Method for calculating ultraviolet statistical average polarization characteristics of clusters in two-phase flow tail flame

Abstract

The invention relates to an ultraviolet statistical average polarization characteristic calculation method for clusters in two-phase flow tail flame, which comprises the following steps of: modeling aluminum oxide clusters in the two-phase flow tail flame; the complex refractive index of the cluster model is initialized, the polarization scattering characteristic of the cluster in the two-phase flow tail flame in the ultraviolet band is calculated, statistical processing is conducted on the polarization scattering characteristic of the cluster in the ultraviolet band, and the polarization scattering characteristic of the cluster in the ultraviolet band is calculated; statistical average polarization scattering elements of clusters with the same number of monomer particles and monomer particle sizes obeying logarithmic normal distribution are obtained, and statistical analysis is carried out on average polarization characteristics of clusters with different numbers of monomer particles on the whole; obtaining a statistical average polarization scattering element of which the number of monomer particles and the radius obey the logarithmic normal distribution cluster, and calculating the ultraviolet statistical average polarization radiation characteristic of the two-phase flow tail flame by combining a spherical harmonic discrete coordinate method; the system, the equipment and the medium are used for realizing the ultraviolet statistical average polarization characteristic calculation method of the aluminum oxide cluster in the two-phase flow tail flame. According to the method, the calculation efficiency is improved, the application range is expanded, and a more accurate calculation result of the ultraviolet polarization scattering characteristics of the cluster in the tail flame is provided.

Description

Technical Field

[0001] The invention relates to the technical field of tail flame spectral polarization radiation, and in particular to a method for calculating ultraviolet statistical average polarization characteristics of clusters in a two-phase flow tail flame. Background Art

[0002] After the aluminum-containing solid fuel engine is ignited, the aluminum powder in the combustion chamber reacts violently with oxygen to generate gaseous aluminum oxide. The subsequent nozzle structure and high-speed flight state cause the aluminum oxide gas to cool rapidly and condense into tiny aerosol particles. Due to the high temperature gradient of the tail flame, these aerosol particles become the nucleation points of clusters, adsorbing surrounding particles and gases to form larger clusters.

[0003] Polarization scattering of clusters is extremely sensitive to changes in cluster size, shape and surface properties. By analyzing the polarization properties of scattered light, more detailed information about cluster refractive index, surface roughness, etc. can be obtained. Accurate modeling of clusters in two-phase flow is essential for accurately describing the polarization radiation characteristics of plumes, which is particularly critical for high-precision polarization simulation and analysis, and provides theoretical support for polarization detection and early warning of ultraviolet plumes for hypersonic vehicles.

[0004] Most of the current literature uses Mie theory, T matrix method and discrete dipole approximation (DDA), which simplifies cluster particles into individual spheres without considering the influence of monomer number and particle size distribution on the polarization characteristics of clusters. This simplification will lead to insufficient accuracy and low reliability in the calculation of polarization scattering characteristics of clusters in two-phase flow plumes. Especially in the ultraviolet band, due to the shorter wavelength of ultraviolet waves, cluster particles of the same size can be regarded as small particles relative to infrared wavelengths, while the equivalent size parameters of clusters are larger relative to ultraviolet wavelengths, so the structural characteristics of clusters become more important and cannot be ignored. In addition, existing polarized radiation calculation models usually simplify the phase state of aluminum oxide into a single alpha phase, but this is not accurate. In fact, it is necessary to conduct in-depth research on the polarization scattering characteristics of aluminum oxide clusters in the gamma phase and liquid state.

[0005] In summary, the existing calculation models for the polarization scattering characteristics of particles in the tail flame of two-phase flow have the following shortcomings: 1) Modeling problem of aluminum oxide clusters in the tail flame of two-phase flow: The current model usually simplifies the aluminum oxide particles in the tail flame of two-phase flow into single spherical particles of equal volume or area. However, aluminum oxide in the actual tail flame often exists in the form of clusters. This simplified assumption cannot accurately describe the polarization scattering characteristics of cluster particles, resulting in inaccurate prediction and analysis of the polarization scattering characteristics of aluminum oxide clusters in the tail flame, which results in large actual errors in the calculation of polarization radiation characteristics of the tail flame. 2) Computational complexity problem and lack of accurate algorithms: Existing studies have not considered the influence of the number of particles and particle size distribution (usually log-normal distribution) in the cluster on the polarization scattering characteristics. Existing models and calculation methods usually make simplified approximations - using the assumption that the particle size and number of clusters are consistent, ignoring the physical properties of the clusters, and lacking accurate algorithms for the polarization scattering characteristics of the number and particle size of monomer particles in the aluminum oxide clusters that obey the log-normal distribution. This limits the accuracy of the calculation, fails to fully utilize polarization scattering to obtain information such as cluster size and shape, and is difficult to accurately reflect the polarization scattering characteristics of aluminum oxide clusters in the tail flame, affecting the calculation of high-precision polarization radiation characteristics of the tail flame. 3) Ignoring phase changes: Existing studies mainly focus on a single phase of aluminum oxide (such as the alpha phase), and ignore the polarization scattering characteristics of other phases (such as liquid and gamma) of aluminum oxide clusters in the high-temperature and high-pressure tail flame. 4) Insufficient statistical average characteristics: Previous studies have ignored the statistical average polarization scattering characteristics of aluminum oxide clusters per unit volume, which reduces the practical application value of the theoretical model. Summary of the invention

