Evaluation method for TNT equivalent of high-energy propellant

Abstract

The invention discloses a method for evaluating the TNT equivalent of a high-energy propellant. The method comprises the following specific steps: step 1, obtaining enthalpy of formation and an assumed chemical formula of a solid propellant; 2, according to the formation enthalpy of the known solid propellant, the assumed chemical formula and the product composition, the mole number of all combustion products at the adiabatic combustion temperature of 1 kg of the solid propellant is calculated; 3, calculating the total enthalpy of combustion product generation of 1kg of solid propellant under 298K; 4, subtracting the total enthalpy of the combustion product under 298K from the formation enthalpy of the known solid propellant to obtain a theoretical constant pressure detonation heat value QP of the propellant; 5, obtaining theoretical constant-volume explosion heat Qv by utilizing the theoretical constant-pressure explosion heat value of the propellant and the expansion work of the generated gas-phase component; 6, the theoretical constant volume explosion heat of the propellant is divided by the explosion heat of the standard TNT, and the theoretical TNT equivalent coefficient CTNT of the propellant is obtained. The evaluation method has the advantages of few calculation steps, high efficiency, high calculation precision and wide application range.

Description

Technical Field

[0001] The invention relates to a method for evaluating TNT equivalent, and in particular to a method for evaluating TNT equivalent of high-energy propellant. Background Art

[0002] With the increasing application of high-energy solid composite propellants in high-tech weapons and equipment such as rockets and missiles, the safety of high-energy composite propellants has become increasingly prominent. Usually, the research on the TNT equivalent of solid composite propellant explosion is mainly based on experiments. The method of determining the TNT equivalent of explosives by actual explosion output is studied, which is time-consuming and labor-intensive, and seriously restricts the application of high-energy composite propellants. How to quickly evaluate the TNT equivalent of high-energy propellants has become the key.

[0003] Constant-pressure detonation heat refers to the heat released when 1 kg of solid propellant at a temperature of 298 K is adiabatically burned at constant pressure in an inert gas, and the combustion products drop from the constant-pressure adiabatic combustion temperature to the initial temperature of the propellant before combustion (298 K). According to the basic principles of thermodynamics, constant-pressure detonation heat is equal to the difference between the initial enthalpy of propellant combustion and the sum of the formation enthalpy of the final combustion products of the detonation heat.

[0004] The initial enthalpy of the propellant combustion process is equal to the propellant formation enthalpy, and its value is known. The formation enthalpy of the final combustion product of the deflagration should be the sum of the molar number of various products and the product's standard formation enthalpy at 298.15 K. The final combustion products of the deflagration and their content are the key to the deflagration evaluation.

[0005] The relationship between constant volume detonation heat and constant pressure detonation heat can be converted according to the amount of gaseous product substances in the propellant combustion products. The propellant TNT equivalent coefficient can be obtained according to the ratio of constant volume detonation heat to standard TNT detonation heat.

[0006] He Ning, Xiang Cong, Zhai Haoyu. Calculation of TNT equivalent of solid composite propellant and development of its visualization software[J]. Journal of Ordnance Equipment Engineering, 2019, (4). This paper assumes that the detonation products of solid propellant are composed of 13 substances, namely H 2 O, H 2 , O 2 , CO 2 , CO, NO, N 2 、Cl、HCl、Al 2 O、Al 2 O 3 , Al solid, C solid. Al is not considered specifically 2 O 3 Crystal form, according to the principle of minimum free energy and atomic conservation equation, use Matlab programming to calculate the amount of substance of the components when the system is in equilibrium.

