Method for determining actual constant-pressure combustion temperature of solid propellant by calorimetry

Abstract

The application discloses a method for determining actual constant-pressure combustion temperature of solid propellant by a calorimetric method, and comprises the following steps: calculating the combustion efficiency of the propellant and an initial value of the actual constant-pressure combustion temperature; calculating the average value of the initial value of the actual constant-pressure combustion temperature and a theoretical constant-pressure combustion temperature, and calculating the first iteration combustion efficiency of the propellant; calculating the average value of the first iteration value of the actual constant-pressure combustion temperature and the theoretical constant-pressure combustion temperature, and calculating the second iteration combustion efficiency of the propellant; and the like until the residual error between the nth iteration combustion efficiency of the propellant and the combustion efficiency of the propellant is less than a predetermined value, and the combustion temperature corresponding to the nth iteration combustion efficiency of the propellant is taken as the actual constant-pressure combustion temperature. According to the correlation between the measured constant-pressure explosion heat value, the theoretical constant-pressure explosion heat value, the theoretical constant-pressure combustion temperature and the actual constant-pressure combustion temperature of the propellant, the actual constant-pressure combustion temperature of the propellant is measured by the calorimetric method and the iteration method.

Description

Technical Field

[0001] This invention belongs to the field of solid propellant combustion and energy characteristic characterization, and particularly relates to a method for determining the actual isobaric combustion temperature of solid propellants using calorimetry. Background Technology

[0002] Combustion temperature is a crucial parameter characterizing the energy properties of solid propellants. It forms the basis for propellant combustion mechanism research and combustion model establishment, and is also a critical factor in rocket engine design and insulation protection. Contact temperature measurement primarily uses thermocouples, typically placing the sensing element directly into the test object for measurement. However, this method is limited by the thermocouple's melting point; the highest melting point thermocouple, tungsten-rhenium, can only measure temperatures up to 2600K. Since the theoretical combustion temperature of high-energy solid propellants is generally above 3000K, far exceeding the thermocouple's measurement range, it cannot meet the measurement requirements for high-energy propellants. Optical temperature measurement requires high-precision, high-reliability calibration standards and suffers from problems such as easily contaminated optical windows, demanding calibration requirements, complex spectral characteristics of high-temperature combustion products requiring complex algorithms to invert the temperature field, leading to significant error accumulation. Summary of the Invention

[0003] The purpose of this invention is to provide a method for determining the actual isobaric combustion temperature of solid propellants using calorimetry. Based on the positive correlation between the isobaric heat of explosion and the isobaric combustion temperature of a given propellant, the isobaric combustion temperature of high-energy propellants is measured by calorimetry.

[0004] This invention employs the following technical solution: a method for determining the actual isobaric combustion temperature of solid propellants using calorimetry, comprising:

[0005] Step 1: Based on the measured pressure heat of explosion, theoretical isobaric heat of explosion, and theoretical isobaric combustion temperature of the propellant, calculate the initial iterative values ​​of the propellant's combustion efficiency and actual isobaric combustion temperature; wherein, the measured pressure heat of explosion is obtained by calorimetry, and the theoretical isobaric heat of explosion and theoretical isobaric combustion temperature are obtained by calculation;

[0006] Step 2: Calculate the initial value of the actual isobaric combustion temperature and the average value of the theoretical isobaric combustion temperature. Use this average value as the first iterative value of the actual isobaric combustion temperature, and use the calorimetric temperature measurement iterative relationship to calculate the first iterative combustion efficiency of the propellant.

[0007] Step 3: When the first iteration combustion efficiency of the propellant is less than the combustion efficiency of the propellant calculated in Step 1, calculate the average of the first iteration value of the actual isobaric combustion temperature and the theoretical isobaric combustion temperature. Use this average value as the second iteration value of the actual isobaric combustion temperature, and use the calorimetric temperature measurement iterative relationship to calculate the second iteration combustion efficiency of the propellant.

[0008] Step 4: Repeat step 3 until the residual between the propellant's nth iteration combustion efficiency and the propellant combustion efficiency calculated in step 1 is less than a predetermined value, and use the combustion temperature corresponding to the propellant's nth iteration combustion efficiency as the actual constant pressure combustion temperature.

