Method for calculating theoretical constant-pressure heat of explosion of solid propellant

Abstract

The application discloses a kind of theoretical constant pressure explosion heat calculation methods of solid propellant, consisting of the following steps: step S1: according to the enthalpy of raw material of known solid propellant and assumed chemical formula, the mole number and mass of all combustion products of 1kg the propellant adiabatic combustion to constant pressure adiabatic are calculated using thermodynamic software;Step S2: determine the combustion products of the solid propellant at 298K;Step S3: calculate the content of each element, step S4: calculate the total enthalpy H of 1kg fixed propellant combustion products at 298K 298 , step S5: the total enthalpy of combustion products at 298K is obtained by subtracting the enthalpy of raw material of known solid propellant from the theoretical constant pressure explosion heat value of the propellant;The calculation method of the application eliminates the combustion products that may exist in the minimum free energy method at 298K but are difficult to obtain in actual reaction, obtains the specific content of each combustion product, and improves the accuracy of theoretical explosion heat.

Description

Technical Field

[0001] This invention belongs to the field of theoretical heat of explosion of solid propellants, and particularly relates to a method for calculating the theoretical heat of explosion at constant pressure of solid propellants. Background Technology

[0002] Heat of explosion is a performance parameter that measures the energy of a propellant. It is defined as the heat released when 1 kg of propellant is converted into combustion products at the same temperature under specified initial temperature (typically 298 K) and oxygen-free conditions. Heat of explosion tests typically require sample amounts in the range of a few grams, much smaller than those required by engine-based methods, making them economical. However, because theoretical heat of explosion is not readily comparable to actual heat of explosion, it is not a focus of research in this field.

[0003] Existing technology suggests that the deflagration products of a sample at 298 K can be obtained using the minimum free energy method. However, thermodynamic calculations of the propellant show that although the calculated products are theoretically the most stable substances at room temperature, this result differs significantly from the actual experimental results. The actual combustion products can only reach a certain metastable state at most. Summary of the Invention

[0004] The purpose of this invention is to provide a method for calculating the theoretical isobaric heat of explosion of solid propellants, in order to solve the problem that the calculation results of propellant combustion products at 298K using the minimum free energy method deviate too much from the actual results.

[0005] This invention employs the following technical solution: a method for calculating the theoretical isobaric heat of explosion of solid propellants, comprising the following steps: Step S1: Based on the known enthalpy of the raw material and the assumed chemical formula of the solid propellant, use thermodynamic software to calculate the number of moles and the mass of all combustion products of 1 kg of the propellant under constant pressure and adiabatic conditions. Step S2: Determine the combustion products of the solid propellant at 298 K; Step S3: Calculate the content of each element. Step S4: Calculate the total enthalpy H of combustion products of 1 kg of fixed propellant at 298 K. 298 , Step S5: Subtract the total enthalpy of combustion products at 298K from the known enthalpy of the raw material of the solid propellant to obtain the theoretical isobaric heat of explosion of the propellant.

[0006] Furthermore, the total enthalpy H of the combustion products 298 The calculation method is as follows: In the formula, H 298 The total enthalpy of the combustion products of 1 kg of propellant at 298 K is given in kJ / kg; n iLet be the molality of the i-th combustion product, in mol / kg; is the standard enthalpy of the i-th combustion product at 298 K, in kJ / mol.

[0007] Furthermore, the method for determining the combustion products of the solid propellant in step S2 is as follows: under constant pressure and adiabatic conditions, based on the rate constants and reaction conditions of the relevant reactions during propellant combustion: When the propellant elemental composition is C, H, O, N, Cl, and Al, the combustion products after cooling to 298K are CO, CO2, H2, H2O, N2, HCl, AlCl3, and Al2O3. When the propellant elemental composition is C, H, O, N, Cl, Al, and Fe, the combustion products after cooling to 298K are CO, CO2, H2, H2O, N2, HCl, AlCl3, Al2O3, and FeCl2.

