A photoionization computational model for pure SF6 gas streams, its construction method, and its application.

Abstract

This invention belongs to the field of plasma fluid modeling technology, and relates to a photoionization calculation model for pure SF6 gas streams, its construction method, and its application. The process includes: constructing a quantitative photoionization source term integral model based on specific SF6 spectral data; fitting the pressure-reduced absorption function into an exponential sum form to obtain an exponential absorption function model, substituting it into the integral model to obtain the total photoionization source term model and Helmholtz-type partial differential equations; determining the quenching pressure and average photoionization efficiency, and calibrating the ionizing radiation efficiency through simulation; fitting Helmholtz parameters at various pressure points over a wide atmospheric pressure range to form a standard data lookup table. This invention can solve the problems of missing nonlocal effects, poor numerical convergence, and low prediction accuracy of stream structure and breakdown voltage caused by simplification in existing models, and can more realistically reflect the impact of photoionization on stream propagation dynamics.

Description

Technical Field

[0001] This invention belongs to the field of plasma fluid modeling technology, specifically relating to a photoionization calculation model for pure SF6 gas streams, its construction method, and its application. Background Technology

[0002] Sulfur hexafluoride (SF6) gas has been widely used as a key insulating medium in gas-insulated electrical equipment (such as GIS and GIL) for nearly 70 years due to its excellent insulation and arc-quenching properties. Under the influence of a high-voltage electric field, streamer discharge may occur in SF6, which is a critical early stage in the gas breakdown process. The morphology, propagation dynamics, and whether the streamer will eventually lead to complete breakdown (i.e., the formation of a through-conductive channel) directly determine the reliability of the insulation system. Therefore, accurate simulation and prediction of streamer discharge in SF6 is of significant engineering and scientific importance for the design, insulation performance evaluation, and fault early warning of high-voltage electrical equipment.

[0003] In numerical simulations of SF6 streamers, plasma-fluid models are the mainstream tool for analyzing their spatiotemporal microscopic properties. However, as a highly electronegative gas, SF6 discharge simulations face challenges such as spatial numerical convergence difficulties, especially in the trailing edge region of the stream head. Due to strong electron attachment and electric field shielding effects, a steep electron density gradient forms, making computational convergence difficult. Photoionization is considered a key physical mechanism for providing seed electrons to these regions, thereby alleviating the convergence problem. Currently, in the simulation of streamer fluids for pure SF6 or SF6-containing mixtures, the photoionization source term... There are several approximate or simplified methods for processing this: 1) Constant source term approximation: Some studies directly set a spatially uniform photoionization source term S0 in the simulation and use a fixed constant term to replace the actual photoionization process.

[0004] 2) Background ionization approximation: Another part of the study uses a pre-set uniform initial electron density n0 in the computational domain to equivalently simulate the background seed electrons provided by photoionization.

[0005] 3) Simplified or qualitative models: Some works have used other simplified alternative methods to qualitatively model SF6 photoionization, but these models usually lack sufficient quantitative evidence and are difficult to meet the needs of accurate prediction.

[0006] 4) Explicit particle simulation: Although explicit dynamic methods such as particle mesh models exist to simulate photoionization, their computational cost is extremely high, making them unsuitable for fluid simulation frameworks for large-scale engineering problems. Despite the fact that photoradiation has been identified as a key parameter controlling SF6 discharge, to date, a quantitative, accurate, and computationally efficient pure SF6 photoionization calculation model is still lacking within a framework applicable to engineering fluid simulation.

[0007] Based on the closest existing technology mentioned above, its main defects and shortcomings are as follows: 1) Inability to accurately simulate the nonlocal effects of photoionization: Both the constant source term and background ionization are spatially uniformly distributed, completely ignoring the nonlocal nature of photoionization. The actual photoionization rate depends on the integral contribution of all radiation source points in space, exhibiting distinctly different behavior at the leading and trailing edges of the stream head. Existing simplification methods destroy this physical property.