[0009] Furthermore, the formula for calculating the combustion efficiency of the propellant in step 1 is:

[0010]

[0011] In the formula, η is the combustion efficiency of the propellant; Q p_exp To measure the heat of explosion at actual pressure, kJ / kg; Q p_th The value is the theoretical isobaric heat of explosion, in kJ / kg.

[0012] Furthermore, the formula for calculating the initial value of the actual isobaric combustion temperature in step 1 is as follows:

[0013]

[0014] In the formula, Q p_exp To measure the heat of explosion at actual pressure, kJ / kg; Q p_th The theoretical isobaric heat of explosion is expressed in kJ / kg; T p_exp0 Tp_th is the initial value of the actual isobaric combustion temperature, K; Tp_th is the theoretical isobaric combustion temperature, K.

[0015] Furthermore, the iterative relationship for calorimetric temperature measurement in step 3 is as follows:

[0016]

[0017] In the formula, η i C represents the combustion efficiency of the propellant in the i-th iteration; p (T) represents the isobaric heat capacity of the propellant combustion products; Q p_exp To measure the heat of explosion at actual pressure, kJ / kg; Q p_th The theoretical isobaric heat of explosion is expressed in kJ / kg; T p_expi Tp_th is the i-th iteration value of the actual isobaric combustion temperature, K; Tp_th is the theoretical isobaric combustion temperature, K.

[0018] Where i ≤ n.

[0019] Furthermore, the predetermined value in step 4 is 0.0001.

[0020] Furthermore, when repeating step 3, if the combustion efficiency of the propellant in the i-th iteration is greater than the combustion efficiency of the propellant calculated in step 1, the average of the i-th iteration value and the (i-1)-th iteration value of the actual constant pressure combustion temperature is taken as the i+1-th iteration value of the actual constant pressure combustion temperature, and the i+1-th iteration combustion efficiency of the propellant is calculated using the calorimetric temperature measurement iteration relationship.

[0021] The beneficial effects of this invention are:

[0022] This invention obtains the actual isobaric combustion temperature of a propellant by measuring its measured pressure heat of explosion, theoretical isobaric heat of explosion, and the correlation between the theoretical isobaric combustion temperature and the actual isobaric combustion temperature using calorimetry and iterative methods, based on the correlation between the measured pressure heat of explosion, theoretical isobaric heat of explosion, theoretical isobaric combustion temperature and actual isobaric combustion temperature of the given propellant.

[0023] Based on the definition of heat explosion, this invention provides an integral relationship between the heat release (heat explosion) during the cooling process of propellant combustion products and the temperature (cooling down from the isobaric combustion temperature to 298K). By comparing the theoretical isobaric heat explosion value and the measured isobaric heat explosion value with the theoretical isobaric combustion temperature and the actual isobaric combustion temperature, respectively, an iterative relationship for calorimetric temperature measurement is established.

[0024] This invention decomposes the integral relationship of the theoretical isobaric heat of explosion into the sum of the measured isobaric heat of explosion and the integral of the high-temperature segment. This solves the problem of the inability to continuously integrate the material changes and phase transitions that occur during the large temperature span cooling of propellant combustion products. Since the temperature of the complex reaction during the cooling process of high-temperature products cannot be determined, segmented integration is also impossible. Simultaneously, it avoids the problems related to the composition and C content of the combustion products in the low-temperature segment. p (T) Problems that cannot be determined using the minimum free energy method;

[0025] This invention determines the initial value of the actual isobaric combustion temperature based on the principle that "combustion temperature and heat release are directly proportional." The appropriate selection of this initial value improves iteration efficiency and significantly shortens the number of iteration steps. Furthermore, this invention quantitatively characterizes the correlation between the measured pressure heat of explosion, theoretical isobaric heat of explosion, theoretical isobaric combustion temperature, and actual isobaric combustion temperature of a given propellant. Simultaneously, the quantitative characterization calculation process addresses the problem of the inability to integrate material changes and phase transitions across a large temperature range from high to low temperatures, while also avoiding issues related to the composition of combustion products and C in the low-temperature range. p (T) The problem that cannot be determined by the minimum free energy method has been solved; the isobaric combustion temperature of high-energy propellants has been measured by calorimetry. Detailed Implementation

[0026] The present invention will now be described in detail with reference to specific embodiments.

