Method for simulating polarization state of tail flame by considering particle size distribution of solid-phase particles

Abstract

The invention relates to a tail flame polarization state simulation method and device considering solid-phase particle size distribution, a medium and equipment. The method comprises the following steps: constructing a particle size distribution function; determining a cumulative distribution function based on the particle size distribution function, discretizing the cumulative distribution function, and calculating the representative particle size of each region; optical factors of the solid-phase particles in all the areas are calculated; calculating optical parameters of the particle swarm; taking each representative particle size and number density as particle phase input of an N-S equation of fluid mechanics to obtain two-phase flow tail flame flow field data and nozzle outlet data under different particle size distribution conditions; the method comprises the following steps of: taking a plurality of grids as input of a tail flame polarization radiation transfer model, calculating each solid phase parameter of each grid, taking an extinction coefficient and a single scattering coefficient of each cell as input of a two-phase flow tail flame vector radiation transfer equation, and outputting a polarization state of the tail flame. And the tail flame polarized radiation closer to the reality is obtained through simulation.

Description

Technical Field

[0001] The embodiments of the present application relate to the field of modeling and simulation calculation of polarized radiation characteristics of tail flames of high-speed aircraft, and in particular to a method, device, equipment and medium for simulating the polarization state of tail flames taking into account the particle size distribution of solid phase particles. Background Art

[0002] With the widespread application of high-speed aircraft in detection and early warning, as well as the continuous development of new propulsion systems, the importance of utilizing the richer characteristic dimensions provided by the polarization spectral radiation of the tail plume to achieve related research on the detection and identification of high-speed aircraft has become increasingly prominent. Existing experimental results on particle size measurement in gas-solid two-phase tail plumes show that Al2O3 particles in the tail plume are spatially non-uniformly distributed, and the particle size varies on multiple scales, generally following a log-normal distribution. Factors such as particle size and the complex refractive index of the particles determine the polarization scattering characteristics of the particles, which in turn affect the polarization radiation characteristics of the tail plume. Traditional methods for calculating polarization radiation based on a single particle size fail to fully reflect the size distribution characteristics of Al2O3 particles in the actual gas-solid two-phase flow tail plume, resulting in the calculation results of the polarization spectral radiation model of the two-phase flow tail plume deviating from the actual detection spectrum. The tail flame polarization transmission model considering particle size distribution established in this application comprehensively considers the impact of changes in the optical properties of particles in the tail flame on the spectral characteristics of the gas-solid two-phase plume flow field, and further analyzes the changes in the polarization spectral radiation characteristics of the tail flame caused by these changes, providing theoretical support for the simulation of tail flame polarization radiation that is closer to the actual situation. It has very important theoretical significance and practical application prospects for improving the detection capability of high-speed target tail flames and developing more efficient early warning systems. At the same time, this research can also provide reference and basis for the research and development and design of new propellants and propulsion systems.

[0003] Existing two-phase flow tail plume polarization radiation transfer models are usually based on the Monte Carlo method and the Vector Spherical Harmonics Discrete Ordinate Method (VSHDOM). However, in their calculations and engineering applications, they still simplify the particles into spherical particles with a single particle size and rely on the empirical formula proposed by Hermsen et al. to estimate the mass-weighted average diameter of Al2O3 particles. D 43. The actual distribution characteristics of particle size and the spatial non-uniformity of particle size are ignored. The single-particle plume polarized radiation transfer model cannot describe the actual changes in particle size in the plume when the propellant composition, engine structure or flight conditions vary.

[0004] In summary, there is currently a lack of technical approaches to combine the particle size distribution of Al2O3 particles in the tail plume of a gas-solid two-phase plume with the polarized spectral radiation of the tail plume. As a result, the optical parameters of the tail plume cannot be dynamically updated with changes in particle size, which limits the application of the tail plume polarized radiation transmission model in practical needs such as multi-condition simulation and polarization remote sensing modeling. Summary of the Invention

[0005] In view of this, an embodiment of the present application proposes a method for simulating the polarization state of the tail flame taking into account the particle size distribution of solid-phase particles, aiming to solve the technical problem that the optical parameters of the tail flame cannot be dynamically updated with changes in particle size, which limits the application ability of the tail flame polarization radiation transmission model in practical needs such as multi-working condition simulation and polarization remote sensing modeling.

[0006] To achieve the above-mentioned purpose, an embodiment of the present application provides a method for simulating the polarization state of a tail flame taking into account the particle size distribution of solid-phase particles, including: dividing the three-dimensional space of the tail flame into grids to obtain each grid; in each grid, based on the experimental data of the particle size measurement of Al2O3 particles in the tail flame of two-phase flow, constructing a particle size distribution function of Al2O3 particles that obeys the log-normal distribution; determining the cumulative distribution function based on the particle size distribution function, and discretizing the cumulative distribution function according to a preset particle ratio to obtain each particle size distribution area, and calculating the representative particle size of each area based on the particle size distribution area; calculating the average volume of Al2O3 particles based on the representative particle size of each area, and calculating the number density of Al2O3 particles in the tail flame based on the average volume; using the representative particle size as a parameter of the Mie algorithm, calculating the solid-phase particles in each area. optical factors; the optical factors, number density, representative particle size, and particle ratio of the solid phase particles are used as parameters of the particle group optical calculation formula to calculate the optical parameters of the particle group; the representative particle size and number density are used as the particle phase input of the NS equation of fluid mechanics to obtain the two-phase flow tail flame flow field data under different particle size distribution conditions, as well as the nozzle outlet data; a tail flame polarization radiation transmission model under the particle size distribution function is constructed, and the two-phase flow tail flame flow field parameters and nozzle outlet data are used as the tail flame polarization radiation transmission model to calculate the solid phase parameters of each grid, and the extinction coefficient and single scattering coefficient of each unit cell are calculated based on the gas phase parameters and optical parameters, and the extinction coefficient and single scattering coefficient of each unit cell are used as the input parameters of the two-phase flow tail flame vector radiation transmission equation, and the polarization state of the tail flame is described using the Stokes parameter.

[0007] Optionally, the cumulative distribution function is determined based on the particle size distribution function, and the cumulative distribution function is discretized according to a preset particle proportion to obtain each particle size distribution area, and the representative particle size of each area is calculated according to the particle size distribution area, including: obtaining the particle proportion; constructing an integral factor expression with the continuous particle diameter as a parameter based on the continuous particle diameter, the mass median diameter and the standard deviation of the particle size distribution function; constructing a cumulative distribution function with the continuous particle diameter as a parameter based on the integral factor expression, wherein the cumulative distribution function is the integral of the particle size distribution function; dividing the distribution area of ​​each particle size in each cumulative distribution function based on the cumulative distribution function and the particle proportion; and using the median point of the cumulative distribution function in each particle size distribution area as the parameter of the inverse cumulative distribution function to infer the representative particle size of each particle size distribution area.

[0008] Optionally, the method of constructing an integral factor expression with the continuous particle diameter as a parameter based on the continuous particle diameter, mass median diameter and standard deviation of the particle size distribution function includes: calculating the standard deviation of the particle size distribution function; calculating the geometric standard deviation based on the exponential standard deviation; calculating the mass median diameter of the Al2O3 particles in the nozzle based on the three free parameter model; D 43 particle size, and based on D Calculate the mass median diameter by multiplying the particle size by the natural index, wherein the parameter of the exponential part of the natural index is the natural logarithm of the geometric standard deviation; calculate a first ratio of the continuous particle diameters to the mass median diameter, calculate the natural logarithm of the first ratio, and calculate the natural logarithm of the geometric standard deviation; calculate a second ratio of the natural logarithm of the first ratio to the natural logarithm of the geometric standard deviation; and obtain an integral factor expression based on a weighted sum of the second ratio and the natural logarithm of the geometric standard deviation.

[0009] Optionally, the dividing the distribution area of ​​each particle size in each cumulative distribution function based on the cumulative distribution function and the particle proportion includes: dividing the cumulative distribution function into multiple areas, wherein the cumulative probability difference in each area is equal to the particle proportion; determining the upper limit and the lower limit of the particle size according to the cumulative probability difference of each area; and determining the distribution area of ​​the particle size based on the upper limit and the lower limit of the particle size.

[0010] Optionally, the median point of the cumulative distribution function in each particle size distribution area is used as the parameter of the inverse cumulative distribution function, and the expression used to infer the representative particle size of each particle size distribution area is:

[0011] in, represents the mass median diameter, represents the median point of the cumulative distribution function, erfinv represents the inverse function of CDF, represents the geometric standard deviation.