[0008] 2) Distortion in Streamer Structure Prediction: Due to the inability to accurately simulate nonlocal effects, using a constant source term results in an abnormally diffuse space charge distribution at the streamer head, underestimating electron density and peak electric field, and leaving unrealistically high electron density within the streamer channel. This prevents the simulation from accurately reproducing the typical coherent structure of "isolated streamer head and ion-conducting channel" in highly electronegative gases, thus reducing the accuracy of streamer morphology and spatial structure predictions.

[0009] 3) Inability to effectively guarantee numerical convergence: In highly electronegative gases such as SF6, the electron depletion region at the trailing edge of the stream head is a major challenge for numerical convergence. Background ionization cannot specifically replenish seed electrons in this region, leading to potential computational interruptions or convergence failures even when using fine meshes. Existing simplification methods have limited effectiveness or are unreliable in improving spatial numerical convergence.

[0010] 4) Impact on Breakdown Voltage Prediction Accuracy (Especially for Positive Streams): Photoionization intensity has a significant impact on stream development, especially the breakdown threshold of positive streams. Existing technologies, due to the inaccuracy of the models themselves, struggle to provide a reliable reference for photoionization intensity. Artificially enhancing photoionization to "improve convergence" (e.g., simply amplifying the source term by 50 times) will lead to a severe underestimation of the positive stream breakdown voltage (an error exceeding 0.5 kV), thus significantly reducing the engineering practicality of breakdown voltage prediction.

[0011] 5) Twisted Stream Propagation Dynamics: Artificially enhanced photoionization intensity significantly alters the propagation dynamics of a normal stream. This leads to a non-physical increase in the head radius of the normal stream and a substantial decrease in its head electric field intensity (exceeding 700 Td), which is inconsistent with actual physical processes. Existing models lack an accurate benchmark, thus failing to reliably assess the true impact of photoionization on propagation dynamics and making them unsuitable for studying complex phenomena such as stream bifurcation.

[0012] In summary, the fundamental problem with existing photoionization simulation methods is that they sacrifice physical realism in pursuit of computational convergence. This sacrifice ultimately results in simulation results that neither conform to the actual physical process nor meet the accuracy and reliability required for engineering design. In SF6 streamer discharge simulations, the physical realism, numerical convergence, and engineering accuracy of the photoionization model cannot be simultaneously achieved. Summary of the Invention

[0013] The purpose of this invention is to provide a photoionization calculation model for pure SF6 gas streams, its construction method, and its application, which solves the problems in existing simulation technologies caused by the use of simplification methods such as constant source terms and background ionization, including the lack of nonlocal effects, difficulty in numerical convergence, distortion in stream structure prediction, insufficient accuracy in breakdown voltage (especially in positive streams), and inability to truly reflect the influence of photoionization on propagation dynamics.

[0014] This invention is achieved through the following technical solution: A method for constructing a photoionization computational model for a pure SF6 gas stream includes the following steps: Construct a quantitative photoionization source term integral model based on specific SF6 spectral data; By fitting the pressure-reduced absorption function into an exponential sum form, we obtain the exponential absorption function model. Substituting the exponential absorption function model into the quantitative photoionization source term integral model yields the total photoionization source term model and the Helmholtz-type partial differential equation. Determine the quenching pressure and average photoionization efficiency required in the quantitative photoionization source term integral model; calibrate the ionizing radiation efficiency required in the quantitative photoionization source term integral model through simulation experiments; Within a wide atmospheric pressure range, for each selected pressure point, the exponential absorption function model is fitted to obtain a set of corresponding Helmholtz parameters, thus obtaining the Helmholtz parameters for all pressure points and forming a standard data lookup table. The standard data lookup table is used to find the Helmholtz parameters for a certain pressure point and substitute them into a Helmholtz-type partial differential equation.

[0015] Furthermore, the expression for the quantitative photoionization source term integral model is: (1) in, Here, is the absorption function, used to describe the probability that a photon arrives at the observation point without being absorbed; Represents the radiation source point Photon yield at a given location is used to describe the number of effective photons emitted per unit volume per unit time. The space representing the integral; k represents the characteristic wavelength of ionizing radiation.

[0016] Furthermore, the expression for the exponential absorption function model is: ; in, The number of exponent terms, and These are Helmholtz parameters; Here, is the absorption function, used to describe the probability that a photon arrives at the observation point without being absorbed; The distance between two points; For the observation point, As the radiation source point; This is the working air pressure.