[0027] The propellant combustion products can be considered as a closed system, and the relationship between its isobaric heat of explosion and isobaric combustion temperature is shown in equation (1):

[0028]

[0029] In the formula, Q p It is a constant pressure explosion, kJ / kg; T p The isobaric combustion temperature of the propellant, K; C p (T) represents the isobaric heat capacity of the propellant combustion products, in kJ / (kg / propellant).

[0030] From equation (1), it can be seen that if the isobaric heat capacity is known and the isobaric heat explosion is obtained through experimental testing, then the actual isobaric temperature T can be calculated. p However, since the constant-pressure combustion temperature of propellants is generally 2000K to 4000K, the material changes and phase transitions that occur during the large temperature range of propellant combustion products during cooling cannot be continuously integrated. Furthermore, the temperature of the complex reactions during the cooling process of high-temperature products cannot be determined, making segmented integration impossible. Additionally, the composition and C content of the combustion products in the low-temperature range are also problematic. p (T) cannot be determined by the minimum free energy method, so solving the constant pressure combustion temperature by equation (1) is not practically possible.

[0031] To obtain the actual isobaric combustion temperature, the actual isobaric heat of explosion is correlated with the actual isobaric combustion temperature, and the theoretical isobaric heat of explosion is correlated with the theoretical isobaric combustion temperature. This establishes the basic relationship for calorimetric temperature measurement:

[0032]

[0033] In the formula, Q p_exp To measure the heat of explosion at actual pressure, kJ / kg; Q p_th The theoretical isobaric heat of explosion is expressed in kJ / kg; T p_th The theoretical isobaric combustion temperature, K; T p_exp The actual constant-pressure combustion temperature is K.

[0034] Integrating the theoretical isobaric heat of explosion in equation (2) piecewise, we get:

[0035]

[0036] Equation (2) can then be written as:

[0037]

[0038] Among them, the measured pressure explosion heat value Q p_exp The theoretical isobaric heat of explosion, Q, can be obtained through calorimetric experiments. p_th and theoretical isobaric combustion temperature T p_th All of them can be calculated.

[0039] The measured heat of explosion Q is introduced through equation (3). p_exp As 298K to T p_exp The integral result transforms the final expression into one that depends only on the minimum temperature range C in the high-temperature segment. p The calculation form of (T) is shown in equation (4), thus solving the problem that the material changes and phase transitions that exist in the large temperature span from high temperature to low temperature cannot be integrated, while avoiding the composition of combustion products and C in the low temperature range. p (T) Problems that cannot be determined by the minimum free energy method. Since the combustion efficiency of solid propellants is generally greater than 90%, both the actual and theoretical isobaric combustion temperatures belong to the high-temperature range. The composition of the isobaric combustion products and C at different temperatures within this range are crucial factors. p (T) can all be obtained by thermodynamic calculation based on the minimum free energy.

[0040] Therefore, this invention discloses a method for determining the actual isobaric combustion temperature of solid propellants using calorimetry, comprising:

[0041] Step 1: Based on the measured pressure heat of explosion, theoretical isobaric heat of explosion, and theoretical isobaric combustion temperature of the propellant, calculate the initial iterative values ​​of the propellant's combustion efficiency and actual isobaric combustion temperature; wherein, the measured pressure heat of explosion is obtained by calorimetry, and the theoretical isobaric heat of explosion and theoretical isobaric combustion temperature are obtained by calculation.

[0042] The formula for calculating the combustion efficiency of the propellant in step 1 is as follows:

[0043]

[0044] In the formula, η is the combustion efficiency of the propellant; Q p_exp To measure the heat of explosion at actual pressure, kJ / kg; Q p_th The value is the theoretical isobaric heat of explosion, in kJ / kg.