[0007] Northwestern Polytechnical University. A method for calculating the theoretical constant-pressure detonation heat of a solid propellant: China, CN202211018227.X[P].2022-12-2. The patent believes that when the propellant element composition is C, H, O, N, Cl, and Al, the combustion products after the temperature is reduced to 298K are CO, CO 2 , H 2 , H 2 O、N 2 、HCl、AlCl 3 、Al 2 O 3 First, FactSage is used to calculate the adiabatic combustion products of 6.86Mpa propellant, which mainly include Al, AlCl, AlCl 2 、AlCl 3 、AlH、AlHCl、AlHCl 2 , AlO, AlOCl, AlOH, AlOHCl, AlOHCl 2 、Al(OH) 2 、Al(OH) 2 Cl, Al(OH) 3 、Al 2 O、Al 2 O 2 ,CO,CO 2 , Cl, Cl 2 、H、HAlO、HAlO 2 、HCN、HCO、HCl、HNC、H 2 , H 2 O, N, NH, NH 2 NH 3 、NO、N 2 , O, OH, O 2 、Al 2 O 3 (L) A total of 40 products. Assuming that H 2 The contents of O and HCl remain unchanged at 298K. The remaining six CO, CO 2 , H 2 、N 2 、AlCl 3 、Al 2 O 3 The number of moles of product.

[0008] These calculation methods are complex and inefficient. The "Calculation Method for the Theoretical Constant-Pressure Detonation Heat of a Solid Propellant" requires first calculating the content of 40 products, and then determining the amount of material after the combustion product is cooled to 298K through the law of mass conservation. In addition, the calculation results have a large error with the measured results.

[0009] The two calculation methods of "Calculation of TNT equivalent of solid composite propellant and its visualization software development" and "Calculation method of theoretical constant pressure explosion heat of solid propellant" are used. As can be seen from the table, method (1) reports an error and cannot obtain results, and method (2) has a large error in the results. The calculated values ​​of TNT equivalent of two high-energy propellants in the calculation literature and the measured TNT equivalent are shown in the following table:

[0010] Table 1 Calculated and measured TNT equivalents of two high energy propellants

[0011] Summary of the invention

[0012] The technical problem to be solved by the present invention is to provide a method for evaluating the TNT equivalent of a high-energy propellant, so as to solve the problem of determining the explosion heat value generated by the detonation of a solid composite propellant, and to provide a basis for accurately determining the hazard level of the solid composite propellant, the hazard level of a storage plant and the safety distance of the plant environment.

[0013] In order to solve the existing technical problems, the technical solution adopted by the present invention is as follows: a method for evaluating the TNT equivalent of a high-energy propellant, the specific steps are as follows:

[0014] Step 1: Obtain the formation enthalpy and assumed chemical formula of the solid propellant;

[0015] Step 2: Based on the known enthalpy of formation of the solid propellant and the assumed chemical formula and product composition, use the following formula to calculate the number of moles of all combustion products of 1 kg of solid propellant at the adiabatic combustion temperature. These stable products are the combustion products of the solid propellant at 298 K, and their content remains constant during the cooling process;

[0016]

[0017] Where G is the total Gibbs free energy of the system, R 0 is the universal gas constant, 8.314 J / (mol·K), p is the combustion pressure, G i，m and G j，m are the molar Gibbs free energy of the i-th gas phase and the j-th condensed phase at temperature T, N k is the number of moles of the kth element in the solid propellant component, l is the total number of elements, n ig is the number of moles of the i-th gas phase product, m is the total number of gas phase products, a ik represents the number of kth element contained in the i-th gas phase product, n js The number of moles of the jth condensed phase product, n g is the total number of condensed phase products, a jk represents the number of k-th element contained in the j-th condensed phase product, λk is the Lagrange multiplier, there are l of them, where T is the combustion temperature, H i，f，T and H j，f，T are the molar formation enthalpies of the i-th gas phase and the j-th condensed phase at the combustion temperature, respectively;

[0018] Step 3: Calculate the total enthalpy of combustion products of 1 kg solid propellant at 298 K. The total enthalpy of combustion products of solid propellant and the initial enthalpy of solid propellant combustion process H r，f Equal, that is,

[0019]

[0020] Where N p is the total number of combustion products, n j is the number of moles of the jth combustion product of the solid propellant, H j，f is the molar enthalpy of formation of the combustion products at the combustion temperature;

[0021] Step 4: Use the known solid propellant formation enthalpy minus the total enthalpy of the combustion products at 298K to obtain the theoretical constant-pressure detonation heat value Q of the propellant. P

[0022]

[0023] In the formula, H r，f is the initial enthalpy of solid propellant combustion, m is the total number of gas phase products, n is the total number of condensed phase products, and n ig is the number of moles of the i-th gas phase product, n js The number of moles of the condensed phase product, H i，f，298 and H j，f，298 are the molar formation enthalpies of the i-th gas phase and the i-th condensed phase at 298K respectively;