[0008] Furthermore, in step S3, the content of each element is calculated. The method for calculating the content of each element consists of the following steps: Step S301: Calculate the number of moles of N2 based on the conservation of N element. The calculation formula is as follows: , Step S302: Set the H2O content under high temperature and high pressure. and HCl content The concentration of H2 remains constant at 298K. Based on the conservation of H, the number of moles of H2 can be calculated using the following formula: , Step S303: Calculate the number of moles of AlCl3 based on the conservation of Cl element. The calculation formula is as follows: , Step S304: Calculate the number of moles of Al2O3 based on the conservation of Al element. The calculation formula is as follows: , Step S305: Calculate the number of moles of CO and CO2 based on the conservation of C and O elements. , Step S306: Calculate the number of moles of liquid HCl based on the solubility of HCl in H2O and the content of H2O. The number of moles of HCl dissolved in H2O can be calculated using the following formula: ,in, For the volume of water, Step S307: Calculate the number of moles of gaseous HCl, using the following formula: ,in, This refers to the total number of moles of HCl calculated in step S302. The number of moles of gaseous HCl. This refers to the number of moles of liquid HCl calculated in step S306.

[0009] The beneficial effects of this invention are as follows: The calculation method of this invention eliminates combustion products that may exist under the minimum free energy method at 298K but are difficult to obtain in actual reactions, thus obtaining the specific content of each combustion product and improving the accuracy of theoretical heat of explosion. Due to the poor comparability between theoretical and actual heat of explosion, existing technologies often use specific impulse efficiency or characteristic velocity efficiency to characterize the energy performance of engines, without considering heat of explosion efficiency. This application solves the problem of determining the theoretical combustion products of propellants at 298K. At the same time, the accuracy of the calculation results is verified by gas chromatography. The obtained heat of explosion efficiency matches well with the specific impulse efficiency or characteristic velocity efficiency under the engine method. Using this invention, the heat of explosion method can replace the engine method, obtaining the same accurate results with less propellant, which is economical, safe, and efficient. Detailed Implementation

[0010] The present invention will now be described in detail with reference to specific embodiments.

[0011] The theoretical heat of explosion of the propellant is obtained based on the Hess triangle diagram. The enthalpy of formation of the propellant at 298 K can be obtained by consulting relevant handbooks. Therefore, determining the standard enthalpy of formation of the combustion products at 298 K is crucial for calculating the theoretical heat of explosion. It is generally believed that the minimum free energy method should be used to calculate the combustion products at 298 K. However, this application argues that this method of determining the combustion products is unreasonable for the following reasons: Given the assumed chemical formula of a certain propellant Table 1 shows the combustion products of this propellant at 298 K using the minimum free energy method. The propellant was subjected to a deflation test, and the collected products were analyzed by gas chromatography.

[0012] The test results are shown in Table 2, which indicate that H2 and CO dominate the gaseous products. Actual test results show that although the components in Table 1 represent the theoretically absolute steady state after atomic rearrangement at 298K for this formulation, the actual combustion products reach a metastable state rather than an absolute steady state after cooling from an adiabatic high temperature to room temperature. Therefore, the minimum free energy method cannot be used to determine the heat-induced combustion products of the propellant at 298K.

[0013] Table 1 Combustion products of the propellant at 298K under the minimum free energy method Table 2. Gas Chromatography Detection Results of Propellant Combustion Products This invention discloses a method for calculating the theoretical isobaric heat of explosion of solid propellants, comprising the following steps: Step S1: Based on the known enthalpy of the raw material and the assumed chemical formula of the solid propellant, use thermodynamic software to calculate the number of moles and the mass of all combustion products of 1 kg of the propellant under constant pressure and adiabatic conditions. Step S2: Determine the combustion products of the solid propellant at 298 K; Step S3: Calculate the content of each element. The method for calculating the content of each element consists of the following steps: Step S4: Calculate the total enthalpy H of combustion products of 1 kg of fixed propellant at 298 K. 298 , Step S5: Subtract the total enthalpy of combustion products at 298K from the known enthalpy of the raw material of the solid propellant to obtain the theoretical isobaric heat of explosion of the propellant.

