Calculation of TNT Equivalence of Composite Propellant and
Visualized Software Development
HE Ning1，ZHANG Qi，XIANG Cong，QIN Bin
(1.State Key Laboratory of Explosion Science and Technology, Beijing institute of technology,
Beijing 100081, China)
Abstract: Because the nitramine explosive has high mechanical sensitivity and shock wave
sensitivity, the attention is given to the security of modern high energy propellant. It is one of the
main factors on safety researching that effective measures should be taken to determine the TNT
equivalence of Composite propellant. The text based on the minimum free energy method,
compiled Matlab procedures for calculating equilibrium products of composite propellant
detonation and the TNT equivalence of composite propellant with different ratio of propellant.
Based on the Matlab procedures, visualized software was developed for calculating the TNT
equivalence of composite propellant, therefore avoiding a number of consuming experiments.
According to the calculating of different ratio of composite propellant, the results indicate that the
same qualities of composite propellant, the more fraction of aluminum have a burst of higher
calorific value, and higher thermal damage to the environment. Meanwhile increasing the
components of the mass fraction of solid explosives, the combustion properties of propellant can
be effectively improved. The obtained conclusion provided theoretical of the risk assessment on
composite propellant and provides a basis for understanding to improve the safety performance of
Keywords: Composite Propellant; TNT equivalence; Minimum Free Energy Method;
Solid propellant is the power source of rocket and missile engines, it is difficult to distinguish
between the nature of the solid propellant and explosives from chemical nature. Its reaction heat
and energy density match conventional high efficiency explosives or even higher1-2. However,
composite solid propellant is not only a according to fixed law burning material, and with the
potential danger of explosion or detonation. On the other hand, due to a variety of high-energy
propellant manufacturing process involved to add high-energy explosives, the design of
manufacture, processing and storage warehouse studio should be based on the actual risk of
having to determine the risk level of the building and a safe distance. However, for the research on
the safety of high-energy propellant system in our country has not yet been carried out, it is no
doubt that the process of high-performance weapons and equipment would be hindered. With the
increasing applications of high-energy propellant in rockets, missiles and other high-tech weapons
and equipment, this problem has become increasingly prominent. Therefore, to determine the TNT
equivalence of composite propellant is an essential task.
In previous studies, the determination of TNT equivalence of composite propellant is
mainly in experimental study3-7. Using the simulation pressure - scaled distance relations
consistent with the experiment results got from TNT and composite propellant explosion are
obtained by the least squares algorithm and curve regression8-10. However, on the system risk
analysis point of view, lacking of the research on the greatest damage energy; on the other hand,
experimental studies do not consider composite propellant thermal explosion of different ratio.
The text based on the minimum free energy method, compiled Matlab procedures for calculating
equilibrium products of composite propellant detonation and the TNT equivalence of composite
propellant with different ratio of propellant to improve the safety performance of composite
propellant and provide reference the risk of internal and external security distance of composite
2 Determine the TNT equivalent of composite propellant
Detonation is a limit state of explosion11, on the system security analysis point of view should
be considered a state of composite propellant detonation of the physical parameters of the basic
indicators for the safety assessment. Composite propellant detonation parameters are the important
indicators of procedural security. Consider the composite propellant detonation process in a given
temperature and pressure conditions, the system may also contain gas and condensed phase
products (if complete combustion of carbon particles)12-15. Assuming that a chemical with L
element composition, combustion product generation n gaseous product and n-m condensed
product matter of a system, and its free energy function as follows16-19:
G xg G
G (n) i 1 [ x m xig ln p xig ln ig ] i m1 xicd m
m g n
i RT RT
i x i (1)
G g (x g )
Where G(n) is the function of system total free energy; i i is the free energy function of i
gaseous component; Gi ( xi ) is the free energy function of i condensed component; m is the
material standard free energy; is the amount of i gaseous components; is the amount of
i condensed component; n is the system amount of substance including all components; T is the
system temperature; P is the system pressure.
Atomic conservation equation is
n j aij xig d ij xicd
i 1 i m 1 (j=1,2,3,l) (2)
nj a ij
where is the j amount of substance; is the j amount of substance in the i gaseous
components; is the j amount of substance in the i condense components.