[0024] Step 5: Use the theoretical constant pressure explosion heat value of the propellant plus the expansion work of the generated gas phase component to obtain the theoretical constant volume explosion heat Q v ,

[0025] Q P =Q v -n g R 0 T

[0026] Where n g is the total content of gas phase components, R 0 is the universal gas constant, 8.314 J / (mol·K), and T is 298.15 K;

[0027] Step 6: Divide the theoretical constant volume explosion heat of the propellant by the explosion heat of standard TNT to obtain the theoretical TNT equivalent coefficient C of the propellant. TNT ,

[0028]

[0029] In the formula, Q TNT The explosion heat value of TNT is 4187 kJ / kg.

[0030] Furthermore, the element composition of the solid propellant of the present invention is preferably C, H, O, N, Cl and Al.

[0031] Beneficial Effects

[0032] The evaluation method of the present invention has few calculation steps and high efficiency. It eliminates the conversion and calculation steps of the types and contents of the products after the explosion-heated final product is cooled to room temperature, and does not need to assume that H 2 The contents of O and HCl remain unchanged at 298 K, and only 11 products need to be calculated, which greatly improves the calculation efficiency.

[0033] The evaluation method of the present invention has high calculation accuracy and a wide range of applications, and is particularly suitable for hydroxybutyl propellants and high-energy propellants whose propellant element compositions are C, H, O, N, Cl, and Al. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 Flow chart of the evaluation method of TNT equivalent of high energy propellant;

[0035] Figure 2 Calculation program interface diagram. DETAILED DESCRIPTION

[0036] To make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0037] Constant-pressure detonation heat refers to the heat released when 1 kg of solid propellant at a temperature of 298 K is burned adiabatically at constant pressure in an inert gas, and the combustion products drop from the constant-pressure adiabatic combustion temperature to the initial temperature of the propellant before combustion (298 K). According to the basic principles of thermodynamics, constant-pressure detonation heat Q P Equal to the initial enthalpy of propellant combustion H r，f The difference between the sum of the formation enthalpy of the products of combustion in the final state of explosion.

[0038]

[0039] The initial enthalpy of the propellant combustion process is equal to the propellant formation enthalpy, and its value is known. The formation enthalpy of the final combustion product of the explosion heat should be the number of moles of various products n j The standard enthalpy of formation of the product at 298.15K is j，f，298 Therefore, it is necessary to determine the final combustion products and their contents.

[0040] Constant volume hot Q v With constant pressure explosion heat Q P The relationship between is calculated according to the following formula, where n g Refers to the amount of gaseous product substances in 1 kg of propellant combustion products.

[0041] Q P =Q v -n g R 0 T

[0042] Propellant TNT equivalent coefficient C TNT According to the following calculation, Q TNT The explosion heat value of TNT is 4187 kJ / kg.

[0043]

[0044] The key to calculation is to calculate the theoretical explosion heat. The key to calculation is to determine the final state enthalpy of the combustion products, which requires first determining the composition and amount of the final state products. At present, it is impossible to determine all the final state products of explosion heat by effective experimental methods at home and abroad, and they can only be determined by theoretical calculation.

[0045] The principle of the minimum free energy method for calculating the equilibrium components of the propellant is as follows: the Gibbs free energy of the system takes the minimum value, that is, the following formula takes the minimum value:

[0046]

[0047] The constraints are conservation of mass and conservation of energy.

[0048]

[0049] Where G is the total Gibbs free energy of the system, R 0 is the universal gas constant, 8.314 J / (mol·K), p is the combustion pressure, G i，m and G j，m are the molar Gibbs free energies of the i-th gas phase and the i-th condensed phase at temperature T, respectively. k is the number of moles of the kth element in the propellant component, l is the total number of elements, n ig is the number of moles of the i-th gas phase product, m is the total number of gas phase products, a ik represents the number of kth element contained in the i-th gas phase product, n js The number of moles of the condensed phase product, n is the total number of condensed phase products, a jk represents the number of k-th element contained in the j-th condensed phase product, n g It is the total amount of gaseous products in the combustion products. N p is the total number of combustion products, Hj，f is the molar enthalpy of formation of the combustion products at the combustion temperature.

