Modeling method of shock wave light field in hypersonic flow field

Abstract

The invention belongs to the field of numerical simulation, and particularly relates to a modeling method for a shock wave light field in a hypersonic flow field, which comprises the following steps: carrying out gradient clustering on flow field data by adopting an unsupervised learning algorithm, and determining the position of a shock wave in a flow field domain and the inner and outer boundaries of a shock wave domain; constructing a mixed dimension numerical value continuity and discretization strategy, determining the main direction of the light based on the strategy, performing continuous medium approximation processing on the main direction of the light, and performing structured grid discretization processing on the non-main direction of the light; on the basis of the analogy of the Fermat principle and the Mopedor principle, transmission of light in a refractive index field is analogous to movement of equivalent physical particles in a refractive index potential energy field, and a dynamic relation between the equivalent physical particles and the refractive index potential energy field is established; based on the dynamic relationship, the transmission path of light in the shock wave is simulated, and modeling of the shock wave light field in the hypersonic flow field is achieved. According to the method, the modeling efficiency and precision of the shock wave light field of the hypersonic flow field are remarkably improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of numerical simulation, and particularly relates to a modeling method of a shock wave light field in a hypersonic flow field. BACKGROUND

[0002] With the rapid development of aircraft technology, the flight speed has been increased from subsonic speed to hypersonic speed range. In the hypersonic flight state, the flow field around the aircraft presents strong space-time dynamic characteristics, resulting in deflection and high-frequency jitter of the light beam passing through the flow field, and further causing imaging blur and jitter, i.e. aerodynamic optical effect.

[0003] In order to study the aerodynamic optical effect, a traditional wind tunnel experiment method is adopted, but this method is high in cost and difficult to flexibly adjust space-time parameters. Therefore, a numerical simulation method becomes an important means for studying the light field transmission behavior in the hypersonic flow field.

[0004] In the prior art, an algorithm based on light ray tracing is widely applied to light field modeling. This kind of method solves the light ray equation by using a high-order Runge-Kutta method, and needs to repeatedly interpolate the flow field data and its density gradient, so that the calculation resource consumption is large and the efficiency is low. Especially in the hypersonic flow field, in order to ensure the space-time resolution, the computational fluid dynamics simulation needs to adopt a nanosecond-level time step, resulting in a huge amount of data, and the traditional light ray tracing method cannot meet the real-time and high-efficiency requirements of dynamic light field modeling.

[0005] In addition, although high-precision flow field simulation can generate ten million grid data, not all flow field regions have a significant influence on optical transmission. Among them, the shock wave region plays a leading role in light ray deflection. If light ray tracing is performed point by point in the entire flow field, a large amount of redundant calculation will be caused, and fast modeling of the light field cannot be realized.

[0006] Therefore, there is an urgent need for a method capable of efficiently and accurately modeling the light field in the shock wave region in the hypersonic flow field to overcome the shortcomings of the prior art. SUMMARY

[0007] Therefore, the present application aims to provide a modeling method of a shock wave light field in a hypersonic flow field, which can efficiently and accurately model the light field in the shock wave region in the hypersonic flow field to overcome the shortcomings of the prior art.

[0008] To achieve the above-mentioned purpose, the technical scheme of the present application is as follows: A modeling method of a shock wave light field in a hypersonic flow field, comprising the following steps: S1: using an unsupervised learning algorithm to perform gradient clustering on the flow field data, determining the position of the shock wave in the flow field domain, the inner and outer boundaries of the shock wave domain, and obtaining the inner and outer boundaries of the shock wave domain and the spatial distribution analytical expression of the shock wave by numerical fitting; S2: Construct a mixed-dimension numerical continuous and discrete strategy, determine the main direction of the light ray based on the strategy, implement continuous medium approximation processing on the main direction of the light ray, and implement structured grid discrete processing on the non-main direction of the light ray; S3: Based on the analogy of Fermat's principle and the Mopedy principle under the condition of energy conservation, the transmission of light in the refractive index field is analogous to the motion of equivalent real particles in the refractive index potential field, thereby establishing the dynamic relationship between the equivalent real particles and the refractive index potential field; S4: Based on the dynamic relationship between the equivalent real particles and the refractive index potential field, the straight line equation of the light ray and the spatial distribution analytical expression of the inner boundary of the shock domain are solved simultaneously to simulate the transmission path of the light in the shock, and the modeling of the shock light field in the hypersonic flow field is realized.