[0012] Optionally, the optical parameters include a solid-phase scattering coefficient, a solid-phase extinction coefficient and a solid-phase absorption coefficient, and the gas-phase parameters include a gas-phase extinction coefficient and a gas-phase absorption coefficient; the extinction coefficient and single scattering coefficient of each unit grid are calculated based on the gas-phase parameters and the optical parameters, including: calculating the extinction coefficient of each unit grid based on the sum of the gas-phase absorption coefficient and the solid-phase extinction coefficient; and obtaining the single scattering coefficient based on the ratio of the solid-phase scattering coefficient to the sum of the gas-phase absorption coefficient, the solid-phase absorption coefficient and the solid-phase scattering coefficient.

[0013] Optionally, the three-dimensional space of the tail flame is gridded to obtain each grid, including: constructing a tail flame coordinate axis based on the three-dimensional space model of the tail flame, wherein the tail flame coordinate axis includes an x-axis, a y-axis and a z-axis; determining a central symmetry axis plane based on the x-axis and the y-axis, and dividing the tail flame into m times n grid points along the x-axis and the y-axis on the central symmetry axis plane; processing the m times n grid points based on an interpolation algorithm, and obtaining each grid point in the three-dimensional space of the tail flame by rotational symmetry.

[0014] To achieve the above-mentioned purpose, an embodiment of the present application further provides a tail flame polarization state simulation device, comprising: a grid division module for gridding the tail flame three-dimensional space to obtain each grid; a parameter calculation module for constructing, in each grid, a particle size distribution function of Al2O3 particles that obeys a log-normal distribution based on the particle size measurement experimental data of Al2O3 particles in the two-phase flow tail flame; determining a cumulative distribution function based on the particle size distribution function, and discretizing the cumulative distribution function according to a preset particle ratio to obtain each particle size distribution area, and calculating a representative particle size of each area based on the particle size distribution area; calculating an average volume of Al2O3 particles based on the representative particle size of each area, and calculating the number density of Al2O3 particles in the tail flame based on the average volume; using the representative particle size as a parameter of the Mie algorithm, calculating the solid phase particles in each area. The optical factor of the particles; the optical factor, number density, representative particle size, and particle ratio of the solid phase particles are used as parameters of the particle group optical calculation formula to calculate the optical parameters of the particle group; the simulation module is used to use each representative particle size and number density as the particle phase input of the NS equation of fluid mechanics to obtain the two-phase flow tail flame flow field data under different particle size distribution conditions, as well as the nozzle outlet data; a tail flame polarization radiation transmission model under the particle size distribution function is constructed, and the two-phase flow tail flame flow field parameters and nozzle outlet data are used as the tail flame polarization radiation transmission model to calculate the solid phase parameters of each grid, and the extinction coefficient and single scattering coefficient of each unit cell are calculated based on the gas phase parameters and optical parameters, and the extinction coefficient and single scattering coefficient of each unit cell are used as input parameters of the two-phase flow tail flame vector radiation transmission equation, and the polarization state of the tail flame is described using the Stokes parameter.

[0015] To achieve the above object, embodiments of the present application further provide a server, comprising: at least one processor; and a memory connected with the at least one processor in communication; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to perform the above-mentioned plume polarization state simulation method considering the particle size distribution of solid phase particles.

[0016] To achieve the above object, embodiments of the present application further provide a computer readable storage medium storing a computer program, and the computer program is executable by a processor to implement the above-mentioned plume polarization state simulation method considering the particle size distribution of solid phase particles.

[0017] Embodiments of the present application propose a plume polarization state simulation method, device, equipment and storage medium considering the particle size distribution of solid phase particles. The plume three-dimensional space is divided into grids, and the particle size distribution function of Al2O3 particles obeying the lognormal distribution is constructed in each grid based on the particle size measurement experimental data of Al2O3 particles in the two-phase flow plume. The lognormal distribution Al2O3 particle size distribution function in the plume is constructed by combining the Al2O3 particle size measurement experiment in the two-phase flow plume, replacing the existing single particle size model. The cumulative distribution function is determined based on the particle size distribution function, and the cumulative distribution function is discretized according to the preset particle proportion to obtain each particle size distribution region. The representative particle size of each region is calculated according to the particle size distribution region. The average volume of Al2O3 particles is calculated based on the representative particle size of each region, and the number density of Al2O3 particles in the plume is calculated according to the average volume. The optical factor of the solid phase particles in each region is calculated by taking the representative particle size as the parameter of the Mie algorithm, overcoming the complexity of the particle size distribution function calculation, using the discretization approximation to replace the particle size distribution function, and combining the Mie theory to calculate the polarization scattering characteristics of Al2O3 particles considering the particle size distribution, taking into account the calculation efficiency and accuracy. The optical parameters of the particle group are calculated by taking the optical factor, number density, representative particle size, and particle proportion of the solid phase particles as the parameters of the particle group optical calculation formula. The particle phase input of the N-S equation of fluid mechanics is taken as the representative particle size and number density to obtain the two-phase flow plume flow field data and nozzle outlet data under different particle size distribution conditions. The plume polarization radiation transfer model under the particle size distribution function is constructed, and the two-phase flow plume flow field parameters and nozzle outlet data are taken as the plume polarization radiation transfer model to calculate the solid phase parameters of each grid. The existing single particle size model ignores the plume temperature, gas mole fraction and particle spatial distribution, and the extinction coefficient and single scattering coefficient of each unit cell are calculated based on the gas phase parameters and optical parameters. The extinction coefficient and single scattering coefficient of each unit cell are taken as the input parameters of the two-phase flow plume vector radiation transfer equation, and the plume polarization state described by the Stokes parameter is output. The particle thermal radiation and scattering under the particle size distribution and the mixed gas thermal radiation are coupled and calculated, and the plume polarization radiation closer to the actual plume polarization radiation is simulated. The above improvements can provide more accurate model support for high-speed vehicle target plume polarization detection in complex environments. BRIEF DESCRIPTION OF DRAWINGS

[0018] Figure 1 is a two-phase flow plume polarization radiation transfer model schematic diagram; Figure 2 is a calculation process of a polarization spectrum radiation model combined with a particle size distribution function; Figure 3 is experimental particle size distribution data and lognormal distribution fitting curve of Al2O3 particles in a two-phase flow plume; Figure 4This is a comparison chart of the temperature distribution simulation on the center symmetry plane of the tail flame, which is a traditional model that only considers a single particle size distribution and a polarization spectrum radiation model that combines the particle size distribution function. Figure 4 (a) is a simulation diagram of the temperature distribution on the central symmetry plane of the tail flame using a traditional model that only considers a single particle size; Figure 4 (b) is a simulation diagram of the temperature distribution on the central symmetry plane of the tail flame under the polarization spectral radiation model combined with the particle size distribution function; Figure 5 This is a simulation comparison of the temperature distribution along the center axis of the tail flame and the mole fraction of each typical gas, which is a traditional model that only considers a single particle size distribution and a polarization spectrum radiation model that combines the particle size distribution function. Figure 5 (a) is a temperature comparison diagram; Figure 5 (b) is a comparison chart of CO2 mole fraction; Figure 5 (c) is a comparison chart of CO mole fraction; Figure 5 (d) is a comparison chart of H2O mole fraction; Figure 6 This is a simulation comparison of the mass density distribution of Al2O3 particles in the tail flame symmetry plane using the traditional model that only considers a single particle size distribution and the polarization spectrum radiation model that combines the particle size distribution function. Figure 6 (a) is a simulation diagram of the mass density distribution of Al2O3 particles in the tail flame symmetry plane using a traditional model that only considers a single particle size; (b) is a simulation diagram of the mass density distribution of Al2O3 particles in the tail flame symmetry plane using a polarization spectrum radiation model that combines the particle size distribution function; Figure 7 This is a simulation comparison of the mass density distribution of Al2O3 particles in the tail flame symmetry plane using the traditional model that only considers a single particle size distribution and the polarization spectrum radiation model that combines the particle size distribution function. Figure 7 (a) is a simulation diagram of the distribution of the extinction coefficient on the tail flame symmetry plane of the traditional model that only considers a single particle size; Figure 7 (b) is a simulation diagram of the extinction coefficient distribution on the tail flame symmetry plane using the polarization spectrum radiation model combined with the particle size distribution function; Figure 8 This is a comparison of the single scattering albedo distribution simulation on the tail flame symmetry plane using the traditional model that only considers a single particle size distribution and the polarization spectral radiation model that combines the particle size distribution function. Figure 8 (a) is a simulation diagram of the single scattering albedo distribution on the tail flame symmetry plane of the traditional model that only considers a single particle size; Figure 8 (b) is a simulation diagram of the single scattering albedo distribution on the tail flame symmetry plane using the polarization spectral radiation model combined with the particle size distribution function; Figure 9The traditional model that only considers a single particle size distribution is different from the tail flame model that combines the polarization spectrum radiation model with the particle size distribution function. I The spatial distribution simulation comparison diagram of the values, where Figure 9 (a) is the traditional model that only considers a single particle size. I Simulation diagram of spatial distribution of values; Figure 9 (b) is the tail flame of the polarization spectrum radiation model combined with the particle size distribution function I Simulation diagram of spatial distribution of values; Figure 10 It is a traditional model that only considers a single particle size distribution, which is different from the tail flame model that combines the polarization spectrum radiation model with the particle size distribution function. Q Value and U The spatial distribution simulation comparison diagram of the values, where Figure 10 (a) is a simplified single particle size model Q Schematic diagram of value simulation; Figure 10 (b) is a simplified single particle size model U Schematic diagram of value simulation; Figure 10 (c) is the particle size distribution function Q Schematic diagram of value simulation; Figure 10 (d) is the particle size distribution function U Schematic diagram of value simulation; Figure 11 It is a traditional model that only considers a single particle size distribution, and the tail flame of the polarization spectrum radiation model that combines the particle size distribution function DOP The spatial distribution simulation comparison diagram of the values, where Figure 11 (a) is the traditional model that only considers a single particle size DOP Simulation schematic diagram; Figure 11 (b) is the polarization spectrum radiation model combined with the particle size distribution function DOP Simulation schematic. DETAILED DESCRIPTION