[0045] To iteratively solve for the actual isobaric combustion temperature of the propellant, and based on the proportional relationship between the isobaric heat of explosion and the isobaric combustion temperature, an initial value T for the actual isobaric combustion temperature is set for iteration. p_exp0 As shown in equation (6), the formula for calculating the initial value of the actual constant-pressure combustion temperature in step 1 is:

[0046]

[0047] In the formula, Q p_exp To measure the heat of explosion at actual pressure, kJ / kg; Q p_th The theoretical isobaric heat of explosion is expressed in kJ / kg; T p_exp0Tp_th is the initial value of the actual isobaric combustion temperature, K; Tp_th is the theoretical isobaric combustion temperature, K.

[0048] Since equation (6) does not consider the phenomenon that the isobaric heat capacity of combustion products increases with increasing combustion temperature compared to equation (2), therefore, for T... p_exp0 T p_exp0 <T p_exp <T p_th .

[0049] Step 2: Calculate the initial value of the actual constant pressure combustion temperature and the average value of the theoretical constant pressure combustion temperature. Use the average value as the first iteration value of the actual constant pressure combustion temperature, and use the calorimetric temperature measurement iteration relationship (8) to calculate the first iteration combustion efficiency of the propellant.

[0050] Step 2 specifically involves using the bisection method to obtain the first iterative value T of the actual isobaric combustion temperature. p_exp1 :

[0051]

[0052] First, T p_exp1 Substituting the calorimetric temperature measurement iterative relationship (8) into equation (8) to begin iteration, the calorimetric temperature measurement iterative relationship is:

[0053]

[0054] In the formula, η i C represents the combustion efficiency of the propellant in the i-th iteration; p (T) represents the isobaric heat capacity of the propellant combustion products; Q p_exp To measure the heat of explosion at actual pressure, kJ / kg; Q p_th The theoretical isobaric heat of explosion is expressed in kJ / kg; T p_expi K is the actual constant-pressure combustion temperature at the i-th iteration; Tp_th is the theoretical constant-pressure combustion temperature, K; i≤n.

[0055] The isobaric heat capacity C of a gas at different temperatures can be obtained through thermodynamic calculations. p (T), thus affecting C p (T) is fitted to the change with temperature. Since T p_exp1 And T p_th It is known that the isobaric heat capacity C can be determined within a defined temperature range. p The combustion efficiency η1 is obtained by effectively fitting the change of temperature (T) with the temperature.

[0056] Step 3: When the first iteration combustion efficiency of the propellant is less than the combustion efficiency of the propellant calculated in Step 1, calculate the average of the first iteration value of the actual isobaric combustion temperature and the theoretical isobaric combustion temperature. Use this average value as the second iteration value of the actual isobaric combustion temperature, and calculate the second iteration combustion efficiency of the propellant using the calorimetric temperature measurement iterative formula.

[0057] Step 4: Repeat Step 3 until the residual between the propellant's combustion efficiency in the nth iteration and the combustion efficiency calculated in Step 1 is less than a predetermined value, and use the combustion temperature corresponding to the propellant's combustion efficiency in the nth iteration as the actual isobaric combustion temperature. The predetermined value in Step 4 is 0.0001.

[0058] Step 4 is as follows: When repeating step 3, if the combustion efficiency of the propellant in the i-th iteration is greater than the combustion efficiency of the propellant calculated in step 1, the average of the i-th iteration value and the (i-1)-th iteration value of the actual constant pressure combustion temperature is taken as the i+1-th iteration value of the actual constant pressure combustion temperature, and the i+1-th iteration combustion efficiency of the propellant is calculated using the calorimetric temperature measurement iteration relationship.

[0059] That is, when η1 > η, we have:

[0060]

[0061] When η1 < η, we have:

[0062]

[0063] When η 1＝ When η is present:

[0064] T p_exp =T p_exp1 (11)

[0066] T p_exp2 Substituting into equation (8), the combustion efficiency η2 is calculated, and equation (12) is used to calculate the combustion efficiency residual.

[0067] E=|η2-η| (12)

[0068] Compare η2 with η, and use equation (9) or equation (10) to perform the next iteration calculation based on the relationship between η2 and η.

[0069] By setting the residual limit E to 0.0001 and iterating repeatedly, the exact solution T for the actual isobaric combustion temperature is obtained. p_expn .

