A method and system for optimizing the design of aluminum-containing propellant formulation based on agglomeration characteristics

Abstract

The present invention discloses a method for optimizing the formulation of aluminum-containing propellants based on agglomeration characteristics. The method designs the propellant formulation through an orthogonal test method, numerical scheme design, a Kriging approximation model, and a multi-objective bat algorithm, thereby obtaining an optimal propellant formulation that meets design indicators and simplifying the solid propellant formulation design procedure. The present invention also provides a system for optimizing the formulation of aluminum-containing propellants based on agglomeration characteristics.

Description

Technical Field

[0001] The present invention relates to the field of propellant formulation optimization design, in particular to an aluminum-containing propellant formulation optimization design method based on agglomeration characteristics. Background Art

[0002] Solid rocket motors (SRMs) provide the primary propulsion power for strategic and tactical missiles and rockets. They offer advantages such as simple structure, easy maintenance, high operational reliability, rapid response, and short launch preparation times. However, their low energy content is a major limitation. The addition of aluminum powder to the propellant can effectively enhance its energy performance, and the solid oxide particles produced by the combustion of aluminum powder can effectively suppress combustion oscillations during engine operation. However, this also introduces additional negative impacts on the propulsion system. In the engine's combustion chamber and nozzle, condensed products and combustion gases form a gas-solid two-phase flow. Velocity and temperature hysteresis of the condensed products result in specific impulse loss in the two-phase flow, which is determined by the particle size and distribution of the condensed products. Condensed products alter the infrared radiation characteristics of the plume, with an increase in condensed product particle size significantly enhancing the plume's infrared characteristics. Furthermore, increased condensed product particle size significantly exacerbates ablation of the nozzle inner wall and combustion chamber insulation, as well as slag deposition within the combustion chamber, increasing the engine's negative mass. The negative effects of the addition of aluminum powder on propellants and solid rocket engines greatly limit the practical application of aluminum-containing composite propellants. Therefore, proposing a reasonable and effective dynamic combustion characteristics optimization method is of great significance to the application and performance improvement of aluminum-containing composite propellants.

[0003] Currently, optimizing the formulation of aluminum-containing composite propellants is the primary approach to improving the dynamic combustion characteristics of aluminum particles. This optimization is still primarily based on trial and error. This involves selecting a preliminary formulation, testing the propellant's relevant properties, and gradually achieving the desired propellant performance through repeated formulation adjustments and ongoing propellant performance testing. This traditional formulation improvement approach has a long development cycle and is subject to uncertainty. It consumes significant research funding and has significant limitations, making comprehensive testing impossible and making it difficult to obtain an optimal propellant formulation that meets all performance indicators. Furthermore, experimental research on the dynamic characteristics of aluminum particles in propellants is complex and cannot be standardized, similar to performance indicators such as the propellant's burning rate. Summary of the Invention

[0004] Purpose of the invention: The purpose of the present invention is to provide a method and system for optimizing the design of aluminum-containing propellant formulations based on agglomeration characteristics, thereby obtaining an optimal propellant formulation that meets design specifications, simplifying the solid propellant formulation design process, and reducing the design cost of solid propellants.

[0005] Technical solution: The present invention provides a method for optimizing the formulation of aluminum-containing propellants based on agglomeration characteristics, comprising the following steps:

[0006] Step 1: Select the components that affect the agglomeration characteristics of the propellant as design parameters, determine the value range of each design parameter, and use the orthogonal test method to perform numerical scheme design for the design parameters;

[0007] Step 2: Use the random loading method to reconstruct the propellant unit of the numerical scheme and obtain the average particle size of the condensed phase products in the propellant;

[0008] Step 3: Take the components that affect the agglomeration characteristics of the propellant as input values, and the characteristic velocity and average particle size of the condensed phase products obtained by thermodynamic calculation of the propellant under various formulations as output values, and establish a Kriging approximation model between the input and output values;

[0009] Step 4: Use the multi-objective bat algorithm to solve the Kriging approximation model and obtain the propellant formula components;

[0010] Step 5: Randomly load the propellant formula components and use thermal calculation methods and agglomeration characteristics simulation to determine whether the design requirements are met. If so, the propellant formula is output and added to the optimal formula set. If not, return to step 3 and reselect the parameters.

