Method and system for simulating electromagnetic characteristics of plasma sheath of hypersonic aircraft

Abstract

The invention discloses a plasma sheath electromagnetic characteristic simulation method and system for a hypersonic flight vehicle, and the method comprises the steps: carrying out the fluid simulation according to the geometric shape and flight parameters of the hypersonic flight vehicle, so as to obtain the information of a flow field containing a plasma sheath region; according to the flow field information, simulation parameters of all positions of the plasma sheath space are determined, and the simulation parameters at least comprise electron density distribution and electron collision frequency distribution; based on the simulation parameters, a three-dimensional model of the plasma sheath is established, the three-dimensional model is layered according to electron density distribution, a layered three-dimensional model composed of a plurality of plasma layers is formed, and each plasma layer has the electron density within a preset range; based on the layered three-dimensional model, establishing a non-uniformly distributed electromagnetic simulation model of the plasma sheath; and carrying out grid division on the non-uniformly distributed electromagnetic simulation model, and carrying out numerical calculation by adopting a numerical solver so as to obtain the electromagnetic characteristics of the plasma sheath. According to the method, the problem of deviation between a simulation result and an actual situation of a traditional simulation model can be solved.

Description

Technical Field

[0001] The present invention relates to the field of electromagnetic simulation technology, and particularly to a method and system for simulating the electromagnetic characteristics of a plasma sheath of a hypersonic vehicle. Background Art

[0002] When a hypersonic vehicle re-enters the atmosphere, its surface undergoes intense friction with the air due to high-speed motion, generating extremely high temperatures. Under such high-temperature conditions, air molecules gain sufficient energy, and electrons break free from the bondage of atomic nuclei, forming a large number of free electrons and ions. These charged particles accumulate around the vehicle, thus forming a plasma sheath. The electron density distribution of the plasma sheath exhibits complex non-uniformity, with a higher electron density near the vehicle surface and gradually decreasing with increasing distance. This is because the ionization effect of the vehicle surface on air molecules is the strongest and weakens gradually outward. In some regions, the electron density can be as high as more than 10 12 per cubic centimeter, which has a significant impact on the propagation of electromagnetic waves. Therefore, it is necessary to analyze the propagation characteristics of electromagnetic waves in the plasma sheath.

[0003] However, in the current research on simulating the electromagnetic characteristics of plasma sheaths, the phenomenon of model simplification is common, and it is difficult to accurately reflect the true electromagnetic characteristics of the plasma sheath. The actual plasma sheath is affected by various factors, and traditional models often cannot comprehensively consider these factors, resulting in a deviation between the simulation results and the actual situation. Summary of the Invention

[0004] The purpose of the present invention is to overcome the above-mentioned defects or problems existing in the background art, and provide a method and system for simulating the electromagnetic characteristics of a plasma sheath of a hypersonic vehicle, which can improve the problem of deviation between the simulation results and the actual situation existing in the traditional simulation model.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] Technical Solution 1: A method for simulating the electromagnetic characteristics of a plasma sheath of a hypersonic vehicle, which includes the following steps:

[0007] Step 1: Perform fluid simulation based on the geometric shape and flight parameters of the hypersonic vehicle to obtain flow field information including the plasma sheath region; Step 2: Based on the flow field information, determine the simulation parameters at various locations in the plasma sheath space, where the simulation parameters at least include electron density distribution and electron collision frequency distribution; Step 3: Based on the simulation parameters, establish a three-dimensional model of the plasma sheath, and layer the three-dimensional model according to the electron density distribution to form a layered three-dimensional model composed of multiple plasma layers, where each plasma layer has an electron density and collision frequency within a preset range; Step 4: Based on the layered three-dimensional model, establish a non-uniform distribution electromagnetic simulation model of the plasma sheath, where the electromagnetic characteristics of each plasma layer in the model are set according to the simulation parameters determined in Step 2; Step 5: Perform mesh division on the non-uniform distribution electromagnetic simulation model and use a numerical solver for numerical calculation to obtain the electromagnetic characteristics of the plasma sheath.

[0008] Technical solution two based on technical solution one: The fluid simulation in Step 1 includes: solving the hydrodynamic equation using the finite volume method and updating the flow field parameters through iterative operations until a converged state is reached; the flow field information includes density, temperature, pressure, and heat flux.

[0009] Technical solution three based on technical solution one or two: The fluid simulation in Step 1 further includes considering the influence of the applied external electromagnetic field on the flow field.

[0010] Technical solution four based on technical solution one: In Step 2, a chemical reaction model is used to simulate the formation process of the plasma sheath to determine the electron density distribution; the electron collision frequency distribution is determined by the fluid simulation analysis.

[0011] Technical solution five based on technical solution one: In Step 3, the three-dimensional model of the plasma sheath is layered according to a preset electron density threshold or electron density range, and the electron density of each plasma layer is approximately uniform within the preset range, and each plasma layer has separately set material properties.

[0012] Technical solution six based on technical solution one: The non-uniform distribution electromagnetic simulation model established in Step 4 uses the Drude model to describe the electromagnetic characteristics of each layer of the plasma sheath; the parameters of the Drude model are set according to the simulation parameters determined in Step 2.

