a total
duration of 50 milliseconds. The time domain of interest in this work occurs on the order of a few milliseconds and
therefore measurements are sampled at a rate greater than twice the Nyquist frequency10. Since piezoelectric
pressure transducers do not measure static pressures, initial pressure data is recorded using an STI transducer
coupled with an inline amplifier and a desk top computer recording 200 signals every millisecond.
The mass of ZPP in each initiator is approximately 260 mg +/- 10 %. The specific formulation of ZPP used in
this work is 52% Zirconium, 42% Potassium Perchlorate, 5% Viton B binder and 1% graphite. Furthermore, the
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energy content for this specific formulation of ZPP is reported in the literature as 5455 J/g11. The test vessel is
loaded with industrial grade argon gas (99.995 % purity) at pressures varying from 1.72 MPa to 22.4 MPa. Tests are
performed in increments of 1.72 MPa and three test replicates are performed for each experimental condition. In
addition, the test vessel is cleaned prior to each test to remove residual solid combustion products that may influence
the accuracy of the experimental data.
III. Energy Content of ZPP
In order to describe the energy transfer from burning ZPP particles to surrounding argon gas the energy content
for this pyrotechnic composition must be first be known. The specific formulation of the ZPP based initiator used in
this work is 52% Zr, 42% KClO4, 5% Viton B and 1% graphite by weight. Although the energy content for this
specific ZPP formulation is found in the literature11, a thermo-chemical model is developed to estimate the
theoretical energy content of ZPP as a function of zirconium weight fraction. This model is useful when analyzing
the performance of different ZPP formulations. Furthermore, this model is used to validate the MTPPM prediction
for the total energy content of ZPP for the specific formulation used in this work.
In order to develop a model describing the energy content of ZPP as a function of zirconium fuel weight
fraction the simplified global reaction is assumed:
Zr + KClO4 + C + VitonB → ZrO2 + KCl + CO2 + VitonB
(1)
The global reaction described in Equation (1) assumes that Viton B remains inert. The production of carbon dioxide
comes from the complete oxidation of graphite present in the specific ZPP formulation used in this work. The
molecular weights and enthalpies of formation are found using the NIST chemical database12. The mol fraction for
each reactant is found using the molecular weights and the energy from the reaction is determined from the
following:
∆H rxn = YKCl ⋅ ∆H KCl + YZr ⋅ ∆H ZrO2 + YKCl ⋅ ∆H CO2 − YKCl ⋅ ∆H KClO4
(2)
The molecular weight of the ZPP can be found using:
MWZPP = ∑ Yi ⋅ MWi
(3)
i
The energy content of ZPP as a function of weight
fraction can be found using the following equation:
Ec =
∆H rxn
MWZPP
(4)
A model used to predict the energy content of ZPP as a
function of the weight fraction can be formulated based
upon Equations (2-4) and is illustrated in Figure 1. Upon
inspection of Figure 1 the energy content for the specific
formulation of ZPP used in this work is approximately
5750 J/g. Although this prediction is 5.4% above the
reported literature value, it is within the range of
experimental error11.
Figure 1. Energy content of ZPP as a function of weight
fraction of Zirconium
IV. Estimating the Burn Rate Parameters of ZPP
In order to model the energy release characteristics of ZPP based initiators it is convenient to employ Vielle’s
burn rate law6. However, both the burn rate parameter (A) and burn rate exponent (n) for ZPP are required and no
values for these parameters can be found in the literature. Therefore, a method to estimate these unknown burn rate
parameters is developed using the Transient Pressure Predictive Model (TPPM) developed in prior research5.
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The TPPM is comprised of differential equations describing the transient temperature and pressure response of
Argon gas heated by the discharge of a pyrotechnic initiator into an isochoric test vessel. As noted by Poulsen and
Rink the TPPM is only strictly valid for sufficiently high densities of argon gas5. Modifications to the TPPM that
will allow prediction of initiator performance in low initial densities of argon gas are discussed in subsequent
paragraphs.
For clarity, the TPPM equations are shown below:
APt
dT
−
n
E g exp[ −
L
APt
n
t]
L
=0
0.001N Ar (Cp Ar − R )
dt
(5)
where,
E g = mzpp Ec
dP
dt
= X Ar R
(6)
dT
(7)
dt
Equation (5) and Equation (7) describe the transient temperature and pressure response of Argon gas as the total
available energy (Eg) from burning ZPP particles is transferred to the system. To estimate the burn rate parameter
(A) and burn rate exponent (n), Equation (5) and Equation (7) are coupled and evaluated at an initial time zero to
yield:
dP
dt t = 0
=
(
R ⋅ E g APo
n
)
0.001 ⋅ V ⋅ L (Cp Ar − R )
(8)
Where, the characteristic length (L) is assumed to be approximately 45x10-3 cm according to the literature5. Using
the burn frequency defined by Poulsen and Rink and evaluating at time zero provides the initial burn frequency
(ao)5:
ao =
APo
L
n
(9)
Solving Equation (8), the initial burn frequency (ao)
becomes:
ao =
dP
dt t = 0
(
V Cp Ar − R
Eg ⋅ R
)
(10)
The expression for the initial burn frequency is
significant and warrants discussion. The initial pressure
rise rate appearing in Equation (10) can be estimated
through the use of a best fit line to experimental data.