[0009] Further, in step S1, the specific process of gradient clustering of flow field data by using an unsupervised learning algorithm is as follows: S11: Abstract and simplify the flow field data into a one-dimensional data set; wherein the flow field data is composed of node coordinates and flow field attribute data, and the node position is constant; S12: Randomly select two nodes in the flow field data as initial centroids, calculate the density value of each node in the flow field data and the Euclidean distance between the two initial centroids, and according to the size of the Euclidean distance, classify the density value of each node into the cluster corresponding to the nearest initial centroid; S13: Recalculate the new centroid of each cluster to replace the old centroid, and repeat steps S11 and S12 until the centroid and cluster assignment converge and no longer change, and the flow field domain is divided into a far field and a near field; S14: Take the demarcation between the far field and the near field as the outer boundary of the shock domain, perform a downward translation operation on the outer boundary of the shock domain, and when the refractive index gradient reaches a peak value, take the position of the peak value as the position of the shock; S15: Select a node in the outer boundary of the shock domain symmetric to the position of the shock as the inner boundary of the shock domain.

[0010] Further, in step S2, the determination method of the main direction of the light ray is as follows: In a two-dimensional flow field, compare the angles between the light ray and the x-axis, y-axis, select the coordinate axis with the smallest angle as the main direction of the light ray; In a three-dimensional flow field, compare the angles between the light ray and the x-axis, y-axis, z-axis, select the coordinate axis with the smallest angle as the main direction of the light ray.

[0011] Further, in step S2, the specific process of implementing continuous medium approximation processing on the main direction of the light ray is as follows: Along the principal direction of the light ray, select a point on the outer boundary, the shock wave, and the inner boundary of the shock domain. Construct a polynomial equation about the principal direction coordinates based on the coordinates of the three points and the refractive index values. Solve the polynomial equation using Cramer's rule to obtain the analytical expression for the continuous distribution of the refractive index of the shock domain along the principal direction of the light ray, thus achieving the approximate treatment of the continuous medium along the principal direction of the light ray.

[0012] Furthermore, in step S2, the specific process of performing structured mesh discretization on the non-principal directions of the light rays is as follows: In a two-dimensional flow field, the non-principal direction of light rays is divided into equally spaced tiny intervals, and the flow field within a single tiny interval remains continuous in the principal direction of light rays; In a three-dimensional flow field, the non-principal direction of light rays is divided into tiny units of equal size, and the flow field within a single tiny unit remains continuous in the principal direction of light rays.

[0013] Furthermore, in step S3, the specific process of establishing the dynamic relationship between the equivalent physical particle and the refractive index potential energy field is as follows: The variational form of Fermat's principle is: ; in, For refractive index, For the path of light; The Moperdu principle under the condition of energy conservation is: ; in, For light-meaning momentum, Generalized coordinates; By drawing an analogy between Fermat's principle and the Mauper-Duchy principle under the condition of energy conservation, the transmission of light in a refractive index field can be likened to the motion of an equivalent material particle in a refractive index potential energy field. If the mass of the equivalent material particle is set to 1, the established dynamic relationship between the equivalent material particle and the refractive index potential energy field is as follows: ; in, It represents the speed of the equivalent physical particle.

[0014] Furthermore, in step S4, let the refractive index of the initial intersection point be... The specific process of simulating the propagation path of light in the shock wave domain is as follows: If the flow field is a two-dimensional flow field and the principal direction of the light ray is the y-axis, the velocity component expressions of the equivalent physical particle in the principal and non-principal directions of the light ray are obtained based on the dynamic relationship between the equivalent physical particle and the refractive index potential energy field: ; ; in, For the equivalent physical particle, the velocity component in the non-principal direction of the light ray. This represents the velocity component of an equivalent material particle along the principal direction of light. The refractive index distribution along the principal direction of light rays in a two-dimensional flow field. Let be the angle between the light rays at the initial intersection point and the x-axis; The derivation of the velocity component expressions for the equivalent material particle in the principal and non-principal directions of light leads to the differential expression for the position of the equivalent material particle: ; Integrating both sides of the differential expression for the position of the equivalent material particle yields the position expression: ; When the equivalent physical particle passes through a tiny gap in the non-principal direction of the light, update the refractive index n in that tiny gap, and calculate the trajectory of the equivalent physical particle in that tiny gap based on the updated refractive index n. If the flow field is a three-dimensional flow field and the principal direction of the light ray is the y-axis, based on the dynamic relationship between the equivalent material particle and the refractive index potential energy field, the expressions for the velocity components of the equivalent material particle in the non-principal direction plane and the principal direction of the optical path are obtained as follows: ; ; in, These are the velocity components of the equivalent material particle in the xz plane. This represents the velocity component of an equivalent material particle along the principal direction of light. The refractive index distribution along the principal direction of light rays in a three-dimensional flow field. Let be the angle between the light rays at the initial intersection point and the xz plane; Based on the expressions for the velocity components of the equivalent particle in the xz plane and the y-axis, the differential expression for the position of the equivalent particle is derived: ; in, This is the projection of the equivalent material particle onto the xz plane; Integrating both sides of the differential expression for the position of the equivalent material particle yields the position expression: ; When the equivalent physical particle passes through a tiny unit in a non-principal direction of the light, the refractive index n in that tiny unit is updated, and the trajectory of the equivalent physical particle in that tiny unit is calculated based on the updated refractive index n.