[0017] Furthermore, the expression for the total photoionization source term model is: ; For observation point Photoionization source term at the location, For observation point The first j Photoionization source term; The number of exponent terms; The expression for the Helmholtz-type partial differential equation model is as follows:

[0018] in, and These are Helmholtz parameters; For observation point Photon yield at the location; For gradient operators; Working air pressure; ; in, This represents the average photoionization efficiency. To excite the frequency, The ionization frequency, For ionizing radiation efficiency; To quench the air pressure; The collisional ionization yield.

[0019] Furthermore, the expression for the collisional ionization yield is: ; The ionization coefficient; Electron density; For electron mobility, denoted as electric field strength.

[0020] Furthermore, the recommended value for ionizing radiation efficiency is... ; .

[0021] Furthermore, the wide atmospheric pressure range is the operating range of 1 to 15 atmospheres.

[0022] This invention also discloses a photoionization calculation model for pure SF6 gas streams, including a total photoionization source term model, a Helmholtz-type partial differential equation model, a photon yield calculation model, and a standard data lookup table; The expression for the total photoionization source term model is: ; For observation point Photoionization source term at the location, For observation point The first j Photoionization source term; The number of exponent terms; The expression for the Helmholtz-type partial differential equation model is as follows:

[0023] in, and These are Helmholtz parameters; For observation point Photon yield at the location, For gradient operators; Working air pressure; The expression for the photon yield calculation model is as follows: ; in, This represents the average photoionization efficiency. To excite the frequency, The ionization frequency, For ionizing radiation efficiency; To quench the air pressure; For collisional ionization yield; The standard data lookup table is a table relating pressure points to Helmholtz parameters, used to find the corresponding working pressure. The next set of Helmholtz parameters and .

[0024] Furthermore, the expression for the collisional ionization yield is: ; The ionization coefficient; Electron density; For electron mobility, denoted as electric field strength.

[0025] This invention also discloses the application of the aforementioned photoionization calculation model for pure SF6 gas streams, comprising the following steps: Obtain the working air pressure and find a set of Helmholtz parameters for the corresponding working air pressure according to the standard data lookup table; The average photoionization efficiency, ionizing radiation efficiency, quenching pressure, and collisional ionization yield are obtained and input into the photon yield calculation model to solve for the observation points. Photon yield at the location; observation point The photon yield at the observation point, along with the Helmholtz parameters, is input into a Helmholtz-type partial differential equation model to obtain the results. The first j Photoionization source term; observation point The first j The photoionization source term is input into the total photoionization source term model, and the output observation point is... Photoionization source term at the location.

[0026] Compared with the prior art, the present invention has the following beneficial technical effects: This invention discloses a method for constructing a photoionization calculation model for pure SF6 gas streams. The method involves constructing a quantitative photoionization source term integral model; fitting the pressure-reduced absorption function into an exponential form; substituting these forms to obtain the total photoionization source term model and the Helmholtz equations; calibrating the quenching pressure, average photoionization efficiency, and ionizing radiation efficiency; and generating a standard database of Helmholtz parameters over a wide pressure range (1-15 atm). This method achieves efficient transformation of complex integral operations. By converting the nonlinear photoionization integral model into linear Helmholtz partial differential equations, and transforming the nonlocal integral operations in three-dimensional space into a system of differential equations solvable by mature numerical algorithms, the computational complexity is greatly reduced, and the solution speed and convergence of the stream simulation software are improved.

[0027] By systematically calibrating parameters within a typical engineering application range of 1 to 15 atmospheres (covering breakdown scenarios from slightly non-uniform electric fields to extremely non-uniform electric fields), the generated standard data lookup table covers the main operating range of SF6 gas, ensuring the universality and accuracy of the model under different voltage levels and equipment gas pressure configurations, and avoiding the problem of poor adaptability to operating conditions caused by a single parameter.

[0028] This method clarifies the microscopic physical quantity (photon yield) absorption function The complete mapping path from the photoionization process to the macroscopic simulation model (Helmholtz equation) ensures that the physical mechanism of the photoionization process is faithfully reproduced in the model, rather than being a simple black-box fit.