[0013] Technical solution seven based on technical solution one: The formula of the Drude model is as follows: where ω p , ω and ν respectively represent the plasma electron oscillation angular frequency, the incident radar wave angular frequency, and the plasma electron collision frequency; n e is the plasma electron density.

[0014] Technical solution eight based on technical solution one: In step 5, mesh refinement is performed on the boundary region of the plasma sheath or the region where the electron density changes violently; and mesh independence verification is carried out by gradually densifying the mesh and comparing the changes in the calculation results.

[0015] Technical solution nine based on technical solution one: The numerical solver in step 5 is a time-frequency domain solver.

[0016] In addition, the present invention also provides technical solution ten: A system for simulating the electromagnetic characteristics of the plasma sheath of a hypersonic vehicle, which includes: a processor; and a memory, where the memory stores instructions that, when executed by the processor, cause the system to execute the method according to any one of technical solutions one to nine.

[0017] A method and system for simulating the electromagnetic characteristics of the plasma sheath of a hypersonic vehicle provided by the present invention aims to overcome the problem that the simulation results deviate from the actual situation due to model simplification in the background technology. Its beneficial effects are specifically reflected in:

[0018] First, through step 1, the method of the present invention comprehensively integrates the actual geometric shape, flight parameters, and even optional external electromagnetic field information of the hypersonic vehicle for fluid simulation, and obtains detailed flow field information including parameters such as density, temperature, pressure, and heat flux. This constructs a simulation starting point that is more in line with the actual physical process and lays a solid foundation for accurately determining the key parameters of the plasma sheath subsequently.

[0019] Then, based on the accurate flow field information, through step 2, the present invention can accurately obtain the spatial distribution of the plasma electron density and electron temperature, which have a decisive influence on the propagation of electromagnetic waves, within the sheath. Compared with the rough estimation or simplified processing of these key factors in the traditional model, the present invention can more accurately depict the actual state of the plasma, provides the core basis for constructing an electromagnetic model that conforms to the actual situation, and greatly improves the physical authenticity of the simulation model.

[0020] After that, based on the key electron density distribution, through Step 3, the present invention performs a layering process on the established three-dimensional model of the plasma sheath to form a layered three-dimensional model with approximately uniform electron density in each layer and with separate material properties. This layering method can meticulously reflect the complex structure and parameter gradient changes of the plasma sheath in space; due to the significant differences in the electron density of the plasma sheath at different positions, it is difficult for traditional overall uniform models to accurately describe the influence of such changes on electromagnetic characteristics. However, the layered model of the present invention divides the sheath into multiple layers, each layer having relatively clear electromagnetic characteristics, and can more accurately simulate the propagation behavior of electromagnetic waves in regions with different densities (such as refraction, reflection, absorption), thereby effectively reducing the deviation from the actual situation caused by model simplification.

[0021] Subsequently, based on the refined layered three-dimensional model, through Step 4, the present invention uses the Drude model based on physical principles to describe the electromagnetic characteristics of each plasma layer, and the key parameters of the model are directly calculated through explicit physical formulas based on the electron density and electron temperature accurately determined in the previous steps. This ensures that the establishment of the electromagnetic model has a clear physical meaning, and its characteristics are directly related to the actual physical state of the sheath, thereby establishing a non-uniform simulation model that can reflect the spatial variation of the true electromagnetic characteristics of the sheath, making the simulation of processes such as the propagation, scattering, and absorption of electromagnetic waves in the sheath more realistic.

[0022] Finally, through Step 5, the present invention performs reasonable mesh division on the established non-uniform electromagnetic simulation model, especially refines the mesh in key regions such as the boundary layer and the region with drastic changes in electron density, and conducts mesh independence verification to ensure the accuracy and stability of numerical calculations; combined with the use of a suitable numerical solver (such as a time-frequency domain solver), it can effectively capture the subtle changes in the electromagnetic field in a complex plasma environment and obtain accurate and reliable data on the electromagnetic characteristics of the plasma sheath, such as propagation constants, attenuation coefficients, reflection / transmission characteristics, RCS changes, etc.

[0023] In summary, through a series of steps such as integrating fluid simulation, accurately determining plasma parameters, fine layered modeling, constructing a non-uniform electromagnetic model based on physics, and reliable numerical calculations, the present invention significantly improves the accuracy and reliability of the simulation of the electromagnetic characteristics of the plasma sheath of hypersonic vehicles, and its simulation results can better reflect the true physical process. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for the description of the embodiments. Obviously, the following drawings are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0025] Figure 1 This is a schematic flowchart of the simulation method for the electromagnetic characteristics of the plasma sheath of a hypersonic vehicle according to an embodiment of the present invention;

[0026] Figure 2 This is a cloud map of the two-dimensional plasma flow field distribution of the vehicle model in the simulation method for the electromagnetic characteristics of the plasma sheath of a hypersonic vehicle according to an embodiment of the present invention;

[0027] Figure 3 This is a schematic diagram of the three-dimensional physical model of the vehicle model in the simulation method for the electromagnetic characteristics of the plasma sheath of a hypersonic vehicle according to an embodiment of the present invention;

[0028] Figure 4 This is a schematic diagram of the electromagnetic reflection attenuation characteristics in the plasma sheath of the vehicle model in the simulation method for the electromagnetic characteristics of the plasma sheath of a hypersonic vehicle according to an embodiment of the present invention;

[0029] Figure 5 This is the result of the electromagnetic characteristics of the plasma sheath of the vehicle model in the simulation method for the electromagnetic characteristics of the plasma sheath of a hypersonic vehicle according to an embodiment of the present invention.