[0011] Furthermore, in step 1, the components affecting the agglomeration characteristics of the propellant include the aluminum particle content ω Al , initial particle size of aluminum particles D Al 、AP contentω AP , fine AP particle size D AP,f , coarse AP particle size D AP,c , the thickness of the aluminum particle oxide film δ is used as the design parameter.

[0012] Furthermore, in step 3, the formula of the Kriging approximation model is:

[0013]

[0014] Among them, y(x) is the response function to be fitted, β j is the regression coefficient, f j (x) is a polynomial in the variable x, and z(x) is a simulation of a random process established by the spatial correlation of the data.

[0015] The present invention provides an aluminum-containing propellant formulation optimization design system based on agglomeration characteristics, which includes an orthogonal test module, a unit reconstruction module, a Kriging approximation model establishment module, a solution module, and a calculation and judgment module;

[0016] The orthogonal test module is used to select components that affect the agglomeration characteristics of the propellant as design parameters, determine the value range of each design parameter, and use the orthogonal test method to perform numerical scheme design for the design parameters;

[0017] The unit reconstruction module is used to reconstruct the propellant unit of the numerical scheme using a random loading method to obtain the average particle size of the condensed phase products in the propellant;

[0018] A Kriging approximation model module is established to take the components that affect the agglomeration characteristics of the propellant as input values, and the characteristic velocity and average particle size of the condensed phase products obtained by thermodynamic calculation of the propellant under various formulations as output values, and to establish a Kriging approximation model between the input and output values;

[0019] The solution module is used to solve the Kriging approximation model using the multi-objective bat algorithm to obtain the propellant formula components;

[0020] The calculation and judgment module is used to randomly load the propellant formula components and use thermal calculation methods and agglomeration characteristic simulation to determine whether the design requirements are met. If the design requirements are met, the propellant formula is output and added to the optimal formula set. If the design requirements are not met, the module returns to step three and reselects the parameters.

[0021] Furthermore, in the orthogonal test module, the components affecting the agglomeration characteristics of the propellant include the aluminum particle content ω Al , initial particle size of aluminum particles D Al 、AP contentω AP , fine AP particle size D AP,f , coarse AP particle size D AP,c , the thickness of the aluminum particle oxide film δ is used as the design parameter.

[0022] Furthermore, in the Kriging approximation model module, the formula of the Kriging approximation model is:

[0023]

[0024] Among them, y(x) is the response function to be fitted, β j is the regression coefficient, f j (x) is a polynomial in the variable x, and z(x) is a simulation of a random process established by the spatial correlation of the data.

[0025] Beneficial effect: Compared with the existing technology, the present invention has the remarkable feature of designing the propellant formula through orthogonal experimental method, numerical scheme design, Kriging approximation model, and multi-objective bat algorithm, so as to obtain the optimal propellant formula that meets the design indicators and simplify the solid propellant formula design procedure. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 is a flow chart of the present invention;

[0027] Figure 2 It is a schematic diagram of random filling of propellant in the present invention. DETAILED DESCRIPTION

[0028] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0029] Example 1

[0030] The present invention provides a method for optimizing the formulation of aluminum-containing propellants based on agglomeration characteristics. In an Al / AP / HTPB propellant formulation system, the energy characteristics of the propellant must first be met, that is, the characteristic velocity of the propellant must be as large as possible. Then, the particle size of the initial condensed phase product of the propellant must be minimized, requiring the characteristic velocity of the propellant to be no less than 1600 m / s. The method comprises the following steps:

[0031] Step 1: Select the components that affect the agglomeration characteristics of the propellant as design parameters, determine the value range of each design parameter, and use the orthogonal experimental method to design the numerical scheme for the design parameters.