[0015] Furthermore, in step S4, the specific process of solving for the initial intersection point of the ray and the shock domain by simultaneously solving the linear equation of the ray and the spatial distribution analytical expression of the boundary within the shock domain is as follows: In a two-dimensional flow field, the equation of a straight ray is transformed into... The spatial distribution analytical expression of the inner boundary of the shock domain is transformed into... Combining the two equations, we obtain the initial intersection point of the light ray propagating in a straight line with the inner boundary of the shock wave domain: ; In a three-dimensional flow field, the equation of a straight ray is transformed into... The spatial distribution analytical expression of the inner boundary of the shock domain is transformed into... Combining the two, we can obtain the initial intersection point of the light ray propagating in a straight line with the inner boundary of the shock wave domain: .

[0016] Furthermore, in step S4, the specific process of modeling the shock wave optical field in the hypersonic flow field is as follows: Calculate the optical path length of each ray. The calculation formula is: ; in, s i The distance the light travels in each tracking step. n i The refractive index for each tracking step; Calculate the optical path difference for each ray based on its optical path length. The calculation formula is: ; in, For all The average value; Based on the optical path difference of each ray Calculate wavefront aberrations The calculation formula is: ; in, k = 2π / λ , λ The wavelength of light; Based on wavefront aberration Calculate the actual pupil function The calculation formula is: ; in, For the ideal pupil function, Indicates the phase perturbation factor; Based on the actual pupil function Calculate the complex amplitude function The calculation formula is: ; Based on complex amplitude function Calculate the point spread function The calculation formula is: ; in, yes The complex conjugate; Based on point spread function Calculate the optical transfer function The calculation formula is: ; Based on optical transfer function Calculate the modulation transfer function The calculation formula is: .

[0017] Furthermore, multiple light rays are simulated in the shock wave, and the shock wave light field in the hypersonic flow field is modeled based on the multiple light ray transmission paths.

[0018] Compared with the prior art, the present invention can achieve the following beneficial effects: (1) Significantly improved computational efficiency: This invention uses shock domain identification and extraction technology to accurately focus on the shock region that plays a dominant role in the transmission of light field, avoiding the problem of redundant calculation of the entire large flow field in traditional methods. Combined with a hybrid-dimensional numerical strategy (continuous in the principal direction of light and discrete in the non-principal direction of light), the number of complex interpolation operations is greatly reduced, thereby fundamentally reducing the computational complexity and realizing rapid modeling of the light field of hypersonic flow, which is especially suitable for dynamic process analysis.

[0019] (2) High modeling accuracy: The gradient clustering method based on unsupervised learning can accurately identify the shock wave interface and range in a data-driven manner, overcoming the limitations of manually setting thresholds. At the same time, the Hamiltonian optics principle is introduced to equate the propagation behavior of light waves in time-varying refractive index media to the dynamic process of particles with mass in a potential energy field, providing a rigorous dynamic theoretical basis for light field tracing and improving the modeling accuracy of shock wave light fields.

[0020] (3) Low resource consumption and strong practicality: By focusing on key areas (shock domain) and adopting an efficient hybrid dimension strategy, this invention greatly reduces the demand for computer memory and computing resources while ensuring spatial resolution. This makes it possible to realize high-resolution flow field modeling with tens of millions of grids on ordinary computing platforms, reducing the technical threshold and application cost, and has high engineering application value.

[0021] (4) Provides an effective tool for dynamic optical field analysis: Traditional methods are difficult to handle dynamic flow field sequences with high time resolution due to low computational efficiency. The high efficiency of this invention enables it to seamlessly integrate with nanosecond-level time step data generated by computational fluid dynamics simulation, thereby realizing the effective simulation and analysis of the dynamic, high-frequency evolution process of aero-optical effects (such as image blurring and jitter) in hypersonic flow fields, providing a powerful numerical simulation tool for aircraft optical guidance, observation system performance evaluation, etc. Attached Figure Description

[0022] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 A schematic flowchart illustrating the modeling method for shock wave optical field in hypersonic flow field according to an embodiment of the present invention; Figure 2 A schematic diagram of the refractive index distribution of the flow field region as described in the embodiment of the present invention; Figure 3 A schematic diagram of the refractive index gradient distribution of the flow field domain as described in the embodiment of the present invention; Figure 4 A schematic diagram illustrating the boundary between the near field and the far field as described in the embodiments of the present invention; Figure 5 A schematic diagram of the shock domain as described in the embodiments of the present invention; Figure 6 A schematic diagram of the simulated light propagation path in a shock wave in a two-dimensional flow field as described in the embodiment of the present invention; Figure 7 This is a schematic diagram of the simulated light propagation path in a shock wave within a three-dimensional flow field as described in an embodiment of the present invention. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not constitute a limitation thereof.