[0070] Example

[0071] In this embodiment, the classic double-base propellant SQ-2 and the commonly used composite propellant NEPE were selected. According to GJB770B-2024 method 701.2 "Heat of Explosion and Heat of Combustion isothermal method", the measured pressure heat of explosion of the propellant was tested using an isothermal oxygen bomb calorimeter. In order to obtain the test results of the actual constant pressure combustion temperature, a pressure sensor was installed on the oxygen bomb of the calorimeter. The pressure sensor can realize the synchronous acquisition of temperature data in the inner cylinder and pressure data in the oxygen bomb.

[0072] The volume of this oxygen bomb was calibrated according to the JJG259-2005 standard verification procedure for metal measuring instruments, using distilled water and a solution with a density of 0.789 g / cm³. 3 The oxygen bomb was calibrated three times with ethanol, and the effective volume V was found to be 0.287 L.

[0073] (P2-P1)V=n2RT2-n1RT1 (13)

[0074] In the formula, P2 is the pressure inside the oxygen bomb during the steady-state phase of the calorimetric experiment, Pa; P1 is the pressure inside the oxygen bomb before ignition during the calorimetric experiment, Pa; n2 is the amount of gaseous substance during the steady-state phase of the calorimetric experiment, mol; n1 is the amount of gaseous substance before ignition during the calorimetric experiment, mol; T2 is the gas temperature during the steady-state phase of the calorimetric experiment, K; T2 is the gas temperature before ignition during the calorimetric experiment, K.

[0075] In the calorimetric experiment, the amount of propellant used is m grams, and the number of moles of the gaseous fuel gas produced in the steady-state phase is n2-n1. Therefore, the amount of gaseous products in the final stage of the explosion of 1 kg of propellant is n. g It can be obtained through equation (14).

[0076]

[0077] Based on the relationship between isobaric heat of explosion and isochoric heat of explosion (15), the isobaric heat of explosion of the propellant can be obtained:

[0078] Q p =Q v -n g RT (15)

[0079] In the formula, Q p and Q v These represent the isobaric and isochoric heats of the propellant, respectively, in kJ / kg; R is the molar gas constant, with a value of 8.314 J / mol / K; T is the temperature of the steady-state range of the isochoric and isochoric heats, in K; n g The amount of gaseous products during the stable phase of the explosion of 1 kg of propellant is expressed in mol.

[0080] The actual constant-volume explosion Q of SQ-2 propellant was measured experimentally. v_exp =3431.1±21.5kJ / kg, measured compressive heat of explosion Q p_exp= 3344.2 kJ / kg. Actual constant-volume heat of explosion Q of NEPE propellant. v_exp =7098.0±53.1kJ / kg, measured pressure explosion heat Q p_exp =7012.6kJ / kg

[0081] Theoretical calculations show that the theoretical isobaric combustion temperature of SQ-2 propellant is 2236.14 K, the theoretical isobaric heat of explosion is 3427.4 kJ / kg, and the combustion efficiency η is 97.58%. The initial iterative value T for the actual isobaric combustion temperature can be obtained from equation (6). p_exp0 =2189.3±14.5K, and through continuous iteration, the final iterative value T of the actual isobaric combustion temperature is obtained. p_expn =2198.5±14.6K. The calorimetric test showed that the isobaric combustion temperature of SQ-2 propellant was 2198.5K, which is 37.6K different from the theoretical isobaric combustion temperature.

[0082] Similarly, theoretical calculations show that the theoretical isobaric combustion temperature of NEPE propellant is 3742.7 K, the theoretical isobaric heat of explosion is 7319.6 kJ / kg, and the combustion efficiency η is 95.81%. The initial iterative value T for the actual isobaric combustion temperature can be obtained from equation (6). p_exp0 =3595.0±28.2K, and through continuous iteration, the final iterative value T of the actual isobaric combustion temperature is obtained. p_expn =3610.2±28.3K. The actual isobaric combustion temperature of NEPE propellant, determined by calorimetry, is 3610.2K, which differs from the theoretical isobaric combustion temperature by 132.5K.

[0083] Table 1 shows the results of calorimetric measurements of the heat of explosion and temperature of NEPE and SQ-2 propellants.