[0029] This invention also discloses the application of the aforementioned photoionization calculation model. By introducing a standard data lookup table to dynamically match Helmholtz parameters under different working gas pressures, and combining it with a photon yield calculation model that includes key parameters such as average photoionization efficiency and quenching pressure, it avoids the drawbacks of traditional methods that use fixed empirical coefficients or simplified assumptions. This refined parameter coupling mechanism can realistically reflect the photoionization characteristics of SF6 gas under different microscopic pressure environments, making the calculated photon yield at the observation point and subsequent photoionization source terms more consistent with the actual physical process, thus ensuring the accuracy of the simulation results from the source. The total photoionization source term is the core indicator for quantifying the ability of photoionization to induce free electrons. It is used to drive discharge evolution calculations, evaluate insulation reliability, conduct mechanism studies, and provide a basis for the structural optimization and safe operation of high-voltage electrical equipment. Attached Figure Description

[0030] Figure 1 To reduce the electric field E / N and electron density n under different photoionization models and different voltage polarities e The spatiotemporal evolution simulation results; Figure (a) shows the spatiotemporal evolution simulation results using the photoionization calculation model of the present invention with U0 = +7.8 kV; Figure (b) shows the spatiotemporal evolution simulation results using the photoionization calculation model of the present invention, with U0 = -7.8 kV; Figure (c) shows the constant source terms. =5×10 27 m 3 s 1 The spatiotemporal evolution simulation results for U0 = +7.8 kV; Figure (d) shows the constant source terms. =5×10 27 m 3 s 1 The spatiotemporal evolution simulation results for U0 = -7.8 kV; Figure (e) shows the background ionization. n 0=10 13 m 3 The spatiotemporal evolution simulation results for U0 = +7.8 kV; Figure (f) shows the background ionization. n 0=10 13 m 3 The spatiotemporal evolution simulation results for U0 = -7.8 kV. Detailed Implementation

[0031] To make the objectives, technical solutions, and advantages of the present invention clearer, the following detailed description is provided in conjunction with embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention; that is, the described embodiments are only a portion of, and not all, of the embodiments of the present invention.

[0032] The detailed description of the embodiments of the present invention provided below is not intended to limit the scope of the claimed invention, but merely to illustrate one selected embodiment of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0033] This invention discloses a method for constructing a computational model of pure SF6 gas stream photoionization, comprising the following steps: Construct a quantitative photoionization source term integral model based on specific SF6 spectral data; By fitting the pressure-reduced absorption function into an exponential sum form, we obtain the exponential absorption function model. Substituting the exponential absorption function model into the quantitative photoionization source term integral model yields the total photoionization source term model and the Helmholtz-type partial differential equation. Determine the quenching pressure and average photoionization efficiency required in the quantitative photoionization source term integral model; calibrate the ionizing radiation efficiency required in the quantitative photoionization source term integral model through simulation experiments; Within a wide atmospheric pressure range, for each selected pressure point, the exponential absorption function model is fitted to obtain a set of corresponding Helmholtz parameters, thus obtaining the Helmholtz parameters for all pressure points and forming a standard data lookup table. The standard data lookup table is used to find the Helmholtz parameters for a certain pressure point and substitute them into a Helmholtz-type partial differential equation.

[0034] The construction of the quantitative photoionization source term integral model based on specific SF6 spectral data specifically includes the following steps: S1.1: Establishing the theoretical foundation of the model The Zheleznyak photoionization model was used as the framework, and the observation points were... Photoionization source at the location By the definition of space integral: (1) in, Here, is the absorption function, used to describe the probability that a photon arrives at the observation point without being absorbed; The distance between two points; Represents the radiation source point Photon yield at a given location is used to describe the number of effective photons emitted per unit volume per unit time. The space representing the integral; The characteristic wavelength representing ionizing radiation.

[0035] S1.2: Identifying and calibrating the characteristic spectra of SF6 gas Focusing on wavelength The vacuum ultraviolet light band (corresponding to the ionization threshold of SF6 gas, 15.7 eV) was used. It was confirmed that within this band, FI (neutral fluorine atom) radiation is the main contributor to photoionization, while the contribution of FII (primarily ionized fluorine ions) radiation is negligible.