[0019] In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, each embodiment of the present application will be described in detail below with reference to the accompanying drawings. However, it will be understood by those skilled in the art that in each embodiment of the present application, many technical details are proposed to enable the reader to better understand the present application. However, even without these technical details and various changes and modifications based on the following embodiments, the technical solutions claimed in the present application can be implemented. The division of the following embodiments is for convenience of description and should not constitute any limitation on the specific implementation of the present application. The various embodiments can be combined and referenced with each other under the premise of no contradiction.

[0020] One embodiment of the present application proposes a method for simulating the polarization state of a tail flame, taking into account the particle size distribution of solid-phase particles. The method is applied to an electronic device, which can be a terminal or a server. This embodiment and the following embodiments are described using a server as an example. The following describes the implementation details of the method for simulating the polarization state of a tail flame, taking into account the particle size distribution of solid-phase particles, proposed in this embodiment. The following content is provided for ease of understanding and is not required for the implementation of this solution.

[0021] This application relates to the field of modeling and simulation of polarized radiation characteristics of high-speed aircraft tail plumes. Specifically, it relates to a method for calculating the polarized radiation characteristics of tail plumes that considers the particle size distribution of solid-phase Al₂O₃ particles in a two-phase gas-solid tail plume. This method aims to improve the calculation accuracy of tail plume radiation models and accurately reflect the degree to which the tail plume is actually formed, thereby meeting the requirements of target polarization detection systems for tail plume target detection.

[0022] Existing models for calculating polarized radiation from tail plumes generally simplify the Al2O3 particles in the tail plume to spherical particles of a single size, ignoring the actual particle size distribution and spatial variation of the particles in the tail plume. This simplification can lead to significant errors in the calculation of polarized radiation from two-phase flow tail plumes, particularly in terms of tail plume temperature, gas mole fraction, and particle spatial distribution. The simulated polarized intensity distribution of the gas-solid two-phase flow tail plume can deviate significantly from the actual conditions, making it difficult to meet the requirements of high-precision target detection and early warning systems.

[0023] Therefore, this patent application aims to address the following core technical issues: 1) Constructing a size distribution model for Al2O3 particles in the tail plume based on measured data from literature, discretizing the continuous particle size distribution function to calculate the polarization scattering characteristics of Al2O3 particle populations with a size distribution; 2) Efficiently coupling the particle size distribution with the three-dimensional tail plume polarization radiation transfer equation to improve the spatial resolution and accuracy of polarization radiation simulations for gas-solid two-phase flow tail plumes. While simultaneously controlling computational complexity, the patent provides more physically realistic tail plume polarization radiation data for polarization detection systems of two-phase flow tail plumes, balancing engineering applicability with computational accuracy.

[0024] The existing calculation model of polarized radiation transmission in the tail flame of gas-solid two-phase flow has the following shortcomings: (1) The solid phase components are simplified into a single particle size distribution in the existing model, resulting in large errors in the calculation of the spectral model: the existing model generally simplifies the Al2O3 particles in the tail flame of the two-phase flow into spherical particles with a single particle size, ignoring the particle size and spatial distribution characteristics under actual conditions, resulting in insufficient accuracy in the calculation of temperature, gas component mole fraction and polarization characteristics, making it difficult to reflect the characteristics of the coupled interaction between the gas phase and the solid phase components of the particulate matter in the gas-solid two-phase tail flame in polarized radiation. (2) The spatial distribution differences of particles of different particle sizes are ignored: in the simplified model of a single particle size, the Al2O3 particles have the same size in the entire tail flame, which cannot reflect the real spatial distribution phenomenon of "large particles gather at the tail flame axis and small particles distribute at the edge" in the tail flame, especially the spatial distribution of polarized radiation. (3) The empirical calculation formulas for Al2O3 particles in the tail plume are not universal: Common empirical formulas (such as the Hermsen formula) are only applicable to the calculation of single particle size in the tail plume under specific experimental conditions. They are difficult to adapt to the changes in the particle size of Al2O3 particles in the two-phase flow tail plume caused by factors such as different propellant components, engine geometry, flight altitude and speed, resulting in insufficient model reliability. (4) The particle size distribution function and the tail plume polarization radiation model are not uniformly coupled for calculation: In the existing simulation of tail plume polarization radiation characteristics, the particle size distribution and polarization radiation calculation are separated from each other. There is a lack of a systematic modeling framework, and it is impossible to achieve dynamic regulation of the particle size distribution characteristics on the polarization radiation calculation (such as extinction coefficient and single scattering albedo), which limits the calculation efficiency and accuracy in actual engineering application requirements. (5) There is a lack of efficient statistical processing methods for particle size distribution in the tail plume, and the calculation cost is high: Although the introduction of a complete particle size distribution improves the accuracy of the physical model, it will increase the workload of the simulation calculation. If there is no optimization algorithm, the massive calculation will be difficult to meet the requirements of real-time or multi-condition simulation, limiting the usability of the project.

[0025] In order to overcome the above-mentioned technical deficiencies, this application provides a method for calculating the polarized radiation characteristics of a two-phase flow tail flame taking into account the particle size distribution, aiming to improve the physical reality, computational accuracy and engineering applicability of the polarized radiation transmission modeling of a gas-solid two-phase flow tail flame. The specific objectives are as follows: 1) Construct a particle size distribution function of Al2O3 particles in a two-phase flow tail flame that is closer to reality: Combined with the particle size measurement experiment of Al2O3 particles in the two-phase flow tail flame, a log-normally distributed Al2O3 particle size distribution function in the tail flame is constructed to replace the existing single particle size model. 2) Use a discretized approximation algorithm to calculate the polarized scattering characteristics of a group of Al2O3 particles with a particle size distribution: Overcome the complexity of calculating the particle size distribution function, use discretized approximation to replace the particle size distribution function, and combine Mie theory to calculate the polarized scattering characteristics of Al2O3 particles considering the particle size distribution, taking into account both computational efficiency and accuracy. 3) A particle size distribution calculation module is introduced into the polarized radiative transfer model of the tail plume of a three-dimensional two-phase flow. This module addresses the issue of existing single-particle size models that ignore the tail plume temperature, gas mole fraction, and particle spatial distribution. This application calculates the extinction coefficient and single scattering albedo of the tail plume under the particle size distribution condition. This coupling of the gas and solid phase extinction and single scattering albedo into the spectral radiative transfer equation for the gas-solid two-phase flow effectively improves the reliability of the tail plume polarized radiative transfer model. 4) The improved accuracy of the proposed model is verified by comparing the polarized spectral radiative characteristics of the tail plume under the traditional single-particle size model with those of the two-phase tail plume model incorporating the particle size distribution function. The polarized radiative characteristics of the tail plume under the two models are compared, and the impact of the particle size distribution function on the tail plume polarization simulation results is analyzed. 5) The coupled computational capability of the simulation of the polarized radiative characteristics of the tail plume of a gas-solid two-phase flow is enhanced. This solves the problem of existing studies ignoring the non-uniform particle size distribution in the tail plume. This coupling calculation combines the thermal radiation and scattering of particles under the particle size distribution with the thermal radiation of the mixed gas, resulting in a more realistic tail plume polarized radiative simulation. The above improvements can provide more accurate model support for the polarization detection of tail flames of high-speed aircraft targets in complex environments.

