Calculation of TNT Equivalence of Energy Propellant and Visualized

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					       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

composite propellant.
     Keywords: Composite Propellant; TNT equivalence; Minimum Free Energy Method;

1 Introduction
     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

propellant building.

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                                                cd
                               G                       xg                    G   
            G (n)  i 1 [ x  m      xig ln p  xig ln ig ]  i m1 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

                     cd  cd
gaseous component; Gi ( xi ) is the free energy function of i condensed component; m is the

                                            xig                                                        xicd
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
                                                  m                   n
                                         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

                    d ij
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

             m                     l

              Gig ( y)   j a j
             i 1                 j 1
             Cicd    j d ij  0
                           j 1

Iterative partial code is as follows:
          p2=P(2);%T=[500 2250 3999];
               if (P(3)-P(1))<5
                     if P22>P(2)
                if count2>100
                     disp('不收敛 2');

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
                 Ammonium                                                      RDX(%)
    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

three steps.

                                                                  Figure 1

       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.
                                              Figure 2

                                              Figure 3

    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.

5 Conclusions
     (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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