[0036] Based on the measured SF6 emission spectrum, the relative intensities of the main FI radiation lines (including 78.1 nm, 75.1 nm, and 71.1–73.6 nm) were corrected using absolute cross-sectional data, resulting in the calibrated intensity ratios. This forms a standard spectrum for subsequent quantitative analysis.

[0037] The radiation band corresponding to 78.1 nm (FI(3d) level) can be regarded as the dominant radiation of SF6 photoionization, while the 75.1 nm band (FI(4d,5s) level) is related to the photoionization source term. The contribution can be mathematically represented as the contribution to Apply a multiplier factor The contribution of radiation in the 71.1–73.6 nm range to photoionization is negligible.

[0038] in, The excitation frequency is in the 78.1nm band. It is the ionization frequency; It is the ionizing radiation efficiency (the ratio of excitation frequency to ionization frequency).

[0039] Constructing the exponential absorption function model involves the following steps: S2.1: Establish the analytical model of the absorption function. This step aims to obtain the absorption function. The parsed or semi-analyzed expression.

[0040] The pressure-reduced absorption function is calculated by the following formula: (2) The integration range is the wavelength range of the radiation under consideration (for 78.1nm radiation, we take 77.2-79nm). The spectrally resolved photoionization efficiency can be calculated as follows: ; and These are the photoionization cross section and light absorption cross section of SF6, respectively. The pressure-reduced spectral absorption coefficient can be calculated as follows: , Boltzmann's constant; The temperature of the stream gas; The spectral absorption coefficient represents wavelength resolution.

[0041] S2.2: Numerical solution of the absorption function Input the above standard spectral and cross-sectional data into the PHOTOPIC software, and numerical solutions will yield different results. Discrete data points under the value The cross-sectional data here includes... and .

[0042] S2.3: Fit the absorption function to an exponential sum form. The data obtained in step S2.2 is fitted into the following form to facilitate subsequent transformation into differential equations: (3) in, The number of exponent terms, and These are Helmholtz parameters.

[0043] As a preferred embodiment of the present invention, taking To achieve the best balance between computational accuracy and efficiency.

[0044] For the fitting method, optimization algorithms such as the Nelder-Mead simplex direct search method are used to calculate the data. For the target, for the parameters Perform a fitting operation. Save the results; this is the Helmholtz parameter set at a given atmospheric pressure.

[0045] Substituting the exponential absorption function model into the quantitative photoionization source term integral model yields the total photoionization source term model and the Helmholtz-type partial differential equations. This process specifically includes the following steps: Substituting formula (3) into formula (1), and after mathematical transformation, the total photoionization source term can be decomposed as: (4) like ,but Each sub-source item Satisfies a Helmholtz-type partial differential equation: (5) in, For gradient operators; For observation point Photon yield at the location.

[0046] Photon yield The calculation expression is: ; in, This represents the average photoionization efficiency. To excite the frequency, The ionization frequency, For ionizing radiation efficiency; For collisional ionization yield, Working air pressure (unit: Torr or atm). To quench the air pressure.

[0047] The definitions, theoretical basis, and determination methods of each physical quantity are as follows: is the collisional ionization rate. Wherein, The ionization coefficient; Electron density; For electron mobility, denoted as electric field strength.

[0048] To quench the gas pressure, reflecting the collisional quenching between excited-state particles and neutral particles, the calculation is as follows: .in, Boltzmann's constant; The temperature of the stream gas; The collision quenching rate of the FI excited state; For the excited state lifetime (78.1 nm radiation of the FI(3d) level) (Approximately 20 ns). For the radiation band corresponding to 78.1 nm, the calculation yields... .

[0049] The average photoionization efficiency is expressed in terms of relative intensity. As weighted, the photoionization efficiency with spectral resolution The weighted average can be calculated as follows: For the radiation band corresponding to 78.1 nm, the calculation yields... . This represents the minimum wavelength corresponding to a specific type of ionizing radiation. It represents the maximum value of the wavelength corresponding to a specific ionizing radiation.