[0024] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0025] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on this invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, features defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0026] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "assembly," "connection," and "joining" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0027] The invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0028] like Figure 1 As shown, this invention provides a method for modeling the shock wave optical field in a hypersonic flow field, comprising the following steps: S1: An unsupervised learning algorithm is used to perform gradient clustering on the flow field data to determine the location of the shock wave and the inner and outer boundaries of the shock wave domain. The inner and outer boundaries of the shock wave domain and the spatial distribution of the shock wave are obtained through numerical fitting.

[0029] This invention employs an unsupervised learning algorithm to perform gradient clustering on flow field data, establishing a shock wave interface identification criterion based on the maximum density gradient modulus. It then performs cluster analysis on the flow field data according to the refractive index gradient, thereby accurately identifying and separating the shock waves that have the most significant impact on the light field within the flow field domain. The inner and outer boundaries of the shock wave domain and the location of the shock waves are determined, and analytical expressions for the spatial distribution of the inner and outer boundaries of the shock wave domain and the shock waves are obtained through numerical fitting. The refractive index distribution and refractive index gradient distribution of the flow field domain are shown in Figures 2 and 3.Figure 3 As shown.

[0030] The specific process of using an unsupervised learning algorithm to perform gradient clustering on flow field data is as follows: S11: Abstract and simplify the flow field data into a one-dimensional dataset.

[0031] Flow field data consists of node coordinates (describing the positional information of flow field nodes in two-dimensional / three-dimensional space) and flow field attribute data (core parameters reflecting the physical state of the flow field, such as density and refractive index). It is a multidimensional dataset. Under the premise of constant node positions, core attribute values ​​(e.g., density values) of each node are extracted in a fixed order (such as a node sequence along a coordinate axis or the node numbering order of the flow field data). These core attribute values ​​are then arranged in an ordered manner according to preset rules, abstracting and simplifying the multidimensional flow field data into one-dimensional data that only reflects the continuous changes in core attribute values. This data can be directly used for subsequent Euclidean distance calculations, significantly reducing clustering complexity. The flow field domain encompasses fluids in different flow states, and the refractive indices of fluids in different states differ significantly. Based on this, the fluid in the flow field domain can be roughly divided into far-field and near-field components.

[0032] S12: Randomly select two nodes in the flow field data as initial centroids, calculate the Euclidean distance between the density value of each node in the flow field data and the two initial centroids, and classify the density value of each node into the cluster corresponding to the nearest initial centroid based on the magnitude of the Euclidean distance.

[0033] The density value of a node in one-dimensional space. With the initial centroid Euclidean distance The calculation formula is: .

[0034] S13: Recalculate the new centroid of each cluster to replace the old centroid. Repeat the operation of density value redistribution and centroid update until the centroid and cluster distribution converges and no longer changes. Divide the flow field into far field and near field and determine the boundary between near field and far field.

[0035] The boundary between the near field and the far field is as follows: Figure 4 As shown.

[0036] S14: Take the boundary between the far field and the near field as the outer boundary of the shock domain, perform a downward translation operation on the outer boundary of the shock domain, and when the refractive index gradient reaches its peak value, take the peak value position as the position of the shock wave.

[0037] S15: Select the node in the outer boundary of the shock domain that is symmetrical to the position of the shock wave as the inner boundary of the shock domain.

[0038] At this point, the shock wave domain was completely separated, as... Figure 5 As shown, this enables effective identification and extraction of shock waves. Shock waves in hypersonic flow fields possess a definite shape.

[0039] Numerical fitting can be used to obtain the inner boundary, outer boundary, and spatial distribution analytical expression of the shock domain. Specifically, the shock location point set (the point with the largest refractive index gradient), the outer boundary point set, and the inner boundary point set of the shock domain are extracted from the flow field data. Based on the physical characteristics of the shock morphology (such as symmetry and curvature), a suitable analytical function form is selected for fitting, such as polynomial functions (e.g., quadratic, cubic), exponential functions, Gaussian functions, and spline functions.

[0040] This invention, by identifying and extracting the shock domain, precisely focuses on the shock region that plays a dominant role in the transmission of the light field, thus avoiding the problem of redundant calculations of the entire large flow field in traditional methods.

[0041] S2: Construct a hybrid-dimensional numerical continuous and discrete strategy, determine the principal direction of the light ray based on this strategy, apply the continuous medium approximation to the principal direction of the light ray, and apply the structured grid discretization to the non-principal directions of the light ray.

[0042] In optical flow field analysis, when using the inverse optical tracing method, light rays start from the entrance pupil of the optical system and are projected into the flow field.