[0084]

[0085]

[0086] As can be seen from Table 1, the initial values ​​T for the two propellants during iteration are... p_exp0 Compared to the final value T of the iteration p_expn The differences are 15.2K and 9.2K, respectively. The small difference between the two proves that the initial value of the iteration is close to the final value of the iteration, which can significantly shorten the number of iteration steps.

[0087] 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 determining the actual isobaric combustion temperature of solid propellants using calorimetry, characterized in that, include: Step 1: Based on the measured pressure heat of explosion, theoretical isobaric heat of explosion, and theoretical isobaric combustion temperature of the propellant, calculate the initial iterative values ​​of the propellant's combustion efficiency and actual isobaric combustion temperature; wherein, the measured pressure heat of explosion is obtained by calorimetry, and the theoretical isobaric heat of explosion and theoretical isobaric combustion temperature are obtained by calculation; Step 2: Calculate the initial value of the actual isobaric combustion temperature and the average value of the theoretical isobaric combustion temperature. Use this average value as the first iterative value of the actual isobaric combustion temperature, and use the calorimetric temperature measurement iterative relationship to calculate the first iterative combustion efficiency of the propellant. Step 3: When the first iteration combustion efficiency of the propellant is less than the combustion efficiency of the propellant calculated in Step 1, calculate the average of the first iteration value of the actual isobaric combustion temperature and the theoretical isobaric combustion temperature. Use this average value as the second iteration value of the actual isobaric combustion temperature, and use the calorimetric temperature measurement iterative relationship to calculate the second iteration combustion efficiency of the propellant. Step 4: Repeat step 3 until the residual between the propellant's nth iteration combustion efficiency and the propellant combustion efficiency calculated in step 1 is less than a predetermined value, and use the combustion temperature corresponding to the propellant's nth iteration combustion efficiency as the actual constant pressure combustion temperature.

2. The method for determining the actual isobaric combustion temperature of solid propellants using calorimetry according to claim 1, characterized in that, The formula for calculating the combustion efficiency of the propellant in step 1 is: In the formula, η is the combustion efficiency of the propellant; Q p_exp To measure the heat of explosion at actual pressure, kJ / kg; Q p_th The value is the theoretical isobaric heat of explosion, in kJ / kg.

3. The method for determining the actual isobaric combustion temperature of solid propellants using calorimetry according to claim 1, characterized in that, The formula for calculating the initial value of the actual isobaric combustion temperature in step 1 is as follows: In the formula, Q p_exp To measure the heat of explosion at actual pressure, kJ / kg; Q p_th The theoretical isobaric heat of explosion is expressed in kJ / kg; T p_exp0 Tp_th is the initial value of the actual isobaric combustion temperature, K; Tp_th is the theoretical isobaric combustion temperature, K.

4. The method for determining the actual isobaric combustion temperature of solid propellants using calorimetry according to claim 1, characterized in that, The iterative relationship for calorimetric temperature measurement in step 3 is: In the formula, η i C represents the combustion efficiency of the propellant in the i-th iteration; p (T) represents the isobaric heat capacity of the propellant combustion products; Q p_exp To measure the heat of explosion at actual pressure, kJ / kg; Q p_th The theoretical isobaric heat of explosion is expressed in kJ / kg; T p_expi Tp_th is the i-th iteration value of the actual isobaric combustion temperature, K; Tp_th is the theoretical isobaric combustion temperature, K. Where i ≤ n.

5. The method for determining the actual isobaric combustion temperature of solid propellants using calorimetry according to claim 1, characterized in that, The predetermined value in step 4 is 0.0001.

6. The method for determining the actual isobaric combustion temperature of solid propellants using calorimetry according to claim 1, characterized in that, When repeating step 3, if the combustion efficiency of the propellant in the i-th iteration is greater than the combustion efficiency of the propellant calculated in step 1, the average of the i-th iteration value and the (i-1)-th iteration value of the actual constant pressure combustion temperature is taken as the i+1-th iteration value of the actual constant pressure combustion temperature, and the i+1-th iteration combustion efficiency of the propellant is calculated using the calorimetric temperature measurement iteration formula.

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