[0006] In order to overcome the shortcomings of the above-mentioned prior art, the purpose of the present invention is to provide a method for calculating the ultraviolet polarization characteristics of cluster particles in a two-phase flow tail flame, by improving the model of a single cluster in the two-phase flow tail flame, calculating the ultraviolet polarization scattering characteristics of the two-phase flow clusters, the polarization scattering characteristics of the clusters under the phase change of aluminum oxide in the two-phase flow tail flame, and the statistical average polarization scattering characteristics of the clusters in the two-phase flow tail flame, the polarization detection accuracy of the two-phase flow tail flame is effectively improved, and multi-dimensional tail flame polarization radiation information is obtained, which provides theoretical support and reference basis for tail flame polarization detection and solid propellant research and development.

[0007] To achieve the above purpose, the technical solution adopted by the present invention is as follows:

[0008] A method for calculating ultraviolet statistical average polarization characteristics of clusters in a two-phase flow tail flame, the method comprising:

[0009] Step 1, modeling the clusters in the tail flame of the two-phase flow to obtain a cluster model, wherein the phase state of the cluster model includes a liquid state, an alpha phase state and a gamma phase state, and the cluster model includes N single clusters, where N is an integer greater than 1;

[0010] Step 2, initializing the complex refractive index of the cluster model of different phases in step 1;

[0011] Step 3, according to the complex refractive index obtained in step 2, combined with the multi-sphere scattering transmission matrix method, calculate the polarization scattering characteristics of the clusters in the tail flame of the two-phase flow in the ultraviolet band;

[0012] Step 4, statistically processing the polarization scattering characteristics of the clusters obtained in step 3 in the ultraviolet band to obtain the statistical average polarization scattering element of clusters with the same number of monomer particles and different monomer particle sizes;

[0013] Step 5, using the statistical average polarization scattering characteristics of clusters with the same number of monomer particles obtained in step 4, statistically average polarization characteristics of clusters with different numbers of monomer particles, to obtain the statistical average polarization scattering element of the clusters;

[0014] Step 6: Calculate the ultraviolet statistical average polarization radiation characteristics of the two-phase flow tail flame based on the statistical average polarization scattering elements of the clusters obtained in step 5 in combination with the spherical harmonic discrete ordinate method.

[0015] The specific process of step 1 is as follows:

[0016] Step 1.1, set the parameters of a single cluster:

[0017] The probability density distribution function of the number of monomer particles in a single cluster is expressed as:

[0018]

[0019] Among them, N s is the number of monomer particles, N g is the mean number of monomer particles, σ g is the standard deviation of the number of monomer particles;

[0020] According to the probability density distribution function of the number of monomer particles in a single cluster, the number of monomer particles contained in the cluster is discretized into N evenly spaced intervals, and the maximum number of monomer particles in a single cluster is N. s_max , that is, the number of monomer particles in a single cluster in the i-th distribution interval The corresponding probability is P n (N s,i );

[0021] The probability density distribution function of the radius of a single particle in a single cluster is expressed as:

[0022]

[0023] Among them, r g is the mean value of the radius of the monomer particles, σg is the standard deviation of the radius of the monomer particles;

[0024] Step 1.2, generating a single cluster structure according to the single cluster parameters set in step 1.1;

[0025] Step 1.3, determine the forward factor and fractal dimension of a single cluster, form a complete condensate structure of a single cluster, and obtain a single cluster model;

[0026] Step 1.4, repeat steps 1.1 to 1.3 to establish N single cluster models to obtain a cluster model.

[0027] The step 1.2 is specifically as follows:

[0028] Determine the radius of the monomer particle, and determine the radius of the monomer particle in each cluster condensation through probability statistical sampling;

[0029] Position setting: setting the position of the central particle of a single cluster;

[0030] Generate other monomer particles and their positions: randomly generate the orientation and walking step length of monomer particles. When the randomly walking monomer particles come into contact with a single cluster center particle, their positions are recorded and updated as new cluster cores.

[0031] Particle aggregation: Continue to randomly generate wandering monomer particles until the number of monomer particles in a single cluster reaches the initial set value;

[0032] Output the center position and radius information of each individual particle in a single cluster.