[0030] Main reference numeral description:

[0031] The vehicle head 10; the vehicle surface 11;

[0032] The plasma sheath 20. Detailed implementation manners

[0033] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are the preferred embodiments of the present invention and should not be regarded as excluding other embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without making creative efforts belong to the scope of protection of the present invention.

[0034] In the claims, the description, and the above-mentioned accompanying drawings of the present invention, unless otherwise clearly defined, when using terms such as "first", "second", or "third", etc., are for distinguishing different objects and not for describing a specific order.

[0035] In the claims, the description and the above-mentioned drawings of the present invention, unless otherwise clearly defined, for directional terms, such as the use of terms "center", "lateral", "longitudinal", "horizontal", "vertical", "top", "bottom", "inner", "outer", "upper", "lower", "front", "rear", "left", "right", "clockwise", "counterclockwise", etc. to indicate the orientation or position relationship are based on the orientation and position relationship shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation or be constructed and operated in a specific orientation, so it should not be construed as limiting the specific protection scope of the present invention.

[0036] In the claims, the description and the above-mentioned drawings of the present invention, unless otherwise clearly defined, if the terms "fixed connection" or "fixedly connected" are used, they should be understood in a broad sense, that is, any connection method without displacement relationship and relative rotation relationship between the two, that is to say, it includes non-detachable fixed connection, detachable fixed connection, being integrated as a whole, and being fixedly connected through other devices or elements.

[0037] In the claims, the description and the above-mentioned drawings of the present invention, if the terms "comprise", "have" and their variants are used, are intended to mean "including but not limited to".

[0038] Referring to Figure 1 , the embodiment of the present invention relates to a method for simulating the electromagnetic characteristics of the plasma sheath of a hypersonic vehicle, and through this method, the problem that the simulation results deviate from the actual situation existing in the traditional simulation model can be improved.

[0039] When a hypersonic vehicle re-enters the atmosphere or flies at a high Mach number, the surface of the vehicle rubs and compresses violently with the surrounding air, resulting in a sharp rise in air temperature, dissociation and ionization of air molecules, and thus a layer of plasma sheath is formed around the vehicle. This plasma sheath has a significant impact on the propagation of electromagnetic waves, and may cause a series of problems such as communication interruption ("blackout" phenomenon), shortening of radar detection range, and change of target characteristics. Therefore, accurately predicting and analyzing the electromagnetic characteristics of the plasma sheath is crucial for the fields of hypersonic vehicle design, communication guarantee, target recognition and stealth, etc.

[0040] At present, the research methods for the electromagnetic characteristics of the plasma sheath mainly include theoretical analysis, experimental measurement and numerical simulation. Theoretical analysis often requires highly simplifying the model and is difficult to handle problems of complex shapes and non-uniform media. Experimental measurement (such as ballistic range, wind tunnel experiment, flight test) is costly, time-consuming, and it is difficult to fully reproduce all flight conditions and obtain detailed spatial parameter distributions. Therefore, numerical simulation has become an indispensable and important means for studying this problem.

[0041] However, when simulating the electromagnetic characteristics of the plasma sheath using numerical simulation methods in the prior art, there are often the following problems, resulting in deviations between the simulation results and the actual physical situation. Based on the above considerations, the present invention proposes a new simulation method for the electromagnetic characteristics of the plasma sheath of a hypersonic vehicle.

[0042] The simulation method includes the following steps:

[0043] Step 1: Perform a fluid simulation based on the geometric shape and flight parameters of the hypersonic vehicle to obtain flow field information including the plasma sheath region;

[0044] Step 2: Based on the flow field information, determine the simulation parameters at various locations in the plasma sheath space, where the simulation parameters at least include the electron density distribution and the electron collision frequency distribution;

[0045] Step 3: Based on the simulation parameters, establish a three-dimensional model of the plasma sheath, and layer the three-dimensional model according to the electron density distribution to form a layered three-dimensional model composed of multiple plasma layers, where each plasma layer has an electron density and a collision frequency within a preset range;

[0046] Step 4: Based on the layered three-dimensional model, establish a non-uniform distribution electromagnetic simulation model of the plasma sheath, where the electromagnetic characteristics of each plasma layer in the model are set according to the simulation parameters determined in Step 2;

[0047] Step 5: Perform mesh division on the non-uniform distribution electromagnetic simulation model, and use a numerical solver for numerical calculation to obtain the electromagnetic characteristics of the plasma sheath.

[0048] Among them, the fluid simulation in Step 1 includes: solving the fluid dynamics equation using the finite volume method, and updating the flow field parameters through iterative operations until a convergence state is reached; the flow field information includes density, temperature, pressure, and heat flux. In addition, the fluid simulation in Step 1 also includes considering the influence of the applied external electromagnetic field on the flow field.

[0049] In Step 2, a chemical reaction model is used to simulate the formation process of the plasma sheath to determine the electron density distribution; the electron collision frequency distribution is determined by the fluid simulation analysis.

[0050] In Step 3, the three-dimensional model of the plasma sheath is layered according to a preset electron density threshold or electron density range. The electron density of each plasma layer is approximately uniform within the preset range, and each plasma layer has separately set material properties.