Furthermore, the remaining parameters in Equation (10)
are all known. Therefore, Equation (10) can be solved
for the initial burn frequency (ao) provided that the
requirement for sufficiently high initial argon gas
densities is satisfied. The values for sufficiently high
Figure 2. Energy content of ZPP as a function of initial
initial argon gas densities are significant and therefore
pressure compared to the experimental maximum determined
from Green et al10.
defined in the subsequent paragraph.
The experimentally determined initiator energy as a
function of initial pressure is shown in Figure 2. The initiator energy is seen to increase as a function of initial
pressure in a manner analogous to the results found in Poulsen and Rink5. As gas density increases, the fraction of
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total initiator energy transferred to the argon increases and the energy
Table 1. Initial pressures and initial burn rate
frequencies of ZPP
content asymptotically approaches a maximum of approximately
5600 J for initial pressures ranging between 19.0 and 22.4 MPa.
Po (MPa)
ao (ms-1)
Upon inspection of Figure 2 a deviation between experimentally
determined energy content and the theoretical value is observed. It
18.77
1.70
should be noted, that the inherent uncertainty in the initiator
18.89
1.71
pyrotechnic load can potentially lead to the liberation of an additional
18.92
1.72
142 J. Recall from Section III that it is assumed that the Viton binder
20.42
1.77
is inert. However, since the test reactors contain small amounts of
20.65
1.78
oxygen prior to filling with argon gas there is a possibility the viton
20.80
1.79
binder will oxidize producing additional carbon dioxide and
liberating an additional 175 J. For these reasons, it is possible that an
22.26
1.85
additional 317 J of energy can be transferred to the argon in high
pressure environments. Therefore, the discrepancy between the experimentally determined energy content and the
theoretical value is expected. Regardless, the range of initial pressures where the energy content approaches a
maximum is between 19.0 and 22.4 MPa and is considered in this work as sufficiently high.
The initial burn frequency (ao) is found from Equation (10) using experimental data obtained over initial
pressures ranging from 19.0 to 22.4 MPa. Results from this analysis are shown in Table 1. Non-linear regression
analysis using Mathematica® performed on the data listed in Table 1 yields a burn rate parameter (A) of 1.94x10-3
cm/ms/MPan with a 95% confidence interval of 1.66x10-3 through 2.21x10-3. In addition, the burn rate exponent (n)
is estimated to be 0.47 with a 95% confidence interval of 0.42 through 0.52. In this work, the values for (A) and (n)
are assumed to be unaffected by the temperature changes due to the combustion process. As mentioned above, the
burn rate parameters (A) and (n) for ZPP are not found in the literature. Therefore, to validate the technique used to
estimate the burn rate parameters for ZPP, burn rate parameters for THPP (which are found in the literature13) are
calculated using the experimental data obtained by Poulsen and Rink5.
It should be noted that the experimental work reported by Poulsen and Rink5 for THPP initiators in argon gas
was conducted in an experimental apparatus identical to that used in this work. The energy content for THPP
initiators was found to asymptotically approach a maximum value as the initial pressure increased5. The reader is
referred to the work of Poulsen and Rink5 for more details. The initial burn frequency and initial pressures obtained
from the work of Poulsen and Rink for THPP are shown in Table 2. Non-linear regression analysis applied to this
data using Mathematica® provides a burn rate parameter for THPP of 2.78x10-3 cm/ms/MPan with a 95 %
confidence interval of 2.64x10-3 through 2.91x10-3 and a burn rate exponent of 0.39 with a 95 % confidence interval
of 0.37 through 0.4. The estimate for the burn rate exponent (n) approximately 0.39 compares very well with the
published value13. Furthermore, the estimated burn rate parameter (A) approximately 2.78x10-3 cm/ms/MPan is
within 15% of the reported value13.