[0032] Components that affect the agglomeration characteristics of propellants include the aluminum particle content ω Al , initial particle size of aluminum particles D Al 、AP contentω AP , fine AP particle size D AP,f , coarse AP particle size D AP,c , aluminum particle oxide film thickness δ, a total of 6 groups of components as design parameters, and determine the value range of each design parameter:

[0033] Design parameters Lower limit Upper limit <![CDATA[Aluminum particle content ω Al %]]> 5 25 <![CDATA[Initial particle size D of aluminum particles Al (μm)]]> 3 30 <![CDATA[AP content ω AP %]]> 20 90 <![CDATA[Particle size D of fine AP AP,f (μm)]]> 20 80 <![CDATA[Particle size D of coarse AP AP,c (μm)]]> 60 300 Aluminum particle oxide film thickness δ (μm) 0.1 1

[0034] The orthogonal experiment method was used to carry out a 6-factor 5-level orthogonal experiment design, that is, for the 6 design parameters, 5 levels were selected within the design range of each parameter, and 25 groups of samples were obtained.

[0035] Step 2: Use the random loading method to reconstruct the propellant unit of the numerical scheme and obtain the average particle size of the condensed phase products in the propellant.

[0036] The propellants in 25 groups of samples were randomly loaded, and the energy characteristics and agglomeration characteristics were simulated and calculated to obtain the characteristic velocity and average particle size of the condensed phase products under each propellant formula:

[0037]

[0038]

[0039] Step 3: Take the components that affect the agglomeration characteristics of the propellant as input values, and the characteristic velocity and average particle size of the condensed phase products obtained by thermodynamic calculation of the propellant under various formulations as output values, and establish a Kriging approximation model between the input and output values.

[0040] The aluminum particle content in the propellant formula ω Al , initial particle size of aluminum particles D Al 、AP contentω AP , fine AP particle size D AP,f , coarse AP particle size D AP,c , the thickness of the aluminum particle oxide film δ is used as the input value, the propellant characteristic velocity and the average particle size of the condensed phase product are used as the output value, and a data sample is established. The Kriging approximation model is used for both the input and output values ​​to establish an approximate model between the characteristic velocity and the average particle size of the condensed phase product and the main component parameters in the propellant formula:

[0041]

[0042] Among them, y(x) is the response function to be fitted, β j is the regression coefficient, f j (x) is a polynomial in the variable x, and z(x) is a simulation of a random process established by the spatial correlation of the data.

[0043] Step 4: Use the multi-objective bat algorithm to solve the Kriging approximation model and obtain the propellant formula components.

[0044] A multi-objective bat algorithm is used to find the propellant formula components with the smallest particle size of the condensed phase product of the propellant while ensuring the energy characteristics of the propellant.

[0045] In the early stages of bat search, bats emit low-frequency ultrasonic waves, which are louder and can search for targets over a large range. After finding the target, the frequency of the ultrasonic waves emitted by bats gradually increases and the loudness of the ultrasonic waves gradually decreases, making it easier for bats to accurately search for targets in a small range until they find the target. The mathematical model simulating its global search method is:

[0046] r i t+1 =r i 0 [1-exp(-γt)]

[0047]

[0048] Among them, r i 0 is the maximum ultrasonic emissivity of bat i, r i t+1is the ultrasonic emission rate of bat i at time t+1, r i 0 The interval is [0,1]; is the loudness of the ultrasonic wave emitted by bat i at time t, is the loudness of the ultrasonic wave emitted by bat i at time t+1; γ is the growth coefficient of the ultrasonic wave emissivity emitted by the bat; α is the attenuation coefficient of the ultrasonic wave loudness emitted by the bat.

[0049] For any α and γ, when t→∞, we have r i t →r i 0 ,when When it approaches 0, it can be considered that the bat has found its prey and will not emit a pulse for the time being. The pulse variation range is set to different numerical intervals according to the needs of the problem. When the bat's position is optimized, the loudness and frequency of the pulse are updated accordingly, that is, the bat is moving towards the optimal position. When it moves to the optimal position, that is, under the premise of ensuring the energy characteristics of the propellant, the propellant formula component with the smallest particle size of the condensed phase product of the propellant is obtained.