[0051] In the non-uniform distribution electromagnetic simulation model established in step 4, the Drude model is used to describe the electromagnetic characteristics of each layer of the plasma sheath; the parameters of the Drude model are set according to the simulation parameters determined in step 2. Among them, the formula of the Drude model is as follows: where ω p , ω and ν respectively represent the angular frequency of plasma electron oscillation, the angular frequency of the incident radar wave, and the plasma electron collision frequency; n e is the plasma electron density.

[0052] In step 5, the boundary region of the plasma sheath or the region where the electron density changes violently is refined; and the grid independence is verified by gradually densifying the grid and comparing the changes in the calculation results. And, the numerical solver in step 5 is a time-frequency domain solver.

[0053] The present invention will be elaborated in detail below in conjunction with specific embodiments.

[0054] Taking the simulation and analysis of the electromagnetic characteristics of the plasma sheath of a RAMC (Radio Attenuation Measurement-C) blunted body aircraft under specific hypersonic flight conditions as an example, the above simulation method is described. Among them, the set flight conditions are as follows: Aircraft model: RAMC blunted body model, the geometric shape of which is well known in the art. Flight altitude H = 20 km. Flight Mach number Ma = 19.2. Flight angle of attack α = 0°.

[0055] Step S101: Perform fluid simulation to obtain flow field information.

[0056] First, according to the known geometric shape of the RAMC aircraft (for example, the geometric data of the aircraft head 10 and the aircraft surface 11) and the above set flight parameters (H = 20 km, Ma = 19.2, α = 0°), a detailed computational fluid dynamics simulation is performed. The purpose of this step is to obtain detailed flow field information of the region around the aircraft including the plasma sheath 20.

[0057] In this embodiment, the fluid simulation can be completed on a professional computational fluid dynamics (CFD) software platform, such as but not limited to the NNW-HyFLOW software. During the simulation process, the finite volume method is usually used to discretize and solve the Navier-Stokes equations describing the high-temperature gas flow, and the chemical non-equilibrium effects of air under high-temperature conditions should be considered, such as the dissociation of molecules, the ionization of atoms, and the related chemical reaction rates. Through iterative calculation, the physical quantities in the flow field are continuously updated until the calculation results reach the preset convergence criterion, such as the residual being less than a certain threshold or the key physical quantities no longer changing significantly.

[0058] Through this fluid simulation, the detailed distribution of the flow field around the aircraft can be obtained. This information includes at least: gas density distribution; gas temperature distribution (including translational temperature, vibrational temperature, etc., depending on the complexity of the model); gas pressure distribution; gas velocity field distribution; mole fraction or number density distribution of each chemical component (such as N, O, N, O, NO, N+, O+, e-, etc.).

[0059] Particularly importantly, through this step, the spatial distribution of key parameters within the plasma sheath region can be obtained, especially the distribution of electron number density (n e ) and electron temperature (T e ). As Figure 2 shown (corresponding to Figure 1 of the first document), this figure clearly shows the electron density distribution contour of the plasma sheath formed around the head of the RAMC model under specific working conditions of this embodiment. It can be seen from the figure that the electron density is higher in the region near the aircraft wall and gradually decays outward, and its numerical range can vary from, for example, 5E+16 m-3 to 1E+18 m-3 or higher. These precise electron density and electron collision frequency distribution data are important inputs for subsequent electromagnetic characteristic simulations.

[0060] In some more complex application scenarios or simulations with higher accuracy requirements, if the possible reaction of the external electromagnetic field (such as the electromagnetic field generated by the aircraft itself or the external strong electromagnetic environment) on the plasma flow field is considered, relevant terms of the electromagnetic field (such as the Lorentz force term, Joule heat term, etc.) can be coupled in the hydrodynamic equations to perform magnetohydrodynamic (MHD) simulations.

[0061] Step S102: Determine electromagnetic simulation parameters based on the flow field information.

[0062] After obtaining the detailed flow field information through step S101, the next step is to accurately determine the key parameters for subsequent electromagnetic simulations based on these flow field data. These parameters mainly describe the electromagnetic characteristics of the plasma sheath 20 at various locations in space, including at least the spatial distribution of plasma electron number density (n e ) and the spatial distribution of electron temperature (T e ).

[0063] Specifically, the electron number density (n e (x, y, z)) and the electron temperature (T eThe three-dimensional spatial distribution data of (x, y, z) can be directly extracted from the fluid simulation results of step S101. CFD software can usually output the numerical values of these physical quantities at the computational grid nodes. Through data post-processing and interpolation techniques, these discrete data can be mapped onto the grids or regions required for subsequent electromagnetic simulations.

[0064] To ensure the accuracy of the electron density distribution, the chemical reaction model adopted in the fluid simulation of step S101 is crucial. Preferably, this chemical reaction model should be able to fully simulate a series of complex physical and chemical processes that occur to the air around a hypersonic vehicle at high temperatures, such as: dissociation reactions of neutral molecules (e.g., O → 2O, N → 2N); ionization reactions of atoms (e.g., O + M → O+ + e- + M, N + M → N+ + e- + M, where M is the third-party collision); charge exchange reactions; recombination reactions of electrons and ions, etc. By including these key reactions and using reliable reaction rate coefficients, the fluid simulation can more realistically predict the formation process of the plasma sheath and the spatial distribution of its electron density.