[0026] In summary, this application introduces the Al2O3 particle size distribution characteristics on the basis of the traditional tail flame polarization radiation model, and constructs a complete, systematic, and engineering-applicable two-phase flow tail flame polarization radiation model calculation method that takes into account the solid phase particle size distribution. It effectively improves the accuracy, stability and computational efficiency of tail flame polarization modeling, and expands its application scope in target warning, detection and other fields.

[0027] The specific process of the calculation method of the tail flame radiation model based on polarization spectrum considering the solid phase particle size distribution of gas-solid two-phase flow proposed in this embodiment can be as follows: Figure 1 As shown, the method for simulating the polarization state of the tail flame considering the particle size distribution of the solid phase particles may include the following execution process: S101, dividing the tail flame three-dimensional space into grids to obtain grids.

[0028] Specifically, S101 may include the following execution process: S1011. Constructing a tail flame coordinate axis based on the three-dimensional space model of the tail flame, wherein the tail flame coordinate axis includes an x-axis and a y-axis; S1012, determining a central symmetry axis plane based on the x-axis and the y-axis, and dividing the tail flame into m x n grid points along the x-axis and the y-axis on the central symmetry axis plane; S1013. Process the m times n grid points based on an interpolation algorithm, and obtain each grid in the three-dimensional space of the tail flame by rotational symmetry.

[0029] In a specific implementation, the processor divides the tail flame into m and n grid points in the x and y directions along the central symmetry axis respectively, and obtains the grid points of the tail flame three-dimensional space after processing by the interpolation algorithm.

[0030] S102, in each grid, based on the experimental data of particle size measurement of Al2O3 particles in the tail flame of two-phase flow, construct a particle size distribution function of Al2O3 particles that obeys the log-normal distribution; determine the cumulative distribution function based on the particle size distribution function, and discretize the cumulative distribution function according to the preset particle proportion to obtain each particle size distribution area, and calculate the representative particle size of each area based on the particle size distribution area; calculate the average volume of Al2O3 particles based on the representative particle size of each area, and calculate the number density of Al2O3 particles in the tail flame based on the average volume; use the representative particle size as a parameter of the Mie algorithm to calculate the optical factor of the solid phase particles in each area; use the optical factor, number density, representative particle size, and particle proportion of the solid phase particles as parameters of the particle group optical calculation formula to calculate the optical parameters of the particle group.

[0031] Based on the measured data of the particle size distribution of Al2O3 particles in the tail flame measured in the literature, the present invention performs distribution fitting of the data characteristics of the particle size, and the obtained particle size distribution satisfies the logarithmic normal distribution, that is, the expression of the particle size distribution function is:

[0032] Where x represents the particle size, represents the standard deviation, a represents the amplitude coefficient, which is used to adjust the amplitude of the function, f0 represents the offset of the function to make the fitting more accurate, and xc represents the geometric mean, which corresponds to the center position of the distribution.

[0033] If the particle size distribution is not considered and a single particle size is used for simplified calculation, Hermsen et al. established a model with three free parameters to predict the mass-weighted mean diameter of Al2O3 particles in the nozzle. D43. They collected the data of the Al2O3 particle size in the solid rocket engine exhaust plume from 1962 to 1978, and found that the nozzle throat diameter, the combustion chamber pressure and the Al2O3 concentration were the main factors affecting the Al2O3 particle size. Specifically, D 43The semi-empirical formula of the particle size is as follows:

[0034] wherein, D is the engine throat diameter, in mm; C is the Al2O3 concentration in the combustion chamber, in mol / 100g; Pc is the pressure in the combustion chamber, in Pa; T is the average residence time of the particles in the combustion chamber, in ms, is the gas density when the propellant is consumed by half, V is the volume of the combustion chamber, is the mass flow rate of the combustion chamber at this time.

[0035] Specifically, S102 can include the following execution process: S1021, acquiring the particle proportion; The traditional single particle size model fails to fully consider the particle size distribution characteristics of the Al2O3 particles in the actual exhaust plume, and the present application re-calculates the optical properties of the particle group under the premise of keeping the calculation of gas thermal radiation unchanged. In the calculation of the scattering properties of the Al2O3 particle group with particle size distribution, a discretization approximation is used to replace the continuous particle size distribution function. Specifically, the particle size discretization is to divide the cumulative distribution function CDF of the particle size distribution function of the Al2O3 particles into N regions, each region containing a certain proportion of particles, i.e. the calculation formula of the particle proportion is as follows:

[0036] S1022, constructing an integral factor expression with the continuous particle diameter as the parameter based on the continuous particle diameter, the mass median diameter and the standard deviation of the particle size distribution function; In an embodiment of the present application, the construction of the integral factor expression with the continuous particle diameter as the parameter based on the continuous particle diameter, the mass median diameter and the standard deviation of the particle size distribution function can include the following execution process: calculating the standard deviation of the particle size distribution function; calculating the geometric standard deviation according to the exponentialized standard deviation; calculating the D 43particle size of the Al2O3 particles in the nozzle based on the three free parameter model, and D43The product of the particle size and the natural index is used to calculate the mass median diameter, where the parameter of the exponential part of the natural index is the natural logarithm of the geometric standard deviation; Exemplarily, is the mass median diameter, which can be calculated by the mass weighted average diameter D 43, that is: .

[0037] A first ratio of the continuous particle diameter and the mass median diameter is calculated, the natural logarithm of the first ratio is calculated, and the natural logarithm of the geometric standard deviation is calculated; A second ratio of the natural logarithm of the first ratio and the natural logarithm of the geometric standard deviation is calculated; An integral factor expression is obtained according to a weighted sum of the second ratio and the natural logarithm of the geometric standard deviation; S1023, constructing a cumulative distribution function with the continuous particle diameter as a parameter based on the integral factor expression, where the cumulative distribution function is an integral of the particle size distribution function; Specifically, the cumulative distribution function CDF corresponding to the particle size distribution function subject to the lognormal distribution is defined as:

[0038] wherein, D represents the particle diameter, and the integral factor expression Z is defined as:

[0039] wherein, is the geometric standard deviation; S1024, dividing the distribution region of each particle size in each cumulative distribution function based on the cumulative distribution function and the particle proportion; In an embodiment of the present application, dividing the distribution region of each particle size in each cumulative distribution function based on the cumulative distribution function and the particle proportion can include the following execution process: The cumulative distribution function is divided into multiple regions, where the cumulative probability difference in each region is equal to the particle proportion; According to the cumulative probability difference of each region, the upper limit of the particle size and the lower limit of the particle size are determined; The distribution region of the particle size is determined based on the upper limit of the particle size and the lower limit of the particle size.

[0040] That is, Δ f =1 / N represents the probability step used to equally divide the cumulative distribution function into N intervals in the probability space, and f(D) in formula (4) is the cumulative distribution function. The processor equally divides the CDF into 1 / N, thereby inversely deducing the upper limit of the particle size and the lower limit of the particle size, and thereby determining the distribution region of the particle size.

[0041] S1025. Using the median point of the cumulative distribution function in each particle size distribution region as a parameter of the inverse cumulative distribution function, inversely deduce the representative particle size of each particle size distribution region.

[0042] Among them, the division j The median point of the cumulative distribution function corresponding to the region is:

[0043] Combining equations (4) and (5), we can get j The representative particle size corresponding to each region is:

[0044] Among them, erfinv is the inverse function of CDF.