[0043] In a two-dimensional flow field, the exit angle of the light ray is... .in, Let be the angle between the ray and the x-axis. Let be the angle between the ray and the y-axis. If Then the y-axis direction is taken as the principal direction of the ray; if Then the x-axis direction is taken as the principal direction of the light ray.

[0044] In a three-dimensional flow field, the exit angle of the light ray is... .in, Let be the angle between the ray and the x-axis. Let be the angle between the ray and the y-axis. Let θ be the angle between the ray and the z-axis. By comparing the magnitudes of θ, φ, and γ, the coordinate axis corresponding to the smallest angle is selected as the principal direction of the ray.

[0045] The specific process of applying the continuous medium approximation to the principal direction of light is as follows: Along the principal direction of the ray, select one point each on the outer boundary, the shock wave, and the inner boundary of the shock domain. Construct a polynomial equation about the coordinates of the principal direction of the ray based on the coordinates of these three points and their refractive index values. Taking the y-axis as the principal direction, the distribution of the refractive index values ​​of the three points along the principal direction of the ray is as follows: , , Based on this, the analytical expression for the continuous refractive index distribution in the principal direction of the shock wave domain can be derived. Substitute the three points into... The polynomial equation is obtained: ; Solve the polynomial using Cramer's rule: ; ; ; ; in, is the determinant of the coefficient matrix of the polynomial equation; For the basic determinant Based on this, The corresponding coefficient column is replaced with the value column of refractive index n. n 1, n 2, n 3) The determinant of the new matrix formed after that; For the basic determinant Based on this, The corresponding coefficient column is replaced with the value column of refractive index n. n 1, n 2, n 3) The determinant of the new matrix formed after that; For the basic determinant Based on this, The corresponding coefficient column is replaced with the value column of refractive index n. n 1, n 2, n 3) The determinant of the new matrix formed after that; The final solution yields the polynomial coefficients. , , : ; ; ; At this point, the flow field along the principal direction of the light rays behaves as a continuous medium, while the flow field along the non-principal directions of the light rays is discrete.

[0046] The specific process of performing structured mesh discretization on the non-principal directions of light is as follows: In a two-dimensional flow field, the non-principal direction of light rays is divided into equally spaced tiny intervals. Within a single tiny interval, the flow field remains continuous in the principal direction.

[0047] In a three-dimensional flow field, the non-principal direction of light rays is divided into tiny units of equal size. Within a tiny unit, the flow field is also continuous in the principal direction of light rays.

[0048] This invention employs a hybrid dimensional numerical continuity and discretization strategy, making the principal direction of light rays continuous while the non-principal directions are discretized. This significantly reduces the number of complex interpolation operations, fundamentally lowering computational complexity and enabling rapid modeling of the optical field in hypersonic flow, making it particularly suitable for dynamic process analysis.

[0049] This invention, by focusing on key regions (shock domains) and employing an efficient hybrid dimension strategy, significantly reduces the demand for computer memory and computing resources while maintaining spatial resolution. This makes it possible to achieve high-resolution flow field modeling with tens of millions of grids on ordinary computing platforms, lowering the technical threshold and application cost, and has high engineering application value.

[0050] S3: Based on the analogy between Fermat's principle and the Moperito principle under the condition of energy conservation, the transmission of light in the refractive index field is compared to the motion of an equivalent material particle in the refractive index potential energy field, thereby establishing the dynamic relationship between the equivalent material particle and the refractive index potential energy field.

[0051] The specific process for establishing the dynamic relationship between the equivalent material particle and the refractive index potential energy field is as follows: The variational form of Fermat's principle is: ; in, For refractive index, For the path of light; The Moperdu principle under the condition of energy conservation is: ; in, For light-meaning momentum, Generalized coordinates; Fermat's principle and Mauper-Duchy's principle under the condition of energy conservation have the same form. By analogy, the transmission of light in a refractive index field can be likened to the motion of an equivalent material particle in a refractive index potential energy field. If the mass of the equivalent material particle is set to 1, then the established dynamic relationship between the equivalent material particle and the refractive index potential energy field is as follows: ; in, It represents the speed of the equivalent physical particle.

[0052] Based on Hamiltonian optics principles, this invention equates the propagation behavior of light waves in time-varying refractive index media to the dynamic process of particles with mass in a potential energy field, providing a rigorous dynamic theoretical basis for light field tracing and improving the modeling accuracy of shock wave light fields.

[0053] S4: Based on the dynamic relationship between equivalent physical particles and refractive index potential energy field, the linear equation of light rays and the spatial distribution analytical expression of the boundary within the shock domain are combined to solve for the initial intersection point of light rays and the shock domain, simulate the propagation path of light rays in the shock wave, and realize the modeling of the shock wave light field in the hypersonic flow field.