According to the basic equations (1)、(2) , the iterative equations (3) are as follows:
l n m
a j (1 u ) r jk j d ij xicd n j aij yig (Cig ln yig ln y )
j 1 i m 1 i 1
Gig ( y) j a j
i 1 j 1
Cicd j d ij 0
Iterative partial code is as follows:
p2=P(2);%T=[500 2250 3999];
3 Examples and Results
In this text, 4 different formulations composite propellant are pleasing to calculate, the mass
ratio of each component see Table1.
Table1 the mass ratio of each component
Groups Aluminum(%) HTPB (%)
1 70 18 12 ——
2 70 5 10 15
3 60 28 12 ——
4 47.4 6 13.8 32.8
Detonation balance products of each group see results in table 2.
Table 2 Detonation balance products of each group1）
Group 1 Group 2 Group 3 Group 4
H2O 0.5455 1.3815 0.3146 1.1897
H2 0.5134 0.2904 0.4943 0.8193
O2 1.17e-16 1.05e-7 2.97e-21 7.09e-11
CO2 0.0951 0.2594 0.0970 0.1981
CO 0.2700 0.3846 0.2637 0.4884
NO 2.60e-11 2.31e-5 2.133e-14 1.62e-7
N2 0.202 0.458 0.144 0.6253
Cl 3.65e-8 1.6e-4 3.790e-10 4.43e-6
HCl 0.404 0.5358 0.288 0.3928
Al2O 2.84e-25 3.48e-13 2.392e-33 2.73e-16
Al2O3(s) 0.2034 0.0783 0.2268 0.1171
Al(s) 0.0452 0.0174 0.1312 0.0261
C(s) 0.2388 0.4505 0.1409 0.7334
1) C-J detonation balance products till now no reliable experimental data for comparison
Based on similar principles of energy conversion by thermal explosion, the TNT equivalent
of four different composite propellant groups see Table 3.
Table 3 TNT equivalent of four different composite propellant groups
Group 1 Group 2 Group 3 Group 4
Thermal explosion Q 6.74
3.616 4.36 4.05
TNT equivalent 0.798 0.95 0.89 1.48
4 Visualization software of TNT equivalent
Visualization software introduction:
The software interface shown in figure 1. Operate the software mainly by setting the initial
conditions and the distribution ratio of propellant group; Calculating; and the results outputting
Taken Group 1 for an example, input data (see Figure 2), clicks 'Start' begin calculation.
Results show that in the interface (see Figure 3). To make a new calculation, click 'Clear Data',
input initial data.
Visualization software features:
(1) Simple, easy to use
Visualization software using Matlab, intuitive interface, simple. Familiar with the operating
system and Matlab researchers can grasp the software as simple as using office software. Under
normal circumstances, the researchers prompted the label in accordance with the interface, simply
input initial parameters, the composition ratio of propellant, and then the calculation will be start.
( This software applies to the current composition of the propellant formulations of AP, Al, RDX
and HTPB，it is possible to further developed to be applied to other components of the formula).
(2) Higher accuracy
Software based the minimum free energy method to calculate the balance components of
detonation products, which can be a very good description of detonation product, and its results
close with the true values. Simple chemical reactions can be balanced to determine the equilibrium
constant component, but the complexity of propellant detonation may be as many as dozens of
products, including C, H, O, N, Cl, F, Al and other elements of its chemical equilibrium
calculation involving dozens of different chemical reactions, required the establishment of large
non-linear equations, it is difficult to accurately determine the chemical equilibrium constant, and
the equations are extremely difficult to solve20-24. Minimum free energy ignores the detailed
chemical reaction process, only considering the final state of equilibrium; build the conditions for
linear equations only by the element conservation and the system smallest free energy condition,
so the calculation is larger simplify.
(1) The results shows that in the same initial conditions, the same quality composite
propellant, which with the Al content increases, the calorific is larger, that is, develop the quality
of Al will improve the thermal contribution. With the solid explosive content in the propellant
increased, the propellant can be improved explosive performance.
(2)Visualization of the composite propellant TNT equivalent software to determine the
product of propellant detonation, TNT equivalent calculation becomes simple, convenient,
avoiding consuming a large number of experiments. The obtained conclusion provided theoretical
of the risk assessment on composite propellant and provides a basis for understanding to improve
the safety performance of composite propellant.
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