[0050] Step 5: Add the propellant formula components as shown in the table below to the aluminum particle content ω Al , initial particle size of aluminum particles D Al 、AP contentω AP , fine AP particle size D AP,f , coarse AP particle size D AP,c , the thickness of the aluminum particle oxide film δ, random filling is performed, and the thermal calculation method and agglomeration characteristic simulation are used to determine whether the design requirements are met. The design requirements are selected within a certain range of variation according to the designer's needs while meeting the characteristic speed. If the design requirements are met, the propellant formula components are output and added to the optimal formula set. If the design requirements are not met, return to step three and reselect the parameters.

[0051] The designer selects a reasonable propellant formula based on the propellant design requirements:

[0052]

[0053] If the designer's main goal is to suppress the particle size of the propellant's condensed-phase products and reduce the negative impact of the condensed-phase products on the engine, when the propellant's energy characteristics only need to meet the design requirements, then formula A can be selected. At this time, formula A has the smallest particle size of the initial condensed-phase products on the basis of meeting certain energy characteristics; when the designer needs to ensure that the propellant's energy characteristics are large enough and has a high tolerance for the particle size of the initial condensed-phase products, formula D can be selected; when the designer chooses a relatively balanced solution between the propellant's energy characteristics and agglomeration characteristics, formula B or formula C can be selected. Formula B takes the particle size of the propellant's condensed-phase products into greater consideration, while the propellant's energy characteristics in formula C are better.

[0054] Example 2

[0055] Corresponding to the aluminum-containing propellant formulation optimization design method based on agglomeration characteristics in Example 1, this Example 2 provides an aluminum-containing propellant formulation optimization design system based on agglomeration characteristics. In the Al / AP / HTPB propellant formulation system, the energy characteristics of the propellant must first be met, that is, the characteristic velocity of the propellant must be as large as possible, and then the particle size of the initial condensed phase product of the propellant must be minimized, requiring the characteristic velocity of the propellant to be no less than 1600 m / s. The system includes an orthogonal test module, a unit reconstruction module, a Kriging approximation model establishment module, a solution module, and a calculation and judgment module.

[0056] The orthogonal test module is used to select components that affect the agglomeration characteristics of the propellant as design parameters, determine the value range of each design parameter, and use the orthogonal test method to design numerical schemes for the design parameters.

[0057] Components that affect the agglomeration characteristics of propellants include the aluminum particle content ω Al , initial particle size of aluminum particles D Al 、AP contentω AP , fine AP particle size D AP,f , coarse AP particle size D AP,c , aluminum particle oxide film thickness δ, a total of 6 groups of components as design parameters, and determine the value range of each design parameter:

[0058] Design parameters Lower limit Upper limit <![CDATA[Aluminum particle content ω Al %]]> 5 25 <![CDATA[Initial particle size D of aluminum particles Al (μm)]]> 3 30 <![CDATA[AP content ω AP %]]> 20 90 <![CDATA[The particle size D of the fine AP AP,f (μm)]]> 20 80 <![CDATA[Particle size D of coarse AP AP,c (μm)]]> 60 300 Aluminum particle oxide film thickness δ (μm) 0.1 1

[0059] The orthogonal experiment method was used to carry out a 6-factor 5-level orthogonal experiment design, that is, for the 6 design parameters, 5 levels were selected within the design range of each parameter, and 25 groups of samples were obtained.

[0060] The unit reconstruction module is used to reconstruct the propellant unit of the numerical scheme using a random loading method to obtain the average particle size of the condensed phase products in the propellant.

[0061] The propellants in 25 groups of samples were randomly loaded, and the energy characteristics and agglomeration characteristics were simulated and calculated to obtain the characteristic velocity and average particle size of the condensed phase products under each propellant formula:

[0062]

[0063] A Kriging approximation model module is established to take the components that affect the agglomeration characteristics of the propellant as input values, and the characteristic velocity and average particle size of the condensed phase products obtained by thermodynamic calculation of the propellant under various formulations as output values, and to establish a Kriging approximation model between the input and output values.