[0065] Similarly, the distribution of the electron temperature (T e ) is also an important parameter that directly affects the electromagnetic characteristics of the plasma, especially having a significant impact on the calculation of the collision frequency. In some fluid simulation models (such as the two-temperature model or multi-temperature model), the electron temperature is solved separately from the heavy particle temperature of the gas as a whole, which can more accurately reflect the non-equilibrium thermodynamic state in the plasma. If the fluid simulation uses a single-temperature model, it is usually assumed that the electron temperature is in thermal equilibrium with the gas temperature, or the electron temperature is estimated through a specific energy balance equation.

[0066] Through this step, we obtain the key parameter fields (n e and T e ) that characterize the non-uniform characteristics of the plasma sheath in three-dimensional space, and these parameter fields will serve as the basis for establishing a refined electromagnetic simulation model in the subsequent steps.

[0067] Step S103: Establish a layered three-dimensional model of the plasma sheath.

[0068] After obtaining the spatial distributions of the key electromagnetic parameters (mainly the electron density n e and the electron temperature T e ) within the plasma sheath in step S102, the purpose of this step is to establish a layered three-dimensional geometric model that can reflect the non-uniform characteristics of the plasma sheath based on these parameter distributions, especially the spatial distribution of the electron density.

[0069] First, based on the geometric shape of the aircraft obtained in step S101 and the approximate range of the plasma sheath determined in step S102, an initial three-dimensional geometric model of the aircraft and its surrounding plasma sheath needs to be constructed. This can be accomplished in professional three-dimensional computer-aided design (CAD) software such as SolidWorks, or directly in electromagnetic simulation software with geometric modeling capabilities. Figure 3 Shown is a schematic diagram of the three-dimensional physical model of the RAMC model and the plasma sheath 20, which can serve as the basis for the initial geometric model.

[0070] Next, the core task is to perform layer-by-layer processing on the plasma sheath 20 region. The basis for layering is mainly the spatial distribution gradient of the electron density n e . Since the electron density of the plasma sheath usually decreases gradually from the high-value region near the aircraft surface outward, showing an obvious gradient change, the sheath region can be divided into multiple discrete plasma layers according to different magnitudes or ranges of electron density.

[0071] The specific layering method can be as follows:

[0072] Determine the electron density threshold or range: According to the electron density distribution data extracted in step S102 (for example, Figure 2 the two-dimensional electron density cloud map shown can be extended to three-dimensional data), a series of electron density thresholds are selected. For example, the electron density isosurface can be selected as the boundary of each layer. As mentioned before, thresholds such as 1E+18 m-3, 5E+17 m-3, 1E+17 m-3, 5E+16 m-3, etc. can be set, thereby dividing the sheath into several layers. Each layer will correspond to a specific electron density range.

[0073] Generate layered geometry: In the three-dimensional modeling environment, according to the selected electron density threshold or isosurface, the continuously varying plasma sheath region is cut or divided into multiple sub-regions (i.e., plasma layers) with different geometric boundaries. Each layer can be regarded as an independent geometric entity.

[0074] Approximation of parameters within the layer: For each plasma layer divided, the electron density inside it can be approximated. A commonly used method is to assume that the electron density within each layer is approximately uniform, and its value can be taken as the average value, median value of the electron density within the layer, or the central value of the electron density range represented by the layer. Similarly, the electron temperature within the layer can also adopt the corresponding average value or representative value.

[0075] Material property assignment: Importantly, each divided plasma layer will be assigned its independent material properties. This means that in subsequent electromagnetic simulations, different complex permittivities can be set for each layer, and these complex permittivities will be calculated through physical models (such as the Drude model) based on the approximate electron density and electron temperature values of that layer.

[0076] Through such layering, the originally continuous and non-uniform plasma sheath is approximated as a structure composed of multiple thin plasma layers with different dielectric properties but approximately uniform within the layer. Compared with the model that regards the entire sheath as a single uniform medium, this layering model can capture the spatial gradient changes of plasma parameters more meticulously, thereby more accurately simulating the propagation, reflection, and absorption behaviors of electromagnetic waves in non-uniform plasmas.

[0077] The number of layers depends on the requirements for simulation accuracy and the limitations of computing resources. The more layers there are, the higher the approximation degree to the original continuous distribution, but the computational cost also increases accordingly.

[0078] Step S104: Establish a non-uniform distribution electromagnetic simulation model of the plasma sheath.

[0079] After constructing the layered three-dimensional geometric model of the plasma sheath in step S103, the goal of this step is to establish a complete simulation model that can reflect the non-uniform electromagnetic characteristics of the plasma sheath in a professional electromagnetic simulation software (such as CST Studio Suite, ANSYS HFSS, COMSOL Multiphysics, etc., CST Studio Suite can be preferably used in this embodiment) based on this layered model.

[0080] This process mainly includes the following aspects:

[0081] Import or construct the geometric model: Import the three-dimensional geometric model containing the aircraft geometry (such as the aircraft head 10 and the aircraft surface 11) and the layered plasma sheath 20 created in step S103 into the electromagnetic simulation software. If the aircraft itself is made of a conductive material (such as metal), the corresponding conductivity should be set for it or it should be defined as a perfect electric conductor (PEC).