[0014] The method for determining the combustion products of solid propellant in step S2 is as follows: under constant pressure and adiabatic conditions, based on the rate constants and reaction conditions of the relevant reactions during propellant combustion: When the propellant elemental composition is C, H, O, N, Cl, and Al, the combustion products after cooling to 298K are CO, CO2, H2, H2O, N2, HCl, AlCl3, and Al2O3. When the propellant elemental composition is C, H, O, N, Cl, Al, and Fe, the combustion products after cooling to 298K are CO, CO2, H2, H2O, N2, HCl, AlCl3, Al2O3, and FeCl2.

[0015] The reasons for determining the combustion products of solid propellants are as follows: Many components in the high-temperature combustion products of isobaric adiabatic combustion undergo dissociation, but such reactions are virtually impossible at 298 K. Dissociation products such as H, Cl, N, O, and OH in the combustion products under adiabatic high pressure do not exist at 298 K. Based on the rate constants of related reactions during propellant combustion, the chloride of Al at 298 K is mainly in the form of AlCl3, the oxide of aluminum is mainly in the form of Al2O3, and the compounds of AlOH and AlH are not present. Therefore, the composition of combustion products at low temperatures can be determined based on the high-temperature products of isobaric adiabatic combustion. Generally, when the propellant elemental composition is C, H, O, N, Cl, Al, the combustion products after cooling to 298K are CO, CO2, H2, H2O, N2, HCl, AlCl3, and Al2O3; when the propellant elemental composition is C, H, O, N, Cl, Al, and Fe, the combustion products after cooling to 298K are CO, CO2, H2, H2O, N2, HCl, AlCl3, Al2O3, and FeCl2.

[0016] In step S3, the content of each element is calculated. The method for calculating the content of each element consists of the following steps. Step S301: Calculate the number of moles of N2 based on the conservation of N element. The calculation formula is as follows: , Step S302: Set the H2O content under high temperature and high pressure. and HCl content The concentration of H2 remains constant at 298K. Based on the conservation of H, the number of moles of H2 can be calculated using the following formula: , Step S303: Calculate the number of moles of AlCl3 based on the conservation of Cl element. The calculation formula is as follows: , Step S304: Calculate the number of moles of Al2O3 based on the conservation of Al element. The calculation formula is as follows: , Step S305: Calculate the number of moles of CO and CO2 based on the conservation of C and O elements. , Step S306: Calculate the number of moles of liquid HCl based on the solubility of HCl in H2O and the content of H2O. The number of moles of HCl dissolved in H2O can be calculated using the following formula: ,in, Given the volume of water, H2O is liquid in this state and will dissolve some gas. Considering the solubility of gases, the state of HCl needs to be recalculated. The solubility of HCl in H2O is 70g / 100ml, based on the molar number of H2O products. Given the relative molecular mass of water (18 g / mol) and the density of water (1 g / mL), the volume of water in the product can be calculated as follows: (Unit: mL).

[0017] Step S307: Calculate the number of moles of gaseous HCl, using the following formula: ,in, This refers to the total number of moles of HCl calculated in step S302. The number of moles of gaseous HCl. The number of moles of liquid HCl calculated in step S306 is compared with the number of moles of gaseous HCl calculated in step S302. In step S306 The size, if Then all HCl is a condensed phase; otherwise, HCl is divided into condensed phases. Harmony ,but .

[0018] Example 1 Step S1: Given a propellant formulation with a raw material enthalpy of -520.8 kJ / kg, assume the chemical formula is... The adiabatic combustion temperature, molar number, and mass of combustion products of 1 kg of this propellant at 6.860 MPa were calculated using Factsage software, as shown in Table 3.

[0019] Table 3. Adiabatic combustion products of 6.86 MPa propellant (3726 K) Step S2: When the propellant elemental composition is C, H, O, N, Cl, and Al, the combustion products after cooling to 298K are CO, CO2, H2, H2O, N2, HCl, AlCl3, and Al2O3.

[0020] Step S301: Based on the conservation of N element, the amount of N2 is calculated to be 7.3536745 mol.