[0033] The polarization scattering characteristics of the clusters in the tail flame of the two-phase flow in the ultraviolet band in step 3 include:

[0034] The field outside the cluster is expressed as:

[0035]

[0036] Among them, E ext is the field outside the cluster, E inc is the incident field of the cluster, E sca is the scattered field of the cluster, i is the i-th ball in the cluster;

[0037] The incident field of the i-th ball in the cluster is expressed as:

[0038]

[0039] Among them, r i is relative to the common target origin (x i ,y i ,z i ), N mnprepresents the general vector spherical harmonics of degree m, order n, mode p = 1, L i Representation and size parameter (2πa i / λ,L i is the radius of a single sphere in the cluster), is the incident field coefficient;

[0040] When a plane wave is incident, the expansion coefficient of the incident field centered at the target origin is expressed as:

[0041]

[0042] in, is a generalized spherical function, PW is a plane wave, τ mmp , τ mnp is the intermediate amount;

[0043] The scattered field of the cluster is expressed as:

[0044]

[0045] in, is a specific polarization state, a mnp is the scattered field coefficient, J i-0 is the conventional VSWF translation matrix, is the polarization state, The incident field of

[0046] For incident polarizations parallel or perpendicular to the scattering plane, the expansion coefficient of the total scattered field is given by:

[0047]

[0048] in, is the scattered field coefficient corresponding to the two incident polarization states;

[0049] Using the outgoing vector spherical wave function in the far-field asymptotic form, the amplitude matrix element is obtained, which is expressed as follows:

[0050]

[0051] Where θ′ is the scattering angle;

[0052] Using the amplitude matrix elements, we get the scattering matrix elements. We assume the clusters to be macroscopically isotropic and mirror-symmetric media, simplify the elements in the scattering phase matrix, and make the scattering phase matrix present a block diagonal structure, which can be expressed as:

[0053]

[0054] Where Θ represents the angle between the incident direction and the scattering direction, F 11(θ) represents the change of linear polarized scattered light under different linear polarized light incident conditions, -F 12 (Θ) / F 11 (Θ) represents the ratio of the circular polarization in the scattered light to the initial linear polarization after the incident polarized light is scattered by the cluster, F 22 (Θ) / F 11 (Θ) represents the non-spherical nature of the cluster particles, F 34 (Θ) / F 11 (θ) represents the change in linear polarization in the scattered light when circular polarization is incident.

[0055] The step 4 is specifically as follows:

[0056] Using the scattering cross section as the weight function, the statistical average polarization scattering phase matrix elements of clusters with the same number of monomer particles are statistically calculated by the log-normal weighted average method. <F ab (θ,Ns)>:

[0057]

[0058] Among them, the values ​​of a and b are 11, 22, 33, 44, 12, 34, and F ab (θ,Ns,i) is the independent element in the scattering phase matrix of the ith cluster with Ns particles, σ sca (Ns,i) is the cluster scattering cross section, and m is the number of clusters with the same number of elementary particles Ns generated in the modeling.

[0059] The statistical average polarization scattering element of the cluster in step 5 is:

[0060]

[0061] Among them, <σ ext (Ns)>,<σ abs (Ns)>,<σ sca (Ns)> are the average extinction, absorption and scattering cross sections of the cluster, respectively.

[0062] A system for calculating ultraviolet statistical average polarization characteristics of clusters in a two-phase flow tail flame, comprising:

[0063] Cluster modeling module: Modeling clusters in the tail flame of the two-phase flow to obtain a cluster model, the phase state of the cluster model includes liquid, alpha phase and gamma phase, and the cluster model includes N single clusters, where N is an integer greater than 1;

[0064] Complex refractive index initialization module: initializes the complex refractive index of cluster models of different phases in the cluster modeling module;

[0065] Polarization scattering characteristic calculation module: Based on the complex refractive index obtained by the complex refractive index initialization module and combined with the multi-sphere scattering transmission matrix method, the polarization scattering characteristics of clusters in the tail flame of the two-phase flow in the ultraviolet band are calculated;

[0066] Module for calculating the statistical average polarization scattering element of the same number of monomer particles: statistically processing the polarization scattering characteristics of clusters in the ultraviolet band obtained by the polarization scattering characteristic calculation module to obtain the statistical average polarization scattering element of clusters with the same number of monomer particles and different monomer particle radii;

[0067] Statistical average polarization scattering element calculation module: using the statistical average polarization scattering characteristics of clusters with the same number of monomer particles obtained by the statistical average polarization scattering element calculation module with the same number of monomer particles, statistically average polarization characteristics of clusters with different numbers of monomer particles as a whole, and obtain the statistical average polarization scattering element of the clusters;

[0068] Ultraviolet statistical average polarization characteristic calculation module: Based on the statistical average polarization scattering elements of the clusters obtained by the statistical average polarization scattering element calculation module, the ultraviolet statistical average polarization radiation characteristics of the two-phase flow tail flame are calculated in combination with the spherical harmonic discrete coordinate method.

[0069] An electronic device, comprising:

[0070] at least one processor;

[0071] and, a memory communicatively coupled to the at least one processor;

[0072] 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 any of the above-described methods for calculating the ultraviolet statistical average polarization characteristics of clusters in the tail flame of a two-phase flow.

[0073] A computer-readable storage medium stores a computer program. When the computer program is executed by a processor, the method for calculating the ultraviolet statistical average polarization characteristics of clusters in a two-phase flow tail flame described in any one of the above items is implemented.

[0074] Compared with the prior art, the beneficial effects of the present invention are:

[0075] 1. The present invention takes into account the influence of the actual structural morphology of aluminum oxide clusters in the tail flame of two-phase flow on the polarization characteristics, and proposes a more sophisticated modeling method of aluminum oxide clusters, rather than simply approximating them as single spherical particles in the traditional method, so as to more realistically reflect the structural characteristics of aluminum oxide clusters in two-phase flow.