[0064] The aluminum particle content in the propellant formula ω Al , initial particle size of aluminum particles D Al 、AP contentω AP , fine AP particle size D AP,f , coarse AP particle size D AP,c , the thickness of the aluminum particle oxide film δ is used as the input value, the propellant characteristic velocity and the average particle size of the condensed phase product are used as the output value, and a data sample is established. The Kriging approximation model is used for both the input and output values ​​to establish an approximate model between the characteristic velocity and the average particle size of the condensed phase product and the main component parameters in the propellant formula:

[0065]

[0066] Among them, y(x) is the response function to be fitted, β j is the regression coefficient, f j (x) is a polynomial in the variable x, and z(x) is a simulation of a random process established by the spatial correlation of the data.

[0067] The solution module is used to solve the Kriging approximation model using the multi-objective bat algorithm to obtain the propellant formula components.

[0068] A multi-objective bat algorithm is used to find the propellant formula components with the smallest particle size of the condensed phase product of the propellant while ensuring the energy characteristics of the propellant.

[0069] In the early stages of bat search, bats emit low-frequency ultrasonic waves, which are louder and can search for targets over a large range. After finding the target, the frequency of the ultrasonic waves emitted by bats gradually increases and the loudness of the ultrasonic waves gradually decreases, making it easier for bats to accurately search for targets in a small range until they find the target. The mathematical model simulating its global search method is:

[0070] r i t+1 =r i 0 [1-exp(-γt)]

[0071]

[0072] Among them, r i 0 is the maximum ultrasonic emissivity of bat i, r i t+1 is the ultrasonic emission rate of bat i at time t+1, r i 0 The interval is [0,1]; is the loudness of the ultrasonic wave emitted by bat i at time t, is the loudness of the ultrasonic wave emitted by bat i at time t+1; γ is the growth coefficient of the ultrasonic wave emissivity emitted by the bat; α is the attenuation coefficient of the ultrasonic wave loudness emitted by the bat.

[0073] For any α and γ, when t→∞, we have r i t →r i 0 ,when When it approaches 0, it can be considered that the bat has found its prey and will not emit a pulse for the time being. The pulse variation range is set to different numerical intervals according to the needs of the problem. When the bat's position is optimized, the loudness and frequency of the pulse are updated accordingly, that is, the bat is moving towards the optimal position. When it moves to the optimal position, that is, under the premise of ensuring the energy characteristics of the propellant, the propellant formula component with the smallest particle size of the condensed phase product of the propellant is obtained.

[0074] The calculation and judgment module is used to convert the propellant formula components into the aluminum particle content ω in the following table Al , initial particle size of aluminum particles D Al 、AP contentω AP , fine AP particle size D AP,f , coarse AP particle size D AP,c , the thickness of the aluminum particle oxide film δ, random filling is performed, and the thermal calculation method and agglomeration characteristic simulation are used to determine whether the design requirements are met. The design requirements are selected within a certain range of variation according to the designer's needs while meeting the characteristic speed. If the design requirements are met, the propellant formula components are output and put into the optimal formula set. If the design requirements are not met, return to the Kriging approximation model module and reselect the parameters.

[0075] The designer selects a reasonable propellant formula based on the propellant design requirements:

[0076]

[0077] If the designer's main goal is to suppress the particle size of the propellant's condensed-phase products and reduce the negative impact of the condensed-phase products on the engine, when the propellant's energy characteristics only need to meet the design requirements, then formula A can be selected. At this time, formula A has the smallest particle size of the initial condensed-phase products on the basis of meeting certain energy characteristics; when the designer needs to meet the propellant's energy characteristics that are large enough and has a high tolerance for the particle size of the initial condensed-phase products, formula D can be selected; when the designer chooses a relatively balanced solution between the propellant's energy characteristics and agglomeration characteristics, formula B or formula C can be selected. Formula B takes the particle size of the propellant's condensed-phase products into greater consideration, while the propellant's energy characteristics in formula C are better.