[0054] The equation of a straight line for light rays Analytical expression of spatial distribution within the shock domain boundary Solve the system of equations simultaneously to find the initial intersection point of the ray equation and the shock domain. The refractive index at the initial intersection point is... .

[0055] In a two-dimensional flow field, the equation of a straight line for a light ray can be transformed into... The analytical expression for the spatial distribution of the boundary within the shock domain can be transformed into... Combining the two, we can obtain the initial intersection point of the light ray propagating in a straight line with the inner boundary of the shock wave domain: .

[0056] In a three-dimensional flow field, the equation of a straight line for a light ray can be transformed into... The analytical expression for the spatial distribution of the boundary within the shock domain can be transformed into... Combining the two, we can obtain the initial intersection point of the light ray propagating in a straight line with the inner boundary of the shock wave domain: .

[0057] The following example illustrates the concept using the y-axis as the principal direction of light. Figure 6 The simulated propagation path of light rays in a shock wave is shown in a two-dimensional flow field. Figure 7 The simulated propagation path of light in a shock wave is shown in a three-dimensional flow field.

[0058] like Figure 6 As shown, in a two-dimensional flow field, based on the dynamic relationship between the equivalent material particle and the refractive index potential energy field, the velocity component expressions of the equivalent material particle in the principal and non-principal directions of the light ray are obtained: ; ; in, For the equivalent physical particle, the velocity component in the non-principal direction of the light ray. For the velocity components of an equivalent material particle along the principal direction of light, The refractive index distribution along the principal direction of light rays in a two-dimensional flow field. Let be the angle between the light rays at the initial intersection point and the x-axis.

[0059] The derivation of the velocity component expressions for the equivalent material particle in the principal and non-principal directions of light leads to the differential expression for the position of the equivalent material particle: .

[0060] Integrating both sides of the differential expression for the position of the equivalent material particle yields the position expression: .

[0061] When the equivalent physical particle passes through a tiny interval in the non-principal direction of the light and reaches the next tiny interval, the refractive index n in that tiny interval is updated, and the trajectory of the equivalent physical particle in that tiny interval is calculated based on the updated refractive index n.

[0062] like Figure 7 As shown, in a three-dimensional flow field, based on the dynamic relationship between the equivalent material particle and the refractive index potential energy field, the velocity component expressions of the equivalent material particle in the non-principal direction plane and the principal direction of the optical path are obtained: ; ; in, These are the velocity components of the equivalent material particle in the xz plane. This represents the velocity component of an equivalent material particle along the principal direction of light. The refractive index distribution along the principal direction of light rays in a three-dimensional flow field. Let be the angle between the light rays at the initial intersection point and the xz plane; Based on the expressions for the velocity components of the equivalent particle in the xz plane and the y-axis, the differential expression for the position of the equivalent particle is derived: ; in, This is the projection of the equivalent material particle onto the xz plane; Integrating both sides of the differential expression for the position of the equivalent material particle yields the position expression: ; When the equivalent physical particle passes through a tiny unit in a non-principal direction of light and reaches the next tiny unit, the refractive index n in that tiny unit is updated, and the trajectory of the equivalent physical particle in that tiny unit is calculated based on the updated refractive index n.

[0063] Repeatedly perform the initial intersection point calculation and propagation path simulation operations to obtain multiple propagation paths of light rays in the shock domain. Based on the propagation paths of multiple light rays, realize the modeling of the shock field in the hypersonic flow field.

[0064] Optical path length of a single ray It is calculated using the following formula:

[0065] in, s i This indicates the distance the light travels in each tracking step. n i Represents the refractive index at each tracking step.

[0066] Optical path difference The expression is: ; in, Indicates all The average value.

[0067] wavefront aberration It can be expressed by the following formula: ; in, k = 2π / λ , λ wavelength of light 。

[0068] wavefront aberration It is to calculate the actual pupil function. The basis: ; in, Represents the ideal pupil function. This represents the phase perturbation factor. Indicates wavefront aberration. It represents the imaginary unit.

[0069] Complex amplitude function It is the actual pupil function Fourier transform: .

[0070] Point spread function It is a complex amplitude function The square of the modulus: ; in, yes .

[0071] Optical transfer function It is a point spread function Fourier transform: .

[0072] Modulation transfer function It is the optical transfer function The model: .

[0073] At this point, the optical field modeling of the shock wave in the hypersonic flow field has been completed, and a numerical model of the interaction between the shock wave and the optical field has been constructed. Based on this, the optical transmission characteristics of the shock wave region were also calculated.

[0074] The high efficiency of the modeling method in this invention enables seamless integration with nanosecond-level time step data generated by computational fluid dynamics simulations. This allows for effective simulation and analysis of the dynamic, high-frequency evolution of aero-optical effects (such as image blurring and jitter) in hypersonic flow fields, providing a powerful numerical simulation tool for aircraft optical guidance and observation system performance evaluation.