[0045] It should be noted that, assuming that the particle size of Al2O3 follows a lognormal distribution, this distribution cannot be directly used for the particle size-by-particle size solution of Mie theory, so it needs to be discretized into a finite set of particle size points. The CDF is introduced here for two purposes: 1. Determine the relative proportion (proportion) of each particle size interval △ f : CDF is the result of integrating the probability density function (PDF). Therefore, the CDF can be used to determine the cumulative probability that the particle size falls within a certain interval, that is, the proportion of particles contained in the interval; 2. Calculate the representative particle size using the inverse function of CDF DJ : Use an evenly divided probability interval (for example, divide the cumulative probability of 0 to 1 into N intervals) and use the inverse function of CDF (i.e., the inverse function of the error function, erfinv) to infer the representative particle size of each area.

[0046] Formula (7) uses the midpoint of the interval after equal probability division as the representative probability point of each group, which is a discrete sampling strategy commonly used in numerical calculations. It is convenient to infer the representative particle size of each group through the CDF inverse function. DJ , thus achieving effective discretization of particle size distribution. It is related to the number of groups selected.

[0047] The processor then calculates the absorption factor, scattering factor, and extinction efficiency factor of the solid phase particles in each region based on each representative particle size in the discretized particle size distribution using Mie theory.

[0048] Next, the processor can calculate the optical properties of the Al2O3 particle group in the two-phase flow tail flame considering the particle size distribution.

[0049] In the particle size distribution model, the average Al2O3 particle volume is calculated as:

[0050] At this time, the number density of Al2O3 particles in the tail flame is Ntot, which can be approximately expressed as:

[0051] in, is the mass of the Al2O3 particle group in the tail flame, Indicates the density of Al2O3 particles.

[0052] The processor then uses the optical factor, number density, representative particle size, and particle ratio of the solid phase particles as parameters for the particle group optical calculation formula. In other words, the processor calculates the scattering coefficient, extinction coefficient, and absorption coefficient of the tail flame Al2O3 particle group in the region based on the absorption factor, scattering factor, and extinction efficiency factor of the solid phase particles in each region. The calculation formula is:

[0053] S103. Use each representative particle size and number density as the particle phase input of the NS equation of fluid mechanics to obtain the two-phase flow tail flame flow field data under different particle size distribution conditions, as well as the nozzle outlet data; construct a tail flame polarization radiation transmission model under the particle size distribution function, use the two-phase flow tail flame flow field parameters and nozzle outlet data as the tail flame polarization radiation transmission model, calculate each solid phase parameter of each grid, and calculate the extinction coefficient and single scattering coefficient of each unit cell based on each gas phase parameter and optical parameter, use the extinction coefficient and single scattering coefficient of each unit cell as the input parameters of the two-phase flow tail flame vector radiation transmission equation, and output the tail flame polarization state described by the Stokes parameter.

[0054] Specifically, the characteristic parameters of the high-temperature mixed gas from the engine combustion chamber to the nozzle outlet plane are obtained from measured parameters. The Al2O3 particle size parameters are used as the particle phase input in computational fluid dynamics. Using the NS equations of fluid dynamics, simulations are performed to obtain two-phase flow field data under different particle size distribution conditions, as well as nozzle outlet data. This data is gridded and includes temperature, pressure, and gas mole fraction.

[0055] Then, based on the interpolated two-phase flow tail flame flow field data and nozzle outlet data, the physical parameters of the Al2O3 particles, and the optical parameters of the particle group, the processor calculates the extinction coefficient and single scattering albedo (that is, the single scattering coefficient) of the two-phase flow tail flame at each unit grid under the particle size distribution function. The calculation can be calculated as follows:

[0056] Next, the processor performs a coupled solution of the two-phase flow tail flame vector radiation transfer equation.

[0057] Specifically, if Figure 1 Schematic diagram of the polarized radiation transmission model of the tail flame of a high-speed aircraft considering the particle size distribution established by the present invention, wherein Indicates the first grid points, In the detection direction Initial total radiance on . Solar zenith angle , which indicates the incident direction of sunlight and Axis angle; solar azimuth , Indicates that sunlight is positive Direction of emission, Indicates positive Direction of emission. Detection zenith angle , Indicates upward detection, detection azimuth , Indicates positive Emitted in the direction of detection. Top, The total Stokes parameter of the input cell After the solution is transferred through this cell, the total Stokes parameter of the next cell is obtained. , as the first The input data of the cell is used to obtain the Stokes parameters of the tail flame boundary grid points in this way to complete the polarization radiation calculation on the path. The present invention uses the Stokes parameters to describe the polarization state of the tail flame, which is defined as follows:

[0058] Where, I Indicates the total intensity of light, that is, the total power of light; Q Represents the intensity difference between horizontal and vertical linear polarized light; U It represents the intensity difference between linear polarized light at 45° and 135°. V Represents the intensity difference between left-handed and right-handed circularly polarized light.

[0059] Two-phase flow tail flame along the detection direction superior The Stokes vector of the point transmission is expressed as:

[0060] Among them, the corner mark Indicates the direction of the corresponding discrete coordinates Vector components, the radiation source function expression of the tail flame is:

[0061] Then, the vector spherical harmonic discrete ordinate method is used to solve the above equations and calculate the polarized radiation values ​​of the two-phase flow tail flame at different detection angles: I 、Q , U and V . In order to quantify the degree of light polarization, the degree of polarization is introduced. The definition of the degree of polarization is:

[0062] The degree of polarization represents the proportion of polarized light in the light. When , the light wave is unpolarized light; when , the light wave is completely polarized light; when , the light wave is partially polarized light. Obviously, the greater the value of , the higher the proportion of polarized light in the light wave. Since in actual measurement and calculation, the V component generally accounts for a small proportion of the total light intensity, it can usually be ignored.

[0063] The specific calculation process of the two-phase flow plume polarized radiation transfer model considering the particle size distribution is shown in Figure 2 .

[0064] In another embodiment of the present application, the comparison results of the traditional single particle size model and the two-phase flow plume polarized radiation transfer model considering the particle size distribution are provided.

[0065] Taking the following experiment as an example, the difference between the results of the traditional single particle size model and the two-phase flow plume polarized radiation transfer model considering the particle size distribution is compared. Laredo et al. used a wedge-shaped probe and an experimental post-sampling method, combined with non-destructive optical detection technology, to measure the particle size distribution of Al2O3 particles in the plume of a scaled solid rocket engine. They measured the particle size distribution at the engine nozzle outlet under the condition of a combustion chamber pressure of 1.4 MPa using a Malvern particle size measuring instrument, as shown in Table 1.

[0066] Table 1: Experimental particle size distribution data of the engine nozzle outlet under the condition of a combustion chamber pressure of 1.4 MPa

[0067] Therefore, the values of the lognormal distribution parameters fitted under this experiment are: = 0.58, a = 27.7, f0= 10.2, xc= 0.96. As shown in Figure 3 , the experimental particle size distribution data of Al2O3 particles in the two-phase flow plume and the lognormal distribution fitting curve according to the present application are shown. In the above experiment of Laredo et al., according to the specific experimental conditions: = 5 mm, , Pc = 1.4 MPa, , the calculation result is . For convenience of expression, the DThe model for calculating the polarization radiation characteristics of the tail flame with a diameter of 43 is called the simplified single particle size model. In this model, D 43 is used as the input parameter for a single particle size. The model that uses the particle size distribution obtained from actual experimental measurements to calculate the polarized radiation of the tail plume is called the particle size distribution model.

[0068] Using the two Al₂O₃ particle size parameters and the calculated high-temperature mixed gas characteristic parameters as flow field inputs, flow field simulation was used to determine the temperature, pressure, and composition characteristics of the two-phase flow plume under different particle size distribution conditions. After interpolation, the plume was divided into 100 grid points in the x-direction with a grid spacing of 0.01 m, and 60 grid points each in the y- and z-directions with a grid spacing of 0.005 m. Figure 4 This is the temperature distribution of the tail flame symmetry plane under different Al2O3 particle size distribution models obtained by flow field simulation.

[0069] contrast Figure 4 In Figures (a) and (b), it is clear that considering the Al₂O₃ particle size distribution significantly affects the temperature distribution in the plume core. When using a simplified single-particle size model, the plume temperature from the nozzle to x = 0.35 m is significantly lower than when using the particle size distribution model, and the radial temperature distribution is also narrowed. However, the overall plume structure remains unchanged.