[0082] Set the material properties for each plasma layer: This is the core of this step. For each plasma layer divided in step S103, it is necessary to calculate and set its macroscopic electromagnetic characteristics, mainly the complex permittivity ε e ) and the average electron temperature T e )(These values are derived from the flow field parameter extraction in step S102 and the in-layer parameter approximation in step S103), mainly the complex permittivity ε r .

[0083] Preferably, the Drude model is used to describe the complex permittivity of each plasma layer. The Drude model is a commonly used physical model to describe the response of plasma to electromagnetic waves. Its complex permittivity ε r has the following expression:

[0084] where: ω is the angular frequency of the incident electromagnetic wave (ω = 2πf, f is the incident wave frequency, for example, it takes values in the 1 - 18 GHz frequency band commonly used in radar detection).

[0085] ω p is the angular frequency of plasma electron oscillation of this specific plasma layer, and its calculation formula is [[]]where n e is in the unit of m-3.

[0086] ν is the electron collision frequency of this specific plasma layer. The collision frequency ν is a parameter that describes the frequency of collisions between electrons and neutral particles or ions, and it significantly affects the energy absorption of electromagnetic waves in the plasma. The calculation of the collision frequency can be based on various models. For example, it can be calculated according to parameters such as the average electron temperature T e of this layer, the background gas density, the collision cross-section, etc. An exemplary collision frequency calculation formula is given in claim 7: (where T e is usually in the unit of Kelvin K, and ω is the incident wave angular frequency rad / s). It should be noted that the specific expression of the collision frequency may vary depending on the main collision processes and gas components considered, and a model suitable for the current physical conditions should be selected.

[0087] Since the values of n e and T e are different for each layer, the εr values calculated through the Drude model will also be different, thus realizing the modeling of the non-uniform electromagnetic characteristics of the plasma sheath.

[0088] Set the excitation source and boundary conditions: Referring to Figure 4 , according to the simulation objective (such as calculating the RCS attenuation), an appropriate electromagnetic wave excitation source needs to be set. For example, a plane wave excitation can be set to simulate the incidence of far-field radar waves. The incident direction, polarization mode, and frequency range (such as 1 - 18 GHz) of the plane wave should be set according to the actual analysis requirements. At the outer boundary of the simulation region, a suitable absorbing boundary condition (such as the PML layer, i.e., the perfectly matched layer) needs to be set to simulate the open space and prevent electromagnetic waves from reflecting back from the boundary to the calculation region and interfering with the results.

[0089] Define observations and outputs: Set the corresponding field monitors and post - processing templates according to the electromagnetic characteristics to be analyzed. For example, to calculate the RCS, far - field scattering information needs to be recorded. To analyze attenuation, the field strength or power - flow density along a specific path may need to be calculated.

[0090] Through the above steps, a complete electromagnetic simulation model including the aircraft entity and the multi - layer non - uniform plasma sheath is established. The core of this model lies in that by stratifying the sheath and applying the Drude model to each layer, the non - uniform distribution of plasma electromagnetic parameters in space and its influence on electromagnetic wave propagation can be approximately reproduced.

[0091] Step S105: Perform numerical calculations to obtain the electromagnetic characteristics of the plasma sheath.

[0092] After successfully establishing a complete electromagnetic simulation model including the aircraft and the stratified non - uniform plasma sheath in step S104, this step will perform numerical solution on this model to obtain various electromagnetic response characteristics of the plasma sheath under the excitation of a preset electromagnetic wave.

[0093] This process mainly includes the following key aspects:

[0094] (1) Meshing:

[0095] Before performing numerical calculations, the entire simulation model (including the aircraft, each plasma layer, and the surrounding free - space region) must be spatially discretized, that is, meshed. The quality and density of the mesh directly affect the calculation accuracy and the consumption of computing resources.

[0096] For the complex geometry and material properties in this embodiment, non - uniform meshes are usually adopted. Special attention needs to be paid to the mesh processing in the following regions:

[0097] ① The surface and sharp edges of the aircraft: The electromagnetic field changes violently in these regions, and finer meshes are required to accurately capture them.

[0098] ② The boundary regions of the plasma sheath: That is, the interfaces between plasma layers and the interface between the outermost plasma layer and free space. These regions may also cause rapid field changes due to the change of dielectric constant, and the meshes need to be appropriately refined.

[0099] ③ Regions where the electron density or electron - temperature gradient changes violently: Even within the same plasma layer, if the parameter gradient is large (although we have assumed approximate uniformity within the layer, the stratification itself is a discretization of the gradient), finer meshes may be required.

[0100] ④ Wavelength correlation: The grid size usually needs to be less than a certain fraction (e.g., 1 / 10 to 1 / 20) of the wavelength of electromagnetic waves in the corresponding medium at the operating frequency to ensure the accuracy of the numerical solution. For broadband simulations, the minimum wavelength corresponding to the highest frequency should be used as the benchmark.

[0101] To ensure the reliability of the calculation results, grid independence verification must be carried out. The specific method is to perform multiple simulation calculations using grids with different densities (e.g., gradually refining the grid) and compare the key calculation results (such as the RCS value or average attenuation value at a specific frequency). When the grid density increases to a certain extent and the calculation results no longer change significantly (e.g., the change is less than a preset tolerance, such as 1% or 0.1 dB), it can be considered that the current grid density is sufficient and the calculation results are independent of the grid.