[0075] It should be understood that the various forms of processes shown above can be used to reorder, add, or delete steps. For example, the steps described in this invention disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this invention can be achieved, and this is not limited herein.

[0076] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A method for modeling the shock wave optical field in a hypersonic flow field, characterized in that, Includes the following steps: S1: Unsupervised learning algorithm is used to perform gradient clustering on flow field data to determine the location of shock waves and the inner and outer boundaries of the shock wave domain. The inner and outer boundaries of the shock wave domain and the spatial distribution of the shock waves are obtained through numerical fitting. S2: Construct a hybrid dimension numerical continuous and discrete strategy, determine the principal direction of the light ray based on the strategy, apply continuous medium approximation to the principal direction of the light ray, and apply structured grid discretization to the non-principal directions of the light ray; S3: Based on the analogy between Fermat's principle and the Moperito principle under the condition of energy conservation, the transmission of light in the refractive index field is compared to the motion of an equivalent material particle in the refractive index potential energy field, thereby establishing the dynamic relationship between the equivalent material particle and the refractive index potential energy field. S4: Based on the dynamic relationship between equivalent physical particles and refractive index potential energy field, the linear equation of light rays and the spatial distribution analytical expression of the boundary within the shock domain are combined to solve for the initial intersection point of light rays and the shock domain, simulate the propagation path of light rays in the shock wave, and realize the modeling of the shock wave light field in the hypersonic flow field.

2. The modeling method for shock wave optical field in hypersonic flow field according to claim 1, characterized in that, In step S1, the specific process of using an unsupervised learning algorithm to perform gradient clustering on the flow field data is as follows: S11: The flow field data is abstracted and simplified into a one-dimensional dataset; wherein the flow field data consists of node coordinates and flow field attribute data, and the node positions are constant; S12: Randomly select two nodes in the flow field data as initial centroids, calculate the Euclidean distance between the density value of each node in the flow field data and the two initial centroids, and classify the density value of each node into the cluster corresponding to the nearest initial centroid based on the magnitude of the Euclidean distance. S13: Recalculate the new centroid of each cluster to replace the old centroid. Repeat steps S11 and S12 until the centroid and cluster assignments converge and no longer change, thus dividing the flow field into far field and near field. S14: Take the boundary between the far field and the near field as the outer boundary of the shock domain, perform a downward translation operation on the outer boundary of the shock domain, and when the refractive index gradient reaches its peak value, take the peak value position as the position of the shock wave. S15: Select the node in the outer boundary of the shock domain that is symmetrical to the position of the shock wave as the inner boundary of the shock domain.

3. The modeling method for shock wave optical field in hypersonic flow field according to claim 1, characterized in that, In step S2, the method for determining the principal direction of the light ray is as follows: In a two-dimensional flow field, compare the angles between the light rays and the x-axis and y-axis, and select the coordinate axis with the smallest angle as the principal direction of the light ray; In a three-dimensional flow field, the angles between the light rays and the x-axis, y-axis, and z-axis are compared, and the coordinate axis with the smallest angle is selected as the principal direction of the light ray.

4. The method for modeling the shock wave optical field in a hypersonic flow field according to claim 1, characterized in that, In step S2, the specific process of applying the continuous medium approximation to the principal direction of the light ray is as follows: Along the principal direction of the light ray, select a point on the outer boundary, the shock wave, and the inner boundary of the shock domain. Construct a polynomial equation about the principal direction coordinates based on the coordinates of the three points and the refractive index values. Solve the polynomial equation using Cramer's rule to obtain the analytical expression for the continuous distribution of the refractive index of the shock domain along the principal direction of the light ray, thus achieving the approximate treatment of the continuous medium along the principal direction of the light ray.

5. The method for modeling the shock wave optical field in a hypersonic flow field according to claim 1, characterized in that, In step S2, the specific process of performing structured mesh discretization on the non-principal directions of the light rays is as follows: In a two-dimensional flow field, the non-principal direction of light rays is divided into equally spaced tiny intervals, and the flow field within a single tiny interval remains continuous in the principal direction of light rays; In a three-dimensional flow field, the non-principal direction of light rays is divided into tiny units of equal size, and the flow field within a single tiny unit remains continuous in the principal direction of light rays.

6. The method for modeling the shock wave optical field in a hypersonic flow field according to claim 5, characterized in that, In step S3, the specific process of establishing the dynamic relationship between the equivalent physical particle and the refractive index potential energy field is as follows: The variational form of Fermat's principle is: ； in, For refractive index, For the path of light; The Moperdu principle under the condition of energy conservation is: ； in, For light-meaning momentum, Generalized coordinates; By drawing an analogy between Fermat's principle and the Mauper-Duchy principle under the condition of energy conservation, the transmission of light in a refractive index field can be likened to the motion of an equivalent material particle in a refractive index potential energy field. If the mass of the equivalent material particle is set to 1, the established dynamic relationship between the equivalent material particle and the refractive index potential energy field is as follows: ； in, It represents the speed of the equivalent physical particle.