[0050] According to the objective function of the conditional extreme value of the Lagrange multiplier method, the Lagrange function is differentiated to obtain a nonlinear equation system, which is solved by the Newton-Raphson method iteration method.

[0051]

[0052] where λ k is the Lagrange multiplier, there are l of them, where T is the combustion temperature, H i，f，T and H j，f，T are the molar formation enthalpies of the i-th gas phase and the i-th condensed phase at the combustion temperature, m is the total number of gas phase products, and n is the total number of condensed phase products. The above equations have (m+n+l+1) variables and (m+n+l+1) nonlinear equations. The m+n+l+1 variables are λ k {k=1,l}、n ig {i=1,m}、n js {j=1,n} and T.

[0053] The calculation process of the evaluation method of the present invention is shown in the attached Figure 1 As shown, it includes inputting the components and formation enthalpy of the propellant, inputting the combustion products of the propellant, inputting the VB (Visual Basic) solver, obtaining the nonlinear equations, using Newton-Raphson to solve the product content, calculating the constant pressure detonation heat, calculating the constant volume detonation heat and calculating the TNT equivalent. The propellant components are input according to the assumed chemical formula, and the product file is input into A1C1 3 ,CO,CO 2 , HCl, Cl, H 2 , NO, O 2 , H 2 O、N 2 and Al 2 O 3 The combustion chamber pressure is set to 7MPa by default, and the pressure change has a negligible effect on the product content. Figure 2 .

[0054] The method is particularly suitable for hydroxybutyl propellant and high energy propellant whose propellant element composition is C, H, O, N, Cl and Al.

[0055] Calculate to obtain n ig {i=1,m}、n js {j=1,n}, calculate the constant pressure explosion heat Q P

[0056]

[0057] Calculate the total content of gas phase components n g

[0058]

[0059] Calculation of constant volume explosion heat Q v , where T is 298.15K

[0060] Q P =Q v -n g R 0 T

[0061] Calculate the TNT equivalent coefficient C of the propellant TNT , where Q TNT The explosion heat value of TNT is 4187 kJ / kg.

[0062]

[0063] Example: High Energy Propellant N-1

[0064] Assume the chemical formula is C 11.9634 H 26.9794 O 24.7402 N 15.7296 Cl 0.9361 Al 6.6729 , the formation enthalpy is -527.19 kJ / kg.

[0065] S1: Enter the first line in the propellant composition text file

[0066] "name,wt(%),Hf(j / kg),Formular"

[0067] The second line contains

[0068] "nepeS1,100,-527.19e3,C11.9634H26.9794024.7402N15.7296C10.9361A16.6729";

[0069] S2: Enter the product name in the propellant product text file,

[0070] “AlCl 3 ,CO,CO 2 , HCl, Cl, H 2 , NO, O 2 , H 2 O、N 2 、Al 2 O 3 (a)”;

[0071] S3: Input calculated pressure, 7MPa;

[0072] S4: Click the calculate button to obtain the product output, as shown in the following table. The software interface is attached. Figure 2 ,

[0073] Table 2 Product output table

[0074]

[0075] Calculate the final enthalpy of the product

[0076]

[0077] S5: Calculate the total content of gas phase components n g

[0078]

[0079] S6: Calculation of explosion heat at constant pressure and constant volume

[0080] Q P =-527.19-(-7554.16)kJ / kg=7026.968kJ / kg

[0081] Q v =Q P +n g R 0 T=7026.968+34.013×8.314×298.15 / 1000kJ / kg=7111.28kJ / kg

[0082] S7: Calculate theoretical TNT equivalent

[0083] C TNT =Q v / Q TNT =7111.28 / 4187=1.70

[0084] This paper has been proved to be feasible through experiments, and the TNT equivalent error is less than 4%.