[0102] (2) Select and run the numerical solver (Solver):

[0103] According to the simulation objectives (such as broadband RCS, scattering at a specific frequency, field distribution, etc.) and the characteristics of the model, select a suitable numerical solution algorithm. Electromagnetic simulation software usually provides multiple solver options, such as:

[0104] ① Time-domain solver: Such as the finite-difference time-domain method (FDTD - Finite-Difference Time-Domain). The FDTD solver directly solves Maxwell's equations in the time domain and can obtain the broadband frequency response through a single simulation. This is very effective for analyzing the characteristics of a relatively wide frequency band such as 1 - 18 GHz.

[0105] ② Frequency-domain solver: Such as the finite element method (FEM - Finite Element Method), the method of moments (MoM - Method of Moments), physical optics / physical theory of diffraction (PO / PTD - Physical Optics / Physical Theory of Diffraction), etc. Frequency-domain solvers usually perform accurate calculations at a single frequency point. If a broadband response is required, scanning calculations need to be carried out at multiple frequency points.

[0106] In this embodiment, since the focus is on the broadband electromagnetic characteristics of 1 - 18 GHz, selecting a time-domain solver (such as the transient solver in CST) is a more efficient choice. As described in claim 9, the numerical solver can be a time-frequency domain solver (here it should be understood that both time-domain solvers and frequency-domain solvers are available, or some solvers have both time-domain calculation and frequency-domain analysis capabilities).

[0107] After selecting the solver, start the simulation calculation. The calculation time depends on the complexity of the model, the number of meshes, the frequency range, and the available computing resources (such as the number of CPU cores, the size of the memory, etc.).

[0108] (3) Post-processing of data and result analysis:

[0109] After the numerical calculation is completed, the electromagnetic simulation software will output a large amount of raw data, such as the spatial electromagnetic field distribution, surface current, scattering parameters, etc. These data need to be post-processed to extract the required electromagnetic characteristic indicators. The specific contents include the following:

[0110] ① Radar cross section (RCS): RCS is an important parameter to measure the scattering ability of a target to radar waves. The monostatic or bistatic RCS can be calculated, and its variation with frequency, incident angle, and polarization mode can be analyzed. The plasma sheath usually leads to a reduction (attenuation) of the RCS.

[0111] ② Reflection attenuation characteristics: The attenuation amount of the radar echo signal intensity caused by the presence of the plasma sheath can be analyzed. This can be directly reflected from the change of the RCS, or calculated by comparing the scattering field intensities with and without the plasma sheath.

[0112] ③ Propagation constant, attenuation coefficient: If the details of the electromagnetic wave propagation inside the plasma layer are concerned, its equivalent propagation constant and attenuation coefficient can be analyzed.

[0113] ④ Field distribution: The distributions of the electric field, magnetic field, or power flow density around the aircraft and inside the plasma sheath can be visualized to intuitively understand the interaction process of the electromagnetic wave and the plasma (such as refraction, reflection, absorption).

[0114] As Figure 5 shown, this figure shows the curve of the RCS attenuation caused by the plasma sheath of the RAMC aircraft obtained by simulating the method of the present invention under the conditions of H = 20 km, Ma = 19.2, a = 0, varying with frequency (for example, 2 - 18 GHz) (as shown by the solid line "H = 20, Ma = 19.2, a = 0 (simulation)" in Figure 5 ). Through such curves, the influence of the plasma sheath on the radar stealth performance at different frequencies can be quantitatively evaluated.

[0115] Through the above steps, the key electromagnetic characteristics of the plasma sheath of the hypersonic aircraft can be systematically obtained, providing important theoretical basis and data support for the design of the aircraft, communication guarantee, target recognition, and stealth performance evaluation, etc.

[0116] In addition, an embodiment of the present invention further relates to a system for simulating the electromagnetic characteristics of a plasma sheath of a hypersonic vehicle, which includes a processor; and a memory. When the instructions stored in the memory are executed by the processor, the system executes the method as described above.

[0117] Specifically, the system can be a general-purpose computer system, such as a personal computer (PC), a workstation, a server, or a dedicated computing device or a distributed computing cluster. The system includes a processor and a memory.

[0118] Among them, the processor can be a central processing unit (CPU), a graphics processing unit (GPU), a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or any combination of these processing units. The processor is responsible for executing computer-executable instructions stored in the memory to implement the simulation method described in the present invention. In some embodiments, a multi-core processor or multiple processors can work in parallel to improve the computing efficiency, especially for the computationally intensive fluid simulation and electromagnetic simulation steps.

[0119] The memory can be a volatile memory (such as a random access memory RAM) and / or a non-volatile memory (such as a read-only memory ROM, a hard disk drive HDD, a solid-state drive SSD, a flash memory, etc.). The memory is used to store: an operating system; a computer program (or multiple program modules) for implementing the simulation method described in the present invention. For example, it may include a CFD simulation module, a plasma parameter calculation module, a geometric modeling module, an electromagnetic simulation module, and a data post-processing and visualization module; input data required during the simulation, such as the geometric model data of the vehicle, flight parameters, a material property library, etc.; intermediate data and final result data generated during the simulation, such as flow field data, electron density / temperature distribution data, a layered model data, electromagnetic characteristic results, etc.