[0076] 2. The present invention comprehensively considers the influence of the number of monomer particles and particle size distribution in aluminum oxide clusters on the polarization scattering characteristics of aluminum oxide clusters. Compared with the traditional method that only considers the number and particle size of single monomer particles, the present invention can more accurately calculate the polarization scattering characteristics of aluminum oxide clusters in two-phase flow.

[0077] 3. The present invention considers the phase change of aluminum oxide in the tail flame of two-phase flow in a high temperature and high pressure complex environment, and combines the change of the corresponding complex refractive index to give the polarization scattering characteristics of alpha, gamma phase and liquid aluminum oxide clusters. At the same time, the present invention is also suitable for the analysis of polarization scattering characteristics of carbon black clusters in the tail flame.

[0078] 4. The present invention takes into account the problem that it takes a long time to calculate the polarization scattering characteristics of a large number of aluminum oxide clusters. By establishing an algorithm based on statistical methods, the statistical average polarization characteristics of aluminum oxide clusters in the tail flame of the two-phase flow can be effectively calculated, thereby improving the calculation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Figure 1 The present invention is a flow chart of the method.

[0080] Figure 2 Schematic diagram of the aluminum oxide cluster particle model with different numbers of elementary particles and particle sizes obeying log-normal distribution in the present invention, wherein (1)-(3)N s =5, (4)-(6)N s =10, (7)-(9)N s =20.

[0081] Figure 3 This is a schematic diagram of the scattering of a plane wave incident on cluster particles in the present invention.

[0082] Figure 4 The figure shows the influence of the number of liquid alumina cluster monomer particles in the tail flame of the two-phase flow on the polarization scattering characteristics in the present invention, wherein (a) is the change in polarization degree of the incident polarized light after passing through the cluster particles; (b) is the non-spherical property of the cluster; and (c) is the change in linear polarization in the scattered light when circularly polarized light is incident.

[0083] Figure 5 The graphs are the statistical average scattering phase function and the statistical average polarization degree curves in different phases when the number of particles and the radius in the aluminum oxide clusters in the present invention obey the log-normal distribution, wherein (a) is the alpha phase; (b) is the gamma phase; and (c) is the liquid state. DETAILED DESCRIPTION

[0084] The technical solution of the present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0085] A method for calculating the ultraviolet statistical average polarization characteristics of clusters in the tail flame of a two-phase flow, such as Figure 1 As shown, the method includes:

[0086] Step 1, modeling the clusters in the tail flame of the two-phase flow to obtain a cluster model, wherein the phase state of the cluster model includes a liquid state, an alpha phase state and a gamma phase state, and the cluster model includes N single clusters, where N is an integer greater than 1;

[0087] The present invention improves the diffusion limited aggregation (DLA) model and introduces the particle size distribution function and the monomer number distribution function. The specific improved aluminum oxide cluster model generation process in the tail flame of the two-phase flow is as follows:

[0088] Step 1.1, set the parameters of a single cluster:

[0089] The number of monomer particles in a single cluster N s The probability density distribution function satisfied is expressed as:

[0090]

[0091] Among them, N s is the number of monomer particles, N g is the mean number of monomer particles, σ g is the standard deviation of the number of monomer particles;

[0092] According to the probability density distribution function of the number of monomer particles in a single cluster, the number of monomer particles contained in the cluster is discretized into N evenly spaced intervals, and the maximum number of monomer particles in a single cluster is N. s_max , that is, the number of monomer particles in a single cluster in the i-th distribution interval The corresponding probability is P n (N s,i );

[0093] The radius of monomer particles in a single cluster follows a log-normal distribution, and its probability density distribution function is expressed as:

[0094]

[0095] Among them, r g is the mean value of the radius of the monomer particles, σ g is the standard deviation of the radius of the monomer particles;

[0096] Step 1.2, generate a single cluster structure according to the single cluster parameters set in step 1.1:

[0097] Determine the radius of the monomer particle, and determine the radius of the monomer particle in each cluster condensation through probability statistical sampling;

[0098] Position setting: setting the position of the central particle of a single cluster;

[0099] Generate other monomer particles and their positions: randomly generate the orientation and walking step length of monomer particles. When the randomly walking monomer particles come into contact with a single cluster center particle, their positions are recorded and updated as new cluster cores.

[0100] Particle aggregation: Continue to randomly generate wandering monomer particles until the number of monomer particles in a single cluster reaches the initial set value;

[0101] Output the center position and radius information of each individual particle in a single cluster.

[0102] Step 1.3, determine the forward factor and fractal dimension of a single cluster, form a complete condensate structure of a single cluster, and obtain a single cluster model;

[0103] In the tail of gas-solid two-phase flow, the forward factor k of the cluster f =1.2, fractal dimension D f =1.75. Figure 2 The schematic diagram of the structure of the aluminum oxide cluster model with different monomer numbers in the present invention, wherein the number of monomer particles in the aluminum oxide cluster follows the mean value N g is 10, standard deviation σ g The lognormal distribution is 1.5, and the radius follows the mean r g is 100nm, standard deviation σ g is a lognormal distribution with a p of 1.5.