[0070] Figure 5 Figures (a), (b), (b), and (d) compare the temperature along the tail flame axis and the mole fractions of CO2, CO, and H2O for two Al2O3 particle size distribution models. Comparing the temperatures reveals that the maximum temperature difference between the two particle size distribution models at the tail flame centerline reaches 1600K, with both peaks occurring near x = 0.02m. The afterburning zone in the particle size distribution model shifts slightly backward, but the temperature drops more rapidly; when x > 0.8m, the temperatures converge. This is because: in the single-size model, the particle diameter is constant and uniformly affected by turbulence; in the particle size distribution model, however, the particle diameters vary significantly, with large particles concentrated along the tail flame centerline, increasing the nozzle outlet temperature. Within the afterburning zone, the Al2O3 particles undergo energy exchange, causing the particle temperature to gradually decrease, leading to temperature convergence between the two particle size distribution models. The gas mole fractions reveal that when the particle size distribution model is simplified to a single particle size model, the CO2 and H2O mole fraction curves at the nozzle outlet both decrease significantly, but the CO mole fraction curve increases. In the tail region, although the CO and H2O mole fraction curves are essentially identical, the CO2 mole fraction curve is higher than the particle size distribution model. Analysis reveals that the single particle phase significantly reduces the tail flame temperature at the nozzle outlet, weakening the combustion reaction. This reduces the consumption of the rich gas CO, leading to a decrease in the production of CO2 and H2O as products.

[0071] Figure 6 Figure 2 shows the mass density distribution of Al2O3 particles along the symmetric plane of the exhaust plume under two particle size distribution models. It can be observed that under the particle size distribution model, the Al2O3 particles in the exhaust plume are more widely distributed in the radial direction and spatially distributed, with a higher density near the central axis. Under the simplified single particle size model, the mass density of Al2O3 particles at the engine nozzle is lower, as the engine structure and turbulence effects cause Al2O3 particles to concentrate in the center and tail of the exhaust plume.

[0072] The particle size distribution data of Al2O3 particles in the tail flame obtained by Laredo et al. are divided into 7 groups, and the diameter of each group of particles is recorded as DJ (in ), and the corresponding proportions are given For each particle diameter in the discretized particle size distribution, Mie theory is used to calculate its corresponding absorption, scattering and extinction efficiency factors. At a detection wavelength of 4.3 μm, Figure 7 Shown are the extinction coefficient distributions along the symmetric plane of the tail plume for two particle size distribution models. As can be seen from the figure, in the simplified single-particle size model, the peak extinction coefficient of the tail plume is significantly higher than that of the particle size distribution model, and its peaks are primarily concentrated at the nozzle exit and on either side of the tail plume's centerline. Influenced by the spatial distribution of the mixed gas and particles, the extinction coefficient of the simplified single-particle size model more clearly depicts the location of the "Mach loop" and the primary spatial distribution of the particles. In contrast, when considering particle size distribution, the spatial distribution of Al2O3 particles in the tail plume is more complex due to the large differences in particle size. Although the extinction coefficient peaks still lie on either side of the tail plume's centerline, the overall distribution is more dispersed.

[0073] like Figure 8 Shown are the single scattering albedo distributions along the symmetric plane of the plume under different particle size distribution models. Analysis shows that the single scattering albedo is closely related to the spatial distribution of particles. When considering particle size distribution, the spatial distribution of the single scattering albedo exhibits a distinct tomographic phenomenon: its radial distribution is wider, with the single scattering albedo in the central axis region being higher than that in the regions to the sides. This phenomenon is attributed to the fact that large particles accumulate near the central axis of the plume, while small particles, influenced by turbulence, migrate to the sides.

[0074] Step (4) calculates the spatial distribution of the Stokes parameters and polarization degree of the plume under different particle size distribution conditions during vertical detection. In this plume polarization radiation transmission model, the radiation source is the plume heat source, the meshing accuracy is 0.03, and the spherical harmonics cutoff accuracy is 0.003. The effects of different particle size distribution models on the plume polarization radiation characteristics are analyzed and discussed. Figure 9 The tail flame under different particle size distribution models IThe spatial distribution of the values, comparing the two images shows that although the tail flames under the two models I The values ​​are all unimodal, but there are significant differences in the values: when the particle size distribution model is used, the tail flame I The value is significantly higher than that obtained under the simplified single particle size model.

[0075] Figure 10 The tail flame under different particle size distribution models Q Value and U The spatial distribution of values. Q From the perspective of the spatial distribution of values, there are obvious differences between the two models: under the simplified single particle size model, the tail flame is in the region from x = 0m to x = 0.5m. Q The values ​​are all positive, indicating that the horizontal polarization component is dominant in this area; when x>0.5m, Q A negative value indicates that the vertical polarization component is stronger in this area. In the particle size distribution model, Q The overall value is significantly higher than that of the simplified single particle size model. Q Value, tail flame centerline area Q The value is positive, the tail flame edge Q The value is negative, which means that the horizontal polarization component is stronger at the axis of the tail flame and the vertical polarization component is stronger at the edge. U Spatial distribution of values, two particle size distributions U The values ​​show obvious alternating characteristics on both sides of the tail flame axis, but the simplified single particle size model U The overall value is smaller than that of the particle size distribution model U value.

[0076] Figure 11 The tail flame under different particle size distribution models DOP The spatial distribution of the values ​​shows that DOP The peak values ​​are all at the edge of the tail flame, but under the simplified single particle size model, DOP The value decreases significantly, with the peak value mainly concentrated in the tail of the tail plume, while its radial distribution range decreases. This shows that although the simplified single particle size model simplifies the calculation, it underestimates the contribution of particles in the tail plume to the polarized radiation characteristics. The main reason for this difference is that different particle size distributions will cause significant changes in the temperature and spatial distribution of the mixed gas in the tail plume flow field. Secondly, in the particle size distribution model, the particle phase space distribution is more dispersed, resulting in a wider spatial range that needs to be considered when calculating the polarized radiation characteristics of the two-phase flow tail plume. In addition, the physical properties of the particles and the calculation of polarized radiation are more complicated, which has a significant impact on the polarized radiation results.

[0077] The step division of the above various methods is only for the purpose of clear description. During implementation, they can be combined into one step or some steps can be split and decomposed into multiple steps. As long as they include the same logical relationship, they are all within the scope of protection of this application; adding insignificant modifications or introducing insignificant designs to the algorithm or process without changing the core design of the algorithm and process are all within the scope of protection of this application.

[0078] In summary, the present invention proposes a calculation method that considers the influence of Al2O3 particle size distribution on the polarized radiation characteristics of the tail flame of two-phase flow. The key technical innovation lies in the systematic modeling and efficient calculation of the polarized radiation characteristics of the tail flame of two-phase flow by introducing the Al2O3 particle size distribution. Specifically, it includes: (1) The present invention constructs an Al2O3 particle size distribution model based on experimental data and empirical formulas Based on measured particle size data (such as the Laredo experiment) and introducing the log-normal distribution function, the present invention fits the particle size distribution law of Al2O3 particles in the tail flame, replacing the single particle size model in the traditional tail flame polarization radiation transmission calculation, realizing a closed-loop mapping from actual measurement to model input, and significantly improving modeling accuracy.

[0079] (2) This paper proposes a discretization method for Al2O3 particle size in the calculation of tail flame polarization radiation and a calculation model for its optical parameters. The present invention discretizes the continuous particle size distribution function and calculates the central particle size of each interval using the cumulative distribution function (CDF). The scattering, absorption, and extinction properties of each particle size interval are then independently calculated using Mie theory. The particle number density is then derived from the average particle volume and the simulated mass density of the particle swarm. Furthermore, expressions for calculating parameters such as the scattering coefficient, extinction coefficient, and absorption coefficient of the Al2O3 particle swarm in the two-phase flow tail plume are given, taking into account the particle size distribution. This enables refined modeling of the optical properties of multi-scale Al2O3 particle swarms in the two-phase flow tail plume.

[0080] (3) Achieved efficient coupling between the particle size distribution model and the three-dimensional two-phase flow tail flame polarization radiation transmission model Based on the characteristic distributions of tail flame temperature, mixed gas mole fraction and particle mass density obtained by simulating the gas-solid two-phase flow field, the present invention obtains the tail flame flow field data through difference and rotation and expands it to three dimensions. By dividing it into multiple spatial grids and combining it with the particle size distribution model, the optical parameters of the gas-solid two-phase tail flame of each three-dimensional spatial grid in the three-dimensional space are provided. By establishing the vector radiation transmission equation of the tail flame containing the solid phase particle size distribution, the vector spherical harmonic discrete coordinate method is used to solve the tail flame spectral radiation transmission equation containing gas-solid coupling multi-source parameters, and the solution of the polarized radiation characteristics of the tail flame considering the particle size distribution is realized. The polarized radiation characteristics of each spatial grid point of the tail flame can dynamically respond to changes in particle size, thereby improving the physical reality and spatial resolution of the model.