[0050] This is the ionizing radiation efficiency (the ratio of excitation frequency to ionization frequency). This parameter is difficult to calculate accurately using first-principles calculations and is a core adjustable parameter that needs to be calibrated experimentally for this model.

[0051] Regarding the selection strategy for the radiation wavelength, to simplify the model without sacrificing major physical accuracy, this invention only explicitly considers the contribution of 78.1 nm radiation in its implementation. Theoretical analysis and numerical tests show that the influence of secondary radiation such as 75.1 nm is mainly reflected in the... A multiplicative factor on the overall amplitude, the effect of which is already implicit in the values ​​obtained through experimental calibration. The final recommended value.

[0052] In plasma fluid simulation, at each time step, the above three scalar partial differential equations, i.e., equations (3) to (5), are solved simultaneously using numerical methods (such as the finite element method and the finite volume method) to obtain the following results. , , Summing these terms yields the final photoionization source term. The method reduces computational complexity from direct integration. The order of magnitude is reduced to solving differential equations Quantity, of which This represents the number of spatial grid cells.

[0053] The determination of the quenching pressure and average photoionization efficiency required in the quantitative photoionization source term integral model; and the calibration of the ionizing radiation efficiency required in the quantitative photoionization source term integral model through simulation experiments, specifically: 1. Determine pressure-independent parameters As mentioned earlier, the quenching pressure is determined. For the radiation band corresponding to 78.1 nm, the calculation yields... .

[0054] 2. Calibrate ionizing radiation efficiency .

[0055] This is the core step in model calibration: a. Experimental baseline acquisition: Under the conditions of rod-plate electrodes, 1 mm gap, and pure SF6 at 1 atmosphere, the maximum breakdown voltage (Max BD) was measured with the assistance of a positive polarity DC power supply and an ultraviolet lamp to obtain the voltage baseline value (approximately 7.6-7.7 kV) for breakdown dominated by the first single streamer.

[0056] b. Simulation-Experiment Iterative Comparison: The photoionization calculation model established in this invention is integrated into a two-dimensional axisymmetric fluid simulation. Positive flow stream breakdown simulation is performed under the same geometric and conditions.

[0057] c. Parameter Adjustment and Matching: Adjusting parameters in the photoionization calculation model The value was adjusted to match the simulated predicted positive streamer breakdown voltage with the experimentally measured Max BD reference value.

[0058] d. Recommended Value Determination: Based on the above comparison, the recommended value for the ionizing radiation efficiency in the local field approximation classical fluid model is determined to be... .

[0059] Within a wide atmospheric pressure range, for each selected pressure point, the exponential absorption function model is fitted to obtain a set of corresponding Helmholtz parameters. This yields the Helmholtz parameters for all pressure points, forming a standard data lookup table. The specific steps include: 1. Set the air pressure point Within the operating range of 1 to 15 atmospheres, a series of discrete pressure points (such as 1.0, 1.2, 1.5, ..., 15.0 atm) are selected.

[0060] 2. For each selected pressure point Recalculate the corresponding absorption function data points according to S2.2. ; Perform three terms on the absorption function data at this pressure ( The exponent and the fit yield a set of corresponding Helmholtz parameters. , , , , , }

[0061] 3. Assembly parameter lookup table All pressure points obtained in step S5.2 and its corresponding parameter group { , , , , , The data is organized into a structured table, as shown in Table 1. Table 1 is an important part of the model of this invention, allowing users to directly look up the table or obtain parameters through interpolation based on the simulated air pressure, without having to repeat the complex modeling and fitting process.

[0062] Table 1

[0063] Table 1 is only an example; the selection of atmospheric pressure points can be even more dense.

[0064] The following describes the integration, verification, and application of the photoionization calculation model constructed in this invention.

[0065] 1. Model Integration Implementation The photoionization calculation model constructed in the preceding steps is embedded as a physical process subroutine into commercial or self-developed plasma fluid simulation software (such as COMSOL Multiphysics with Plasma Module, or self-written FEM / FVM code). The key integration point lies in solving for the electron density. In the continuity equation, the calculated photoionization source term will be... Added as a positive source term. Numerical implementation suggestions: a. Spatial discretization: The finite element method (FEM) is used, combined with streamline diffusion to stabilize the equations for convection dominance.