[0104] Step 1.4, repeat steps 1.1 to 1.3 to establish N single cluster models to obtain a cluster model.

[0105] Step 2, initializing the complex refractive index of the aluminum oxide cluster model in different phases in step 1;

[0106] The complex refractive index of aluminum oxide is expressed as The complex refractive index of gamma-Al2O3 is taken from Anfimov N.A.'s study on the optical property model of Al2O3, and the formula is as follows:

[0107]

[0108] k r =k0+k1+k2+k3

[0109] Among them, k0, k1, k2, k3 represent the absorption of vibration band, free electron transition, edge band and Urbach band respectively. The detailed calculation formula is as follows:

[0110]

[0111] in, Available temperature range 1800K≤T≤3500K.

[0112] The complex refractive index of alpha phase aluminum oxide is taken from the research of Querry et al., and the data is provided in a tabular form. The complex refractive index of liquid aluminum oxide, Kuzmin VA et al. proposed the complex refractive index equation of liquid aluminum oxide:

[0113] n r =1.747+0.0066·λ-0.0068·λ 2 +0.00003·T

[0114] lgk r =-2.19+0.089·λ 0.95 -0.00056·(3200-T)λ -0.45

[0115] Step 3: According to the position and radius information of the cluster particles obtained in step 1, a coordinate system is established, such as Figure 3 In this coordinate system, any position on the cluster is set as the coordinate origin O, and the direction of the incident wave is determined as the positive direction of the z axis. Figure 3 The red emission direction is the scattering direction. The scattering angle and azimuth of the scattering direction in the spherical coordinate system are denoted by θ and According to the complex refractive index of the aluminum oxide clusters in different phases obtained in step 2, combined with the multi-sphere scattering transmission matrix method, the polarization scattering characteristics of the aluminum oxide clusters in the tail flame of the two-phase flow in the ultraviolet band are calculated;

[0116] Specifically:

[0117] The field outside the cluster is represented by the superposition of the incident field and the scattered field. The scattered field is composed of the components radiated by each single sphere in the cluster and is expressed as:

[0118]

[0119] Among them, E ext is the field outside the cluster, E inc is the incident field of the cluster, E sca is the scattered field of the cluster, i is the i-th ball in the cluster;

[0120] The incident field of the i-th sphere in the cluster can be expanded by a spherical vector wave function (VSWF) centered at its own origin, expressed as:

[0121]

[0122] Among them, r i is relative to the common target origin (x i,y i ,z i ), N mnp represents the general vector spherical harmonics of degree m, order n, mode p = 1, L i Representation and size parameter (2πa i / λ,L i is the radius of a single sphere in the cluster), is the incident field coefficient;

[0123] When a plane wave (PW) is incident, the incident field expansion coefficient centered at the target origin is expressed as:

[0124]

[0125] in, is a generalized spherical function, PW is a plane wave, τ mmp , τ mnp is the intermediate amount;

[0126] Similarly, the scattering field of the cluster can also be expanded using an outward spherical vector wave function centered at the target origin. The scattering field of the cluster is expressed as:

[0127]

[0128] in, is a specific polarization state, a mnp is the scattered field coefficient, J i-0 is the conventional VSWF translation matrix, is the polarization state, The incident field of

[0129] For incident polarizations parallel or perpendicular to the scattering plane, the expansion coefficient of the total scattered field is given by:

[0130]

[0131] in, is the scattered field coefficient corresponding to the two incident polarization states;

[0132] Using the outgoing vector spherical wave function in the far-field asymptotic form, the amplitude matrix element is obtained, which is expressed as follows:

[0133]

[0134] Where θ′ is the scattering angle;

[0135] The amplitude matrix elements are used to obtain the scattering matrix elements. For the aluminum oxide cluster model in the present invention, the clusters are assumed to be macroscopically isotropic and mirror-symmetrical media, and the elements in the scattering phase matrix are simplified so that the scattering phase matrix presents a block diagonal structure, which is expressed as:

[0136]

[0137] Where Θ represents the angle between the incident direction and the scattering direction, F 11 (θ) represents the change of linear polarized scattered light under different linear polarized light incident conditions, such as Figure 4 As shown, Figure 4 (a), -F 12 (Θ) / F 11 (Θ) represents the ratio of the circular polarization in the scattered light to the initial linear polarization after the incident polarized light is scattered by the cluster; Figure 4 In (b), F 22 (Θ) / F 11 (θ) represents the non-spherical nature of the cluster particles of the present invention; Figure 4 (c) In 34 (Θ) / F 11 (θ) represents the change in linear polarization in the scattered light when circular polarization is incident.

[0138] Step 4, statistically processing the polarization scattering characteristics of the clusters obtained in step 3 in the ultraviolet band to obtain the statistical average polarization scattering element of clusters with the same number of monomer particles;

[0139] Specifically:

[0140] Using the scattering cross section as the weight function, the statistical average polarization scattering phase matrix elements of aluminum oxide clusters with the same number of monomer particles are statistically calculated by the log-normal weighted average method. <F ab (θ,Ns)>:

[0141]

[0142] Among them, the values ​​of a and b are 11, 22, 33, 44, 12, 34, and F ab (θ,Ns,i) is the independent element in the scattering phase matrix of the ith cluster with Ns particles, σ sca (Ns,i) is the cluster scattering cross section, and m is the number of clusters with the same number of elementary particles Ns generated in the modeling.