[0081] (4) A comparative simulation platform for the polarization radiation characteristics of tail flames of particle size distribution models and simplified single particle size models has been implemented. The present invention can realize the calculation of the polarized radiation characteristics of the tail flame using a single particle size model and a particle size distribution model. Through quantitative comparison of multidimensional parameters such as temperature distribution, gas mole fraction, extinction coefficient, single scattering albedo, Stokes parameter and polarization degree, it is found that the particle size distribution will significantly affect the distribution and polarized radiation of the tail flame particles on the central axis and edge. The influence of the behavior of large-size particles gathering toward the tail flame axis and small particles diffusing toward the edge on the polarization intensity distribution is quantitatively modeled.

[0082] Compared with the existing method for modeling the polarized radiation transmission of tail flames using a single particle size model, the present invention has the following significant advantages in terms of modeling the particle size distribution of Al2O3 particles in the tail flame of two-phase flow, calculating the polarized scattering characteristics of particle groups, coupling the tail flame polarized radiation transmission model with application efficiency, etc.: (1) A polarized radiation transmission model that is closer to the actual tail flame environment is established.

[0083] The traditional model only uses a single D 43 particle size as input, ignoring the multi-scale distribution of the actual Al2O3 particle size in the tail flame. The present invention combines experimental Al2O3 particle size distribution data to fit a log-normally distributed Al2O3 particle size distribution function in the tail flame of a two-phase flow. This continuous particle size distribution function is discretized to obtain calculation results of the optical parameters of Al2O3 particles in the tail flame that are more consistent with the actual physical process, resulting in more accurate numerical calculations.

[0084] (2) The present invention can significantly improve the accuracy of tail flame structure simulation.

[0085] Flow field simulation results using a particle size distribution model show that the temperature in the central axis of the tail flame can be increased to 1600K, reflecting the differences in the heat transfer process of real particles with different particle sizes. Comparison of temperature and mixed gas mole fraction under a simplified single particle size model and a particle size distribution model reveals that the proposed method significantly reduces the spectral radiation errors introduced by simplified modeling, helping to reveal the mechanisms of complex combustion and the coupling between the gas and solid phases, such as scattering and radiation, in the tail flame of a gas-solid two-phase flow.

[0086] (3) The present invention improves the accuracy of the calculation of polarization scattering of Al2O3 particles in the tail flame of two-phase flow.

[0087] The present invention can demonstrate the "central aggregation and edge diffusion" behavior of particles of different sizes in the tail flame, resulting in a significant radial tomographic structure in the mass density distribution of Al2O3 particles in the tail flame. This structure cannot be reflected in traditional single-particle size models, but is particularly critical for actual tail flame polarization detection systems. Compared to methods that use only a single diameter input Mie formula to calculate the polarization scattering characteristics of particles, the present invention separately calculates and statistically weights each discretized particle size, making the resulting polarization scattering matrix of the tail flame Al2O3 particles more accurate at different angles and wavelengths, improving the consistency between tail flame polarization prediction and imaging simulation.

[0088] (4) The present invention improves the accuracy and versatility of the three-dimensional tail flame polarization radiation model.

[0089] Compared to single-particle-size tail plume polarization radiative transfer models, this paper establishes a polarization spectral radiative transfer model for the gas-solid two-phase tail plume that accounts for particle size distribution. This model addresses the inability of existing polarization radiative transfer models to adapt to varying particle size distributions under different operating conditions. The proposed model efficiently calculates the optical parameters of each spatial grid point in a three-dimensional grid, effectively adapting to complex flow conditions such as various flight states and varying particle concentrations, enhancing the model's scalability and engineering versatility.

[0090] (5) The present invention expands the scope of application of the tail flame polarization detection model.

[0091] The method of the present invention is not only applicable to Al2O3 particles, but can also be extended to the modeling and analysis of polarized radiation transmission of tail flames of other solid phase particles such as carbon particles (such as carbon black) and metal oxides. It has good versatility and transferability, and can provide theoretical support for the modeling of polarized spectral radiation characteristics of tail flame targets of various new propulsion systems and various propellant types.

[0092] Based on the above method embodiment, the present application further provides a device for simulating the polarization state of a tail flame taking into account the particle size distribution of solid phase particles. The device may include the following execution modules: The grid division module is used to divide the tail flame three-dimensional space into grids to obtain each grid; the parameter calculation module is used to construct a particle size distribution function of Al2O3 particles that obeys the log-normal distribution in each grid based on the particle size measurement experimental data of Al2O3 particles in the two-phase flow tail flame; the cumulative distribution function is determined based on the particle size distribution function, and the cumulative distribution function is discretized according to the preset particle ratio to obtain each particle size distribution area, and the representative particle size of each area is calculated based on the particle size distribution area; the average volume of Al2O3 particles is calculated based on the representative particle size of each area, and the number density of Al2O3 particles in the tail flame is calculated based on the average volume; the representative particle size is used as the parameter of the Mie algorithm to calculate the optical factor of the solid phase particles in each area; the optical factor of the solid phase particles, The number density, representative particle size, and particle ratio are used as parameters of the particle group optical calculation formula to calculate the optical parameters of the particle group; the simulation module is used to use each representative particle size and number density as the particle phase input of the NS equation of fluid mechanics to obtain the two-phase flow tail flame flow field data under different particle size distribution conditions, as well as the nozzle outlet data; a tail flame polarization radiation transmission model under the particle size distribution function is constructed, and the two-phase flow tail flame flow field parameters and nozzle outlet data are used as the tail flame polarization radiation transmission model to calculate the solid phase parameters of each grid, and the extinction coefficient and single scattering coefficient of each unit cell are calculated based on the gas phase parameters and optical parameters, and the extinction coefficient and single scattering coefficient of each unit cell are used as the input parameters of the two-phase flow tail flame vector radiation transmission equation, and the tail flame polarization state described by the Stokes parameter is output.

[0093] It is not difficult to find that this embodiment is an apparatus embodiment corresponding to the above-mentioned method embodiment, and this embodiment can be implemented in conjunction with the above-mentioned method embodiment. The relevant technical details and technical effects mentioned in the above-mentioned embodiments are still valid in this embodiment, and to reduce repetition, they are not repeated here. Accordingly, the relevant technical details mentioned in this embodiment can also be applied to the above-mentioned embodiments.

[0094] It is worth mentioning that all modules involved in this embodiment are logical modules. In actual applications, a logical unit can be a physical unit, a part of a physical unit, or a combination of multiple physical units. In addition, to highlight the innovation of this application, this embodiment does not introduce units that are not closely related to solving the technical problems proposed by this application. However, this does not mean that other units do not exist in this embodiment.

[0095] Another embodiment of the present application proposes an electronic device, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the tail flame polarization state simulation method considering the solid phase particle size distribution in the above-mentioned method embodiments.

[0096] The memory and processor are connected using a bus, which can include any number of interconnected buses and bridges. The bus connects various circuits of one or more processors and memories. The bus can also connect various other circuits such as peripheral devices, voltage regulators, and power management circuits. These are all well known in the art and therefore will not be described further in this article. The bus interface provides an interface between the bus and the transceiver. The transceiver can be a single component or multiple components, such as multiple receivers and transmitters, providing a unit for communicating with various other devices on a transmission medium. Data processed by the processor is transmitted on a wireless medium via an antenna. Furthermore, the antenna also receives data and transmits it to the processor.

[0097] The processor is responsible for managing the bus and general processing, and may also provide various functions, including timing, peripheral interfacing, voltage regulation, power management, and other control functions. Memory can be used to store data used by the processor while performing operations.

[0098] Another embodiment of the present application relates to a computer-readable storage medium storing a computer program, which implements the above method embodiment when executed by a processor.

[0099] That is, those skilled in the art will understand that all or part of the steps in the above-mentioned embodiments can be implemented by instructing the relevant hardware through a program. The program is stored in a storage medium and includes a number of instructions for causing a device (which may be a single-chip microcomputer, chip, etc.) or a processor to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes: a USB flash drive, a mobile hard drive, ROM (Read-Only Memory), RAM (Random Access Memory), a magnetic disk, or an optical disk, etc., various media that can store program code.