[0066] b. Mesh strategy: Employing an electron density gradient-based approach The adaptive mesh refinement technology automatically refines the mesh in areas with large gradients, such as the stream head, with a minimum mesh spacing of 0.1 μm.

[0067] c. Time stepping: The implicit backward differential formula BDF method is used for time integration. The maximum BDF order is set to 2. To ensure transient accuracy, it is recommended that the maximum time step not exceed 0.1 ps.

[0068] 2. Model Validation The superiority of this invention is quantitatively verified through the following comparative simulations: Compared with the simplified model: Under the same simulation conditions, the photoionization calculation model and constant source term of this invention were run respectively. =5×10 27 m 3 s 1 Background ionization n 0=10 13 m 3 The simulation results are as follows. Figure 1 As shown, from Figure 1 As can be seen from Figures (a)-(f), only the model of this invention can simultaneously achieve stable numerical convergence, accurately capture the isolated coherent structure of the stream head, and reasonably predict the low electron density state in the channel.

[0069] Photoionization intensity sensitivity analysis: using reference intensity ( ) and reinforced strength (50× Simulations were conducted. The results show that the enhancement strength significantly underestimates the positive streamer breakdown voltage by more than 0.5 kV, and does not physically reduce the electric field at the positive streamer head by more than 700 Td or double the head radius. The baseline model of this invention, however, provides a reasonable prediction that matches the experimental results. For negative streamers, the difference is very small, demonstrating the model's applicability to discharges of different polarities.

[0070] 3. Predictive Applications The validated plasma fluid simulation program, which integrates the photoionization model of this invention, can be applied to the design and evaluation of high-voltage insulation equipment to perform the following tasks: Predict the initial discharge voltage and breakdown voltage of SF6 gas under different electrode structures (such as different radii of curvature and spacing) and different gas pressures (1-15 atm).

[0071] The dynamic propagation process of streamer discharge is simulated to obtain key dynamic parameters such as streamer velocity, head electric field, and space charge distribution.

[0072] This tool assesses the insulation strength along the insulator surface or gas gap, providing a quantitative simulation tool for insulation optimization of SF6 power equipment.

[0073] This invention also discloses the application of the aforementioned photoionization calculation model for pure SF6 gas streams, comprising the following steps: Obtain the working air pressure and find a set of Helmholtz parameters for the corresponding working air pressure according to the standard data lookup table; The average photoionization efficiency, ionizing radiation efficiency, quenching pressure, and collisional ionization yield are obtained and input into the photon yield calculation model to solve for the observation points. Photon yield at the location; observation point The photon yield at the observation point, along with the Helmholtz parameters, is input into a Helmholtz-type partial differential equation model to obtain the results. The first j Photoionization source term; observation point The first j The photoionization source term is input into the total photoionization source term model, and the output observation point is... Photoionization source term at the location.

[0074] The present invention has the following technical effects: 1) A computational model is provided that can accurately simulate the nonlocal effects of photoionization of pure SF6 gas, overcoming the physical distortion problems caused by constant source terms and background ionization approximation.

[0075] 2) A photoionization simulation method is provided that can significantly improve the numerical convergence of SF6 stream computational space in plasma fluid simulation.

[0076] 3) Provides a computational tool that can more accurately predict the spatial structure of SF6 streams (including head morphology and channel features).

[0077] 4) A photoionization model with quantitative parameters is provided to support high-precision prediction of SF6 streamer breakdown voltage (especially positive streamer breakdown voltage) and avoid systematic errors caused by inaccurate models.

[0078] 5) It provides a simulation framework that can realistically reflect the influence of photoionization intensity on the propagation dynamics of SF6 streamers (such as head contraction and electric field distribution), providing a reliable foundation for in-depth research on streamer physics.

[0079] 6) A set of SF6 photoionization model parameters covering a wide pressure range of 1-15 atmospheres and which can be directly called is provided, making the model easy to promote and apply in power engineering.

[0080] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for constructing a photoionization calculation model for a pure