[0120] In addition, the system may further include an input / output interface, which is used for the system to interact with external devices or users. It can include: input devices: such as a keyboard, a mouse, a touch screen, a data import interface, etc., for users to input instructions, set simulation parameters, import geometric models, etc.; output devices: such as a display, a printer, a data export interface, etc., for displaying the simulation process, visualizing the simulation results (such as graphics, curves, contour maps), outputting reports, etc.; a network interface: such as an Ethernet card, a Wi-Fi module, etc., for the system to connect to a network for data exchange, remote access, or distributed computing.

[0121] When the system executes the simulation method of the present invention, the processor loads and executes the corresponding computer program instructions from the memory. Specifically: the user provides the geometric model data and flight parameters of the hypersonic vehicle to the system through the input device; the processor calls the corresponding program module to execute the method steps described in the above embodiments; the simulation results can be displayed, visualized or exported through the output device.

[0122] In this embodiment, the memory can be regarded as a non-transitory computer-readable storage medium, on which there is a computer program that can implement the method of the present invention when executed by the processor.

[0123] The above description of the specification and embodiments is used to explain the protection scope of the present invention, but does not constitute a limitation on the protection scope of the present invention. Through the inspiration of the present invention or the above embodiments, those of ordinary skill in the art, combined with common general knowledge, ordinary technical knowledge in the art and / or the prior art, can obtain modifications, equivalent replacements or other improvements to the embodiments of the present invention or some of its technical features through logical analysis, reasoning or limited experiments, which should all be included in the protection scope of the present invention.

Claims

1. A simulation method for the electromagnetic characteristics of the plasma sheath of a hypersonic vehicle, characterized in that It includes the following steps: Step 1: Perform fluid simulation based on the geometric shape and flight parameters of the hypersonic vehicle to obtain flow field information including the plasma sheath region; Step 2: Based on the flow field information, determine the simulation parameters at various locations in the plasma sheath space, where the simulation parameters at least include electron density distribution and electron collision frequency distribution; Step 3: Based on the simulation parameters, establish a three-dimensional model of the plasma sheath, and layer the three-dimensional model according to the electron density distribution to form a layered three-dimensional model composed of multiple plasma layers, where each plasma layer has an electron density and collision frequency within a preset range; Step 4: Based on the layered three-dimensional model, establish a non-uniform distribution electromagnetic simulation model of the plasma sheath, where the electromagnetic characteristics of each plasma layer in the model are set according to the simulation parameters determined in Step 2; Step 5: Perform mesh division on the non-uniform distribution electromagnetic simulation model and use a numerical solver for numerical calculation to obtain the electromagnetic characteristics of the plasma sheath.

2. The electromagnetic characteristic simulation method of the plasma sheath of a hypersonic vehicle according to claim 1, characterized in that The fluid simulation in Step 1 includes: solving the fluid dynamics equation using the finite volume method and updating the flow field parameters through iterative operations until a converged state is reached; the flow field information includes density, temperature, pressure, and heat flux.

3. The electromagnetic characteristic simulation method of the plasma sheath of a hypersonic vehicle according to claim 1 or 2, characterized in that The fluid simulation in Step 1 also includes considering the influence of the applied external electromagnetic field on the flow field.

4. The electromagnetic characteristic simulation method of the plasma sheath of a hypersonic vehicle according to claim 1, characterized in that In Step 2, a chemical reaction model is used to simulate the formation process of the plasma sheath to determine the electron density distribution; the electron collision frequency distribution is determined by the fluid simulation analysis.

5. The electromagnetic characteristic simulation method of the plasma sheath of a hypersonic vehicle according to claim 1, characterized in that, In Step 3, the three-dimensional model of the plasma sheath is layered according to a preset electron density threshold or electron density range. The electron density of each plasma layer is approximately uniform within the preset range, and each plasma layer has separately settable material properties.

6. The electromagnetic characteristic simulation method of the plasma sheath of a hypersonic vehicle as described in claim 1, characterized in that, The non-uniform distribution electromagnetic simulation model established in Step 4 uses the Drude model to describe the electromagnetic characteristics of each layer of the plasma sheath; the parameters of the Drude model are set according to the simulation parameters determined in Step 2.

7. The electromagnetic characteristic simulation method of the plasma sheath of a hypersonic vehicle according to claim 6, characterized in that The formula of the Drude model is as follows: where ω p , ω and ν represent the angular frequency of plasma electron oscillation, the angular frequency of the incident radar wave, and the plasma electron collision frequency, respectively; ne is the plasma electron density.

8. The electromagnetic characteristic simulation method of the plasma sheath of a hypersonic vehicle according to claim 7, characterized in that, In Step 5, the boundary region of the plasma sheath or the region where the electron density changes violently is refined in mesh; and mesh independence verification is performed by gradually densifying the mesh and comparing the changes in the calculation results.

9. The electromagnetic characteristic simulation method of the plasma sheath of a hypersonic vehicle according to claim 8, characterized in that, The numerical solver in Step 5 is a time-frequency domain solver.

10. A system for simulating the electromagnetic characteristics of the plasma sheath of a hypersonic vehicle, characterized in that, It includes: a processor; and a memory storing instructions, which when executed by the processor cause the system to execute the method according to any one of claims 1 to 9.

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