[0021] Step S302: Assuming the contents of H2O and HCl remain constant at 298K under high temperature and pressure, at 3.017528 mol and 0.897629 mol respectively, the content of H2 is calculated based on the conservation of H element: Step S303: Based on the conservation of Cl element, the content of AlCl3 is calculated as follows: Step S304: Calculate the Al2O3 content based on the law of conservation of Al: , Step S305: Based on the conservation of elements C and O, the contents of CO and CO2 are calculated to be 10.848392 mol and 0.725308 mol, respectively.

[0022] Step S306: Calculate the number of moles of liquid HCl based on the solubility of HCl in H2O and the content of H2O. Calculate the number of moles of HCl dissolved in H₂O. Based on the molar number of H₂O (3.017528), the relative molecular mass of water (18 g / mol), and the density of water (1 g / mL), the volume of water in the product can be calculated to be 54.315504 mL. Therefore, the mass of HCl that can dissolve is 54.315504 × 0.7 = 38.020853 g. Since 38.020853 g > 32.7634585 g (total mass of HCl), all HCl is dissolved in H₂O. =0.897629 mol.

[0023] Step S307: Calculate the number of moles of gaseous HCl. Since 38.020853g > 32.7634585g, all HCl is calculated as condensed matter. The amount of gaseous HCl is 0. =0.

[0024] Step S4: Calculate the total enthalpy H of combustion products of 1 kg of fixed propellant at 298 K. 298 The value is -7812.652035 KJ / kg, calculated using the following formula: Table 4 Combustion products of this propellant at 298K Step S5: Subtract the total enthalpy of combustion products at 298K from the known enthalpy of the raw material of the solid propellant to obtain the theoretical isobaric heat of explosion of the propellant. That is, the enthalpy of the raw material -520.8kJ / kg minus the total enthalpy of combustion products -7812.652035kJ / kg equals the calculated theoretical isobaric heat of explosion of the propellant, which is 7291.85kJ / kg.

[0025] The calculation results of this embodiment show that regardless of the pressure selected for adiabatic combustion, the amount of combustion products calculated by this invention at 298K does not change significantly, and the difference from the product enthalpy is less than one-thousandth. Since the enthalpy of the raw materials in the formula is fixed, the theoretical heat of explosion of the formula can be obtained by subtracting the enthalpy of the products from the enthalpy of the raw materials, and the heat of explosion value is unique.

[0026] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calculating the theoretical isobaric heat of explosion of a solid propellant, characterized in that, It consists of the following steps: Step S1: Based on the known enthalpy of the raw material and the assumed chemical formula of the solid propellant, use thermodynamic software to calculate the number of moles and the mass of all combustion products of 1 kg of the propellant under constant pressure and adiabatic conditions. Step S2: Determine the combustion products of the solid propellant at 298 K; Step S3: Calculate the content of each element. Step S4: Calculate the total enthalpy H of combustion products of 1 kg of fixed propellant at 298 K. 298 , Step S5: Subtract the total enthalpy of combustion products at 298K from the known enthalpy of the raw material of the solid propellant to obtain the theoretical isobaric heat of explosion of the propellant; The method for determining the combustion products of solid propellant in step S2 is as follows: under constant pressure and adiabatic conditions, based on the rate constants and reaction conditions of the relevant reactions during propellant combustion: When the propellant elemental composition is C, H, O, N, Cl, and Al, the combustion products after cooling to 298K are CO, CO2, H2, H2O, N2, HCl, AlCl3, and Al2O3. When the propellant elemental composition is C, H, O, N, Cl, Al, and Fe, the combustion products after cooling to 298K are CO, CO2, H2, H2O, N2, HCl, AlCl3, Al2O3, and FeCl2.

2. The method for calculating the theoretical isobaric heat of explosion of a solid propellant according to claim 1, characterized in that, The total enthalpy H of the combustion products 298 The calculation method is as follows: ； In the formula, H 298 The total enthalpy of the combustion products of 1 kg of propellant at 298 K is given in kJ / kg; n i Let be the molality of the i-th combustion product, in mol / kg; is the standard enthalpy of the i-th combustion product at 298 K, in kJ / mol.

Images