[0143] Step 5, using the statistical average polarization scattering characteristics of clusters with the same number of monomer particles obtained in step 4, statistically analyzing the average polarization characteristics of clusters with different numbers of monomer particles, and obtaining the statistical average polarization scattering element of aluminum oxide clusters whose monomer numbers and particle sizes obey log-normal distribution;

[0144] Specifically:

[0145] The statistical average polarization scattering element of the cluster is:

[0146]

[0147] Among them, <σ ext (Ns)>,<σ abs (Ns)>,<σ sca (Ns)> are the average extinction, absorption and scattering cross sections of Al2O3 clusters whose monomer number and particle size obey log-normal distribution, respectively.

[0148] Step 6, according to the statistical average polarization scattering elements of the clusters obtained in step 5, the ultraviolet statistical average polarization characteristics of the clusters in the tail flame of the two-phase flow are calculated in combination with the spherical harmonic discrete ordinate method.

[0149] A system for calculating ultraviolet statistical average polarization characteristics of clusters in a two-phase flow tail flame, comprising:

[0150] Cluster modeling module: Modeling clusters in the tail flame of the two-phase flow to obtain a cluster model, the phase state of the cluster model includes liquid, alpha phase and gamma phase, and the cluster model includes N single clusters, where N is an integer greater than 1;

[0151] Complex refractive index initialization module: initializes the complex refractive index of cluster models of different phases in the cluster modeling module;

[0152] Polarization scattering characteristic calculation module: Based on the complex refractive index obtained by the complex refractive index initialization module and combined with the multi-sphere scattering transmission matrix method, the polarization scattering characteristics of clusters in the tail flame of the two-phase flow in the ultraviolet band are calculated;

[0153] Module for calculating the statistical average polarization scattering element of the same number of monomer particles: statistically process the polarization scattering characteristics of the clusters in the ultraviolet band obtained by the polarization scattering characteristic calculation module to obtain the statistical average polarization scattering element of clusters with the same number of monomer particles and different monomer particle sizes;

[0154] Statistical average polarization scattering element calculation module: using the statistical average polarization scattering characteristics of clusters with the same number of monomer particles obtained by the statistical average polarization scattering element calculation module with the same number of monomer particles, statistically average polarization characteristics of clusters with different numbers of monomer particles as a whole, and obtain the statistical average polarization scattering element of the clusters;

[0155] Ultraviolet statistical average polarization characteristic calculation module: Based on the statistical average polarization scattering elements of the clusters obtained by the statistical average polarization scattering element calculation module, the ultraviolet statistical average polarization radiation characteristics of the two-phase flow tail flame are calculated in combination with the spherical harmonic discrete coordinate method.

[0156] An electronic device, comprising:

[0157] at least one processor;

[0158] and, a memory communicatively coupled to the at least one processor;

[0159] 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 any of the above-described methods for calculating the ultraviolet statistical average polarization characteristics of clusters in the tail flame of a two-phase flow.

[0160] A computer-readable storage medium stores a computer program, characterized in that when the computer program is executed by a processor, it implements the method for calculating the ultraviolet statistical average polarization characteristics of clusters in a two-phase flow tail flame as described in any one of the above items.

[0161] In summary, the present invention provides a refined modeling technology for aluminum oxide clusters in the calculation of ultraviolet polarized radiation of a two-phase flow tail flame, and establishes a statistical average polarization scattering characteristic calculation model for the ultraviolet band. The model takes into account the influence of the actual structural morphology of aluminum oxide clusters in the tail flame of the two-phase flow on the polarization scattering characteristics, and increases the change of the number of monomers and particle size in the aluminum oxide clusters following the logarithmic normal distribution on the polarization scattering characteristics. At the same time, the present invention also considers the influence of the phase change of aluminum oxide clusters in the tail flame on its polarization scattering characteristics. Compared with the traditional method that only considers the single particle, radius and single alpha phase of aluminum oxide in the tail flame of the two-phase flow, the aluminum oxide cluster model of the present invention is closer to the structure of aluminum oxide clusters in the actual tail flame, and can provide more comprehensive polarization information of aluminum oxide clusters in the tail flame. Using the model of the present invention can not only improve the accuracy of the calculation of the polarization radiation characteristics of the tail flame, but also provide theoretical support for the ultraviolet detection and early warning system of hypersonic aircraft. Therefore, the present invention has important practical significance in improving system performance, optimizing design and realizing efficient detection.