[0100] Those skilled in the art will appreciate that the above embodiments are specific embodiments for implementing the present application, and that in actual applications, various changes may be made thereto in form and detail without departing from the spirit and scope of the present application.

Claims

1. A method for simulating the polarization state of a tail flame taking into account the particle size distribution of solid phase particles, characterized in that: include: Divide the tail flame three-dimensional space into grids to obtain grids; In each grid, based on the experimental data of the particle size measurement of Al2O3 particles in the tail flame of two-phase flow, a particle size distribution function of Al2O3 particles obeying the lognormal distribution is constructed; based on the particle size distribution function, the cumulative distribution function is determined, and the cumulative distribution function is discretized according to the preset particle proportion to obtain each particle size distribution area, and the representative particle size of each area is calculated based on the particle size distribution area; based on the representative particle size of each area, the average volume of Al2O3 particles is calculated, and the number density of Al2O3 particles in the tail flame is calculated based on the average volume; the representative particle size is used as a parameter of the Mie algorithm to calculate the optical factor of the solid phase particles in each area; the optical factor, number density, representative particle size, and particle proportion of the solid phase particles are used as parameters of the particle group optical calculation formula to calculate the optical parameters of the particle group; The representative particle size and number density are used as the particle phase input of the NS equation of fluid mechanics to obtain the two-phase flow tail flame flow field data under different particle size distribution conditions, as well as the nozzle outlet data; a tail flame polarization radiation transmission model under the particle size distribution function is constructed, and the two-phase flow tail flame flow field parameters and nozzle outlet data are used as the tail flame polarization radiation transmission model to calculate the solid phase parameters of each grid, and the extinction coefficient and single scattering coefficient of each unit cell are calculated based on the gas phase parameters and optical parameters, and the extinction coefficient and single scattering coefficient of each unit cell are used as the input parameters of the two-phase flow tail flame vector radiation transmission equation, and the polarization state of the tail flame is described using the Stokes parameter as the output.

2. The method for simulating tail flame polarization state considering solid phase particle size distribution according to claim 1, characterized in that: The method of determining a cumulative distribution function based on the particle size distribution function, discretizing the cumulative distribution function according to a preset particle ratio to obtain each particle size distribution area, and calculating a representative particle size of each area according to the particle size distribution area includes: Get the particle ratio; Based on the continuous particle diameter, mass median diameter and standard deviation of the particle size distribution function, an integral factor expression with the continuous particle diameter as the parameter is constructed; Based on the integral factor expression, a cumulative distribution function with continuous particle diameter as a parameter is constructed, wherein the cumulative distribution function is the integral of the particle size distribution function; Based on the cumulative distribution function and particle proportion, the distribution area of ​​each particle size in each cumulative distribution function is divided; The median point of the cumulative distribution function in each particle size distribution area is used as the parameter of the inverse cumulative distribution function to infer the representative particle size of each particle size distribution area.

3. The method for simulating tail flame polarization state considering solid phase particle size distribution according to claim 2, characterized in that: The method of constructing an integral factor expression whose parameter is the continuous particle diameter based on the continuous particle diameter, the mass median diameter and the standard deviation of the particle size distribution function includes: Calculate the standard deviation of the particle size distribution function; Calculate the geometric standard deviation based on the indexed standard deviation; Calculate the D of Al2O3 particles in the nozzle based on the three free parameter model 43 Particle size, and based on D 43 The mass median diameter is calculated by multiplying the particle size by the natural index, where the parameter of the exponential part of the natural index is the natural logarithm of the geometric standard deviation; calculating a first ratio of continuous particle diameters to a mass median diameter, calculating a natural logarithm of the first ratio, and calculating a natural logarithm of a geometric standard deviation; calculating a second ratio of the natural logarithm of the first ratio to the natural logarithm of the geometric standard deviation; The integral factor expression is obtained based on the weighted sum of the second ratio and the natural logarithm of the geometric standard deviation.

4. The method for simulating tail flame polarization state considering solid phase particle size distribution according to claim 2, characterized in that: The method of dividing the distribution area of ​​each particle size in each cumulative distribution function based on the cumulative distribution function and the particle proportion includes: The cumulative distribution function is divided into multiple regions, where the difference in cumulative probability within each region is equal to the particle proportion; According to the cumulative probability difference of each area, the upper limit and the lower limit of the particle size are determined accordingly; The distribution region of the particle size is determined based on the upper limit of the particle size and the lower limit of the particle size.

5. The method for simulating tail flame polarization state considering solid phase particle size distribution according to claim 2, characterized in that: The median point of the cumulative distribution function in each particle size distribution area is used as the parameter of the inverse cumulative distribution function, and the expression used to infer the representative particle size of each particle size distribution area is: Among them, D m represents the mass median diameter, represents the median point of the cumulative distribution function, erfinv represents the inverse function of CDF, σ g represents the geometric standard deviation.

6. The method for simulating tail flame polarization state considering solid phase particle size distribution according to claim 1, characterized in that: The optical parameters include solid-phase scattering coefficient, solid-phase extinction coefficient and solid-phase absorption coefficient, and the gas-phase parameters include gas-phase extinction coefficient and gas-phase absorption coefficient; The step of calculating the extinction coefficient and the single scattering coefficient of each unit cell based on the gas phase parameters and the optical parameters includes: Calculate the extinction coefficient of each unit grid based on the sum of the gas phase absorption coefficient and the solid phase extinction coefficient; The single scattering coefficient is obtained based on the ratio of the solid-phase scattering coefficient to the sum of the gas-phase absorption coefficient, the solid-phase absorption coefficient, and the solid-phase scattering coefficient.

7. The method for simulating tail flame polarization state considering solid phase particle size distribution according to claim 1, characterized in that: The three-dimensional space of the tail flame is divided into grids to obtain grids, including: Based on the three-dimensional space model of the tail flame, a tail flame coordinate axis is constructed, wherein the tail flame coordinate axis includes an x-axis and a y-axis; Based on the x-axis and the y-axis, a central symmetry axis plane is determined, and the tail flame is divided into m times n grid points along the x-axis direction and the y-axis direction on the central symmetry axis plane; Based on the interpolation algorithm, m times n grid points are processed and the grid points of the tail flame three-dimensional space are obtained by rotational symmetry.

8. A device for simulating the polarization state of a tail flame taking into account the particle size distribution of solid phase particles, characterized in that: include: A grid division module is used to divide the tail flame three-dimensional space into grids to obtain each grid; The parameter calculation module is used to construct a particle size distribution function of Al2O3 particles that obeys a log-normal distribution in each grid based on the experimental data of particle size measurement of Al2O3 particles in the tail flame of the two-phase flow; determine the cumulative distribution function based on the particle size distribution function, and discretize the cumulative distribution function according to a preset particle ratio to obtain each particle size distribution area, and calculate the representative particle size of each area based on the particle size distribution area; calculate the average volume of Al2O3 particles based on the representative particle size of each area, and calculate the number density of Al2O3 particles in the tail flame based on the average volume; use the representative particle size as a parameter of the Mie algorithm to calculate the optical factor of the solid phase particles in each area; use the optical factor, number density, representative particle size, and particle ratio of the solid phase particles as parameters of the particle group optical calculation formula to calculate the optical parameters of the particle group; The simulation module is used to use the representative particle size and number density as the particle phase input of the NS equation of fluid mechanics to obtain the two-phase flow tail flame flow field data under different particle size distribution conditions, as well as the nozzle outlet data; construct a tail flame polarization radiation transmission model under the particle size distribution function, use the two-phase flow tail flame flow field parameters and nozzle outlet data as the tail flame polarization radiation transmission model, calculate the solid phase parameters of each grid, and calculate the extinction coefficient and single scattering coefficient of each unit cell based on the gas phase parameters and optical parameters, use the extinction coefficient and single scattering coefficient of each unit cell as the input parameters of the two-phase flow tail flame vector radiation transmission equation, and output the tail flame polarization state described by the Stokes parameter.

9. An electronic device, characterized in that: include: at least one processor; and, a memory communicatively coupled to the at least one processor; The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the tail flame polarization state simulation method considering the solid phase particle size distribution as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the method for simulating the polarization state of a tail flame taking into account the particle size distribution of solid phase particles according to any one of claims 1 to 7 can be implemented.

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