[0085] Method (1), namely “Calculation of TNT equivalent of solid composite propellant and development of its visualization software” and method (2), namely “A calculation method for theoretical constant-pressure detonation heat of solid propellant” are adopted. Compared with method (2), this calculation method eliminates the conversion and calculation steps of the product types and contents after the final detonation products are cooled to room temperature, and does not need to assume that H 2The content of O and HCl remain unchanged at 298K. The applicability of this assumption to different propellants needs to be verified. In addition, method (1) needs to calculate 13 detonation products, and method (2) needs to calculate 40 combustion products of the propellant at a fixed pressure. This method only needs to calculate 11 products, which is more than twice the calculation efficiency of method (2).

[0086] Method (1), namely "Calculation of TNT equivalent of solid composite propellant and development of its visualization software", and method (2), namely "Calculation method of theoretical constant-pressure detonation heat of solid propellant", are used. This method is applicable to HTPB propellant and high-energy propellant whose propellant element composition is C, H, O, N, Cl, Al. Method (2) is only applicable to high-energy propellant, and method (1) is only applicable to HTPB propellant. As can be seen from the table below, the calculation accuracy of method (1) is higher than that of both method (1) and method (2).

[0087] Table 3 Comparison of calculation accuracy

[0088]

Claims

1. A method for evaluating the TNT equivalent of a high-energy propellant, the specific steps are as follows: Step 1: Obtain the formation enthalpy and assumed chemical formula of the solid propellant; Step 2: Based on the known enthalpy of formation of the solid propellant and the assumed chemical formula and product composition, use the following formula to calculate the number of moles of all combustion products of 1 kg of solid propellant at the adiabatic combustion temperature. These stable products are the combustion products of the solid propellant at 298 K, and their content remains constant during the cooling process; Where G is the total Gibbs free energy of the system, R0 is the universal gas constant, 8.314 J / (molxK), p is the combustion pressure, G i，m and G j，m are the molar Gibbs free energy of the i-th gas phase and the j-th condensed phase at temperature T, N k is the number of moles of the kth element in the solid propellant component, l is the total number of elements, n ig is the number of moles of the i-th gas phase product, m is the total number of gas phase products, a ik represents the number of kth element contained in the i-th gas phase product, n js The molar number of the jth condensed phase product, n is the total number of condensed phase products, a jk represents the number of k-th element contained in the j-th condensed phase product, n g is the total amount of gaseous products in the combustion products, λ k is the Lagrange multiplier, there are l of them, where T is the combustion temperature, H i，f，T and H j，f，T are the molar formation enthalpies of the i-th gas phase and the j-th condensed phase at the combustion temperature, respectively; Step 3: Calculate the total enthalpy of combustion products of 1 kg solid propellant at 298 K. The total enthalpy of combustion products of solid propellant and the initial enthalpy of solid propellant combustion process H r，f Equal, that is, Where N p is the total number of combustion products, n j is the number of moles of the jth combustion product of the solid propellant, H j，f is the molar enthalpy of formation of the combustion products at the combustion temperature; Step 4: Use the known solid propellant formation enthalpy minus the total enthalpy of the combustion products at 298K to obtain the theoretical constant-pressure detonation heat value Q of the propellant. P In the formula, H r，f is the initial enthalpy of solid propellant combustion, m is the total number of gas phase products, n is the total number of condensed phase products, and n ig is the number of moles of the i-th gas phase product, n js The number of moles of the jth condensed phase product, H i，f，298 and H j，f，298 are the molar formation enthalpies of the i-th gas phase and the j-th condensed phase at 298K, respectively; Step 5: Use the theoretical constant pressure explosion heat value of the propellant plus the expansion work of the generated gas phase component to obtain the theoretical constant volume explosion heat Q v , Q P =Q v -n g R0T Where n g is the total content of gas phase components, R0 is the universal gas constant, 8.314 J / (molxK), and T is 298.15 K; Step 6: Divide the theoretical constant volume explosion heat of the propellant by the explosion heat of standard TNT to obtain the theoretical TNT equivalent coefficient C of the propellant. TNT , In the formula, Q TNT The explosion heat value of TNT is 4187 kJ / kg.

2. The evaluation method according to claim 1, characterized in that: The solid propellant element composition is C, H, O, N, Cl and Al.

3. The evaluation method according to claim 1, characterized in that: The solid propellant combustion product consists of AlCl3, CO, CO2, HCl, Cl, H2, NO, O2, H2O, N2 and Al2O3.

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