[0162] In summary, the present invention proposes a refined modeling technology for aluminum oxide clusters in the tail flame of a two-phase flow, and establishes a statistical average polarization scattering characteristic calculation model for the ultraviolet band. Compared with the prior art, the main advantages of the present invention are: 1) The present invention considers the influence of the actual structural morphology of the clusters on the polarization scattering characteristics by finely modeling the aluminum oxide clusters in the tail flame of a two-phase flow. Unlike the traditional method of simplifying the aluminum oxide clusters into a single spherical particle, the present invention provides a more realistic cluster structure model. 2) The present invention introduces the number of monomers and the particle size to obey the log-normal distribution in the modeling of aluminum oxide clusters, so that the model more accurately reflects the polarization scattering characteristics of the clusters in the tail flame, and improves the accuracy of the calculation. 3) The present invention takes into account the phase changes of aluminum oxide clusters in the tail flame (such as liquid, alpha phase and gamma phase), which enables the present invention to provide more accurate predictions of polarization scattering characteristics under various environmental conditions. 4) The present invention solves the time-consuming problem of calculating the polarization scattering characteristics of a large number of aluminum oxide clusters in the tail flame. By using statistical methods to establish a statistical average polarization characteristic calculation algorithm for cluster clouds, the calculation efficiency is significantly improved, and larger-scale calculation tasks can be processed. 5) The present invention is not only applicable to aluminum oxide clusters, but can also be used to calculate the polarization average scattering characteristics of carbon black clusters in the tail flame, which expands the application scope of the technology and improves its versatility.

[0163] In summary, the present invention has significant advantages over traditional methods in terms of refined modeling, consideration of structural characteristics and distribution characteristics, increasing phase changes, improving calculation efficiency and expanding the scope of application, and can provide more accurate calculation results of the ultraviolet polarization scattering characteristics of clusters in the tail flame. These improvements make the present invention not only of great significance in theoretical research, but also provide strong support for tail flame polarization detection and related fields in practical applications.

[0164] Those skilled in the art will appreciate that the above embodiments are specific embodiments for implementing the present application, and 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 calculating the ultraviolet statistical average polarization characteristics of clusters in a two-phase flow tail flame, characterized in that: The method comprises: Step 1, modeling the aluminum oxide clusters in the tail flame of the two-phase flow to obtain a cluster model, wherein the phase state of the cluster model includes a liquid state, an alpha phase state and a gamma phase state, and the cluster model includes N single clusters, where N is an integer greater than 1; Step 2, initializing the complex refractive index of the cluster model of different phases in step 1; Step 3, according to the complex refractive index obtained in step 2, combined with the multi-sphere scattering transmission matrix method, calculate the polarization scattering characteristics of the clusters in the tail flame of the two-phase flow in the ultraviolet band; Step 4, statistically processing the polarization scattering characteristics of the clusters obtained in step 3 in the ultraviolet band to obtain the statistical average polarization scattering element of the clusters having the same number of monomer particles but a particle size distribution obeying a log-normal distribution; Step 5, using the statistical average polarization scattering characteristics of clusters with the same number of monomer particles obtained in step 4, statistically average polarization characteristics of clusters with different numbers of monomer particles, to obtain the statistical average polarization scattering element of the clusters; Step 6: Calculate the ultraviolet statistical average polarization radiation characteristics of the two-phase flow tail flame based on the statistical average polarization scattering elements of the clusters obtained in step 5 in combination with the spherical harmonic discrete ordinate method.

2. The method for calculating the ultraviolet statistical average polarization characteristics of clusters in a two-phase flow tail flame according to claim 1, characterized in that: The specific process of step 1 is as follows: Step 1.1, set the parameters of a single cluster: The probability density distribution function of the number of monomer particles in a single cluster is expressed as: Among them, N s is the number of monomer particles, N g is the mean number of monomer particles, σ g is the standard deviation of the number of monomer particles; According to the probability density distribution function of the number of monomer particles in a single cluster, the number of monomer particles contained in the cluster is discretized into N evenly spaced intervals, and the maximum number of monomer particles in a single cluster is N. s_max , that is, the number of monomer particles in a single cluster in the i-th distribution interval The corresponding probability is P n (N s,i ); The probability density distribution function of the radius of a single particle in a single cluster is expressed as: Among them, r g is the mean value of the radius of the monomer particles, σ g is the standard deviation of the radius of the monomer particles; Step 1.2, generating a single cluster structure according to the single cluster parameters set in step 1.1; Step 1.3, determine the forward factor and fractal dimension of a single cluster, form a complete condensate structure of a single cluster, and obtain a single cluster model; Step 1.4, repeat steps 1.1 to 1.3 to establish N single cluster models to obtain a cluster model.

3. The method for calculating the ultraviolet statistical average polarization characteristics of clusters in a two-phase flow tail flame according to claim 2, characterized in that: The step 1.2 is specifically as follows: Determine the radius of the monomer particle: Determine the radius of the monomer particle in each cluster condensation through probability statistical sampling; Position setting: set the position of the central particle of a single cluster; Generate other monomer particles and their positions: randomly generate the orientation and walking step length of monomer particles. When the randomly walking monomer particles come into contact with a single cluster center particle, their positions are recorded and updated as new cluster cores. Particle aggregation: Continue to randomly generate wandering monomer particles until the number of monomer particles in a single cluster reaches the initial set value; Output the center position and radius information of each individual particle in a single cluster.