Claims

1. A method for optimizing the formulation of aluminum-containing propellants based on agglomeration characteristics, characterized in that: The following steps are involved: Step 1: Select the components that affect the agglomeration characteristics of the propellant as design parameters, determine the value range of each design parameter, and use the orthogonal test method to perform numerical scheme design for the design parameters; Step 2: Use the random loading method to reconstruct the propellant unit of the numerical scheme and obtain the average particle size of the condensed phase products in the propellant; Step 3: Take the components that affect the agglomeration characteristics of the propellant as input values, and the characteristic velocity and average particle size of the condensed phase products obtained by thermodynamic calculation of the propellant under various formulations as output values, and establish a Kriging approximation model between the input and output values; Step 4: Use the multi-objective bat algorithm to solve the Kriging approximation model and obtain the propellant formula components; Step 5: Randomly load the propellant formula components and use thermal calculation methods and agglomeration characteristics simulation to determine whether the design requirements are met. If so, the propellant formula components are output and added to the optimal formula set. If not, return to step 3 and reselect the parameters.

2. The method for optimizing the formulation of aluminum-containing propellants based on agglomeration characteristics according to claim 1, characterized in that: In step 1, the components that affect the agglomeration characteristics of the propellant include the aluminum particle content ω Al , initial particle size of aluminum particles D Al 、AP contentω AP , fine AP particle size D AP,f , coarse AP particle size D AP,c , the thickness of the aluminum particle oxide film δ is used as the design parameter.

3. The method for optimizing the formulation of aluminum-containing propellants based on agglomeration characteristics according to claim 1, characterized in that: In step 3, the formula of the Kriging approximation model is: Among them, y(x) is the response function to be fitted, p is the regression quantity, β j is the regression coefficient, f j (x) is a polynomial in the variable x, and z(x) is a simulation of a random process established by the spatial correlation of the data.

4. A system for optimizing the formulation of aluminum-containing propellants based on agglomeration characteristics, characterized in that: It includes orthogonal test module, unit reconstruction module, Kriging approximate model establishment module, solution module, calculation and judgment module; The orthogonal test module is used to select components that affect the agglomeration characteristics of the propellant as design parameters, determine the value range of each design parameter, and use the orthogonal test method to perform numerical scheme design for the design parameters; The unit reconstruction module is used to reconstruct the propellant unit of the numerical scheme using a random loading method to obtain the average particle size of the condensed phase products in the propellant; A Kriging approximation model module is established to take the components that affect the agglomeration characteristics of the propellant as input values, and the characteristic velocity and average particle size of the condensed phase products obtained by thermodynamic calculation of the propellant under various formulations as output values, and to establish a Kriging approximation model between the input and output values; The solution module is used to solve the Kriging approximation model using the multi-objective bat algorithm to obtain the propellant formula components; The calculation and judgment module is used to randomly load the propellant formula components and use thermal calculation methods and agglomeration characteristic simulation to determine whether the design requirements are met. If the design requirements are met, the propellant formula components are output and added to the optimal formula set. If the design requirements are not met, the module returns to step three and reselects the parameters.

5. The aluminum-containing propellant formulation optimization design system based on agglomeration characteristics according to claim 4, characterized in that: In the orthogonal test module, the components that affect the agglomeration characteristics of the propellant include the aluminum particle content ω Al , initial particle size of aluminum particles D Al 、AP contentω AP , fine AP particle size D AP,f , coarse AP particle size D AP,c , the thickness of the aluminum particle oxide film δ is used as the design parameter.

6. The aluminum-containing propellant formulation optimization design system based on agglomeration characteristics according to claim 4, characterized in that: In the Kriging approximate model module, the formula of the Kriging approximate model is: Among them, y(x) is the response function to be fitted, β j is the regression coefficient, f j (x) is a polynomial in the variable x, and z(x) is a simulation of a random process established by the spatial correlation of the data.

7. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 3 are implemented.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 3 are implemented.

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