7. The method for modeling the shock wave optical field in a hypersonic flow field according to claim 6, characterized in that, In step S4, let the refractive index of the initial intersection point be... The specific process of simulating the propagation path of light in the shock wave domain is as follows: If the flow field is a two-dimensional flow field and the principal direction of the light ray is the y-axis, the velocity component expressions of the equivalent physical particle in the principal and non-principal directions of the light ray are obtained based on the dynamic relationship between the equivalent physical particle and the refractive index potential energy field: ； ； in, For the equivalent physical particle, the velocity component in the non-principal direction of the light ray. This represents the velocity component of an equivalent material particle along the principal direction of light. The refractive index distribution along the principal direction of light rays in a two-dimensional flow field. Let be the angle between the light rays at the initial intersection point and the x-axis; The derivation of the velocity component expressions for the equivalent material particle in the principal and non-principal directions of light leads to the differential expression for the position of the equivalent material particle: ； Integrating both sides of the differential expression for the position of the equivalent material particle yields the position expression: ； When the equivalent physical particle passes through a tiny gap in the non-principal direction of the light, update the refractive index n in that tiny gap, and calculate the trajectory of the equivalent physical particle in that tiny gap based on the updated refractive index n. If the flow field is a three-dimensional flow field and the principal direction of the light ray is the y-axis, based on the dynamic relationship between the equivalent material particle and the refractive index potential energy field, the expressions for the velocity components of the equivalent material particle in the non-principal direction plane and the principal direction of the optical path are obtained as follows: ； ； in, These are the velocity components of the equivalent material particle in the xz plane. This represents the velocity component of an equivalent material particle along the principal direction of light. The refractive index distribution along the principal direction of light rays in a three-dimensional flow field. Let be the angle between the light rays at the initial intersection point and the xz plane; Based on the expressions for the velocity components of the equivalent particle in the xz plane and the y-axis, the differential expression for the position of the equivalent particle is derived: ； in, This is the projection of the equivalent material particle onto the xz plane; Integrating both sides of the differential expression for the position of the equivalent material particle yields the position expression: ； When the equivalent physical particle passes through a tiny unit in a non-principal direction of the light, the refractive index n in that tiny unit is updated, and the trajectory of the equivalent physical particle in that tiny unit is calculated based on the updated refractive index n.

8. The method for modeling the shock wave optical field in a hypersonic flow field according to claim 1, characterized in that, In step S4, the specific process of solving for the initial intersection point of the ray and the shock domain by simultaneously solving the linear equation of the ray and the spatial distribution analytical expression of the boundary within the shock domain is as follows: In a two-dimensional flow field, the equation of a straight ray is transformed into... The spatial distribution analytical expression of the inner boundary of the shock domain is transformed into... Combining the two equations, we obtain the initial intersection point of the light ray propagating in a straight line with the inner boundary of the shock wave domain: ； In a three-dimensional flow field, the equation of a straight ray is transformed into... The spatial distribution analytical expression of the inner boundary of the shock domain is transformed into... Combining the two, we can obtain the initial intersection point of the light ray propagating in a straight line with the inner boundary of the shock wave domain: 。 9. The method for modeling the shock wave optical field in a hypersonic flow field according to claim 6, characterized in that, In step S4, the specific process of modeling the shock wave optical field in the hypersonic flow field is as follows: Calculate the optical path length of each ray. The calculation formula is: ； in, s i The distance the light travels in each tracking step. n i The refractive index for each tracking step; Calculate the optical path difference for each ray based on its optical path length. The calculation formula is: ； in, For all The average value; Based on the optical path difference of each ray Calculate wavefront aberrations The calculation formula is: ； in, k=2π / λ , λ The wavelength of light; Based on wavefront aberration Calculate the actual pupil function The calculation formula is: ； in, For the ideal pupil function, Indicates the phase perturbation factor; Based on the actual pupil function Calculate the complex amplitude function The calculation formula is: ； Based on complex amplitude function Calculate the point spread function The calculation formula is: ； in, yes The complex conjugate; Based on point spread function Calculate the optical transfer function The calculation formula is: ； Based on optical transfer function Calculate the modulation transfer function The calculation formula is: 。 10. The method for modeling the shock wave optical field in a hypersonic flow field according to claim 9, characterized in that, Simulate the propagation paths of multiple light rays in a shock wave, and model the shock wave light field in a hypersonic flow field based on the propagation paths of multiple light rays.

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