4. The method for calculating the ultraviolet statistical average polarization characteristics of clusters in a two-phase flow tail flame according to claim 3 is characterized in that: The polarization scattering characteristics of the clusters in the tail flame of the two-phase flow in the ultraviolet band in step 3 include: The field outside the cluster is expressed as: Among them, E ext is the field outside the cluster, E inc is the incident field of the cluster, E sca is the scattered field of the cluster, i is the i-th ball in the cluster; The incident field of the i-th ball in the cluster is expressed as: Among them, r i is relative to the common target origin (x i ,y i ,z i ), N mnp represents the general vector spherical harmonics of degree m, order n, mode p = 1, L i Representation and size parameter (2πa i / λ,L i is the radius of a single sphere in the cluster), is the incident field coefficient; When a plane wave is incident, the expansion coefficient of the incident field centered at the target origin is expressed as: in, is a generalized spherical function, PW is a plane wave, τ mmp , τ mnp is the intermediate amount; The scattered field of the cluster is expressed as: in, is a specific polarization state, a mnp is the scattered field coefficient, J i-0 is the conventional VSWF translation matrix, is the polarization state, The incident field of For incident polarizations parallel or perpendicular to the scattering plane, the expansion coefficient of the total scattered field is given by: in, is the scattered field coefficient corresponding to the two incident polarization states, calculated based on the complex refractive index; Using the outgoing vector spherical wave function in the far-field asymptotic form, the amplitude matrix element is obtained, which is expressed as follows: Where θ′ is the scattering angle; Using the amplitude matrix elements, we get the scattering matrix elements. We assume the clusters to be macroscopically isotropic and mirror-symmetric media, simplify the elements in the scattering phase matrix, and make the scattering phase matrix present a block diagonal structure, which can be expressed as: Where Θ represents the angle between the incident direction and the scattering direction, F 11 (θ) represents the change of linear polarized scattered light under different linear polarized light incident conditions, -F 12 (Θ) / F 11 (Θ) represents the ratio of the circular polarization in the scattered light to the initial linear polarization after the incident polarized light is scattered by the cluster, F 22 (Θ) / F 11 (Θ) represents the non-spherical nature of the cluster particles, F 34 (Θ) / F 11 (θ) represents the change in linear polarization in the scattered light when circular polarization is incident.

5. The method for calculating the ultraviolet statistical average polarization characteristics of clusters in a two-phase flow tail flame according to claim 4, characterized in that: The step 4 is specifically as follows: Using the scattering cross section as the weight function, the statistical average polarization scattering phase matrix elements of clusters with the same number of monomer particles are statistically calculated by the log-normal weighted average method. <F ab (θ,Ns)>: Among them, the values ​​of a and b are 11, 22, 33, 44, 12, 34, and F ab (θ,Ns,i) is the independent element in the scattering phase matrix of the ith cluster with Ns particles, σ sca (Ns,i) is the cluster scattering cross section, and m is the number of clusters with the same number of elementary particles Ns generated in the modeling.

6. The method for calculating the ultraviolet statistical average polarization characteristics of clusters in a two-phase flow tail flame according to claim 5, characterized in that: The statistical average polarization scattering element of the cluster in step 5 is: Among them, <σ ext (Ns)>,<σ abs (Ns)>,<σ sca (Ns)> are the average extinction, absorption and scattering cross sections of the cluster, respectively.

7. A system for calculating the ultraviolet statistical average polarization characteristics of clusters in a two-phase flow tail flame, characterized in that: include: Cluster modeling module: Modeling clusters in the tail flame of the two-phase flow to obtain a cluster model, the phase state of the cluster model includes liquid, alpha phase and gamma phase, and the cluster model includes N single clusters, where N is an integer greater than 1; Complex refractive index initialization module: initializes the complex refractive index of cluster models of different phases in the cluster modeling module; Polarization scattering characteristic calculation module: Based on the complex refractive index obtained by the complex refractive index initialization module and combined with the multi-sphere scattering transmission matrix method, the polarization scattering characteristics of clusters in the tail flame of the two-phase flow in the ultraviolet band are calculated; Module for calculating the statistical average polarization scattering element of the same number of monomer particles: Statistically process the polarization scattering characteristics of clusters in the ultraviolet band obtained by the polarization scattering characteristic calculation module to obtain the statistical average polarization scattering element of clusters with the same number of monomer particles and monomer radius obeying logarithmic normal distribution; Statistical average polarization scattering element calculation module: using the statistical average polarization scattering characteristics of clusters with the same number of monomer particles obtained by the statistical average polarization scattering element calculation module with the same number of monomer particles, statistically average polarization characteristics of clusters with different numbers of monomer particles as a whole, and obtain the statistical average polarization scattering element of the clusters; Ultraviolet statistical average polarization characteristic calculation module: Based on the statistical average polarization scattering elements of the clusters obtained by the statistical average polarization scattering element calculation module, the ultraviolet statistical average polarization radiation characteristics of the two-phase flow tail flame are calculated in combination with the spherical harmonic discrete coordinate method.

8. An electronic device, characterized in that: include: at least one processor; and, a memory communicatively coupled to the at least one processor; Wherein, 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 a method for calculating the ultraviolet statistical average polarization characteristics of clusters in a two-phase flow tail flame as described in any one of claims 1 to 6.

9. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, a method for calculating ultraviolet statistical average polarization characteristics of clusters in a two-phase flow tail flame according to any one of claims 1 to 6 is implemented.

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