The burn rate parameters determined for ZPP combustion are now applied to the MTPPM which is developed to
model the energy release of initiators discharged into low initial density environments. The MTPPM provides a
function describing the energy released by burning pyrotechnic as a function of both the vessel size and the initial
pressure and is:
E g = Ec ⋅ m zpp
(
2 
1 − exp − b ⋅ Po  d 
 3 

)
+ Ei
(11)
Table 2. Initial pressures and initial burn rate
frequencies of THPP
Po (MPa)
27.03
27.27
27.58
30.34
30.78
30.82
34.06
34.59
34.89
ao (ms-1)
2.20
2.21
2.22
2.31
2.31
2.32
2.41
2.42
2.43
The methodology for determining the extinction coefficient (b) and
the energy deposition (Ei) is thoroughly described in the earlier
work of Poulsen and Rink5. Following this method estimates are
found for the extinction coefficient (b) of 0.0128 MPa-1/cm and Ei
of 460 J. The energy deposition (Ei) accounts for energy that may
be released from ZPP in a vacuum condition since some gases are
produced as a product of combustion. In addition, (Ei) accounts for
energy that may be released from the oxidation of the Viton binder,
estimated as approximately 175 J. Equations (1, 3 and 7)
constitute the MTPPM and allow prediction of the transient
pressure response within the isochoric test vessel over all initial
pressures tested. Results from the MTPPM compared to experimental data are presented in the following section.
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V. Results and Discussion
The MTPPM is validated by comparing model
results to experimental pressure data. Unfiltered data is
used for comparison purposes since filtered data can
lead to erroneous conclusions regarding transient
pressures. To examine the model accuracy throughout
the entire range of initial pressures tested, comparisons
are presented for three different initial gas pressures.
Results for initial pressures of 1.72 MPa, 12.1 MPa and
22.4 MPa are shown in Figures 3-5, respectively. In all
cases the model accurately predicts the experimental
data for times greater than two milliseconds. The
MTPPM accurately predicts experimental data over the
entire transient period of interest for the highest initial
densities tested. This characteristic of the MTPPM
agrees with the prior work of Poulsen and Rink for
THPP initiators discharged in argon, in which agreement
between model predictions and experimental data was
best for the highest initial densities tested5.
Agreement between model predictions and
experimental results begins to deviate as initial density
decreases. More specifically, a deviation between model
predictions and experimental data is seen to occur for
times less than two milliseconds at the lowest density
tested. This affect is also observed in the prior work of
Poulsen and Rink5. The deviation between the model
results and experimental data is not unexpected based
upon the complex flow phenomena resulting from
initiator discharge into the closed vessel. The test vessel
is designed so that the transducer is not directly exposed
to hot radiate particles generated from initiator
combustion7. However, the pressures generated during
the combustion of ZPP results in the rupture of the
initiator output can and production of a shock wave. A
simple calculation of the shock velocity based upon
initial conditions coupled with the geometry of the test
vessel indicates that the shock will interact with the
transducer in approximately 0.18 milliseconds.
Therefore, due to complex shock phenomena affecting
the transducer it is not surprising that for low initial
densities the model does not accurately replicate the
experimental data for transient times less than two
milliseconds. Regardless, the MTPPM applied to this
work accurately predicts the transient pressure response
of argon gas heated by the energy transferred from
burning ZPP particles for all initial pressures tested.
In summary, the MTPPM employs the estimated
values for the burn rate parameters of ZPP and the
model accurately represents the transient pressure
response of argon gas as measured in the 100 cm3 test
vessel. Therefore, the method developed in Section IV
to estimate ZPP burn rate parameters appears justified.
Figure 3. Comparison between the MTPPM and experimental
data for the 100 cm3 vessel at an initial pressure of 1.72 MPa.
Figure 4. Comparison between the MTPPM and experimental
data for the 100 cm3 vessel at an initial pressure of 12.1 MPa.
Figure 5. Comparison between the MTPPM and experimental
data for the 100 cm3 vessel at an initial pressure of 22.4 MPa.
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VI. Conclusions and Recommendations
A method is developed that provides estimates for the burn rate parameters of ZPP. The method employs the
TPPM at high initial gas densities in order to determine values for the initial burn frequency (ao). To validate this
approach, burn rate parameters determined for THPP are compared to literature values. In addition, the predicted
and literature values are shown to be in agreement. Therefore, the burn rate exponent (n) and burn rate parameter
(A) of ZPP are determined to be approximately 0.47 and 1.94 x 10-3 cm/ms/MPan, respectively.
The burn rate parameters of ZPP are used as input into the MTPPM to develop a set of differential equations
that describe the transient temperature and pressure response of argon gas heated by burning ZPP particles. The
results of the MTPPM are compared to unfiltered experimental transient pressure data for three different initial
pressure conditions: 1.72 MPa, 12.1 MPa and 22.4 MPa. In general, the MTPPM is found to predict the rate of
pressure increase within the magnitude of experimental error. This provides further validation for both the method
employed to estimate burn rate parameters and the specific values determined for the ZPP formulation used in this
work.
The energy content model and the burn rate parameter estimation method are coupled with the MTPPM. As a
result, the transient pressure response of argon gas heated by the discharge of a ZPP-based initiator into an isochoric
vessel can be accurately modeled. Future work will involve application of this method to other pyrotechnic initiator
formulations. Of specific interest are pyrotechnic formulations for which burn rate parameters are unknown.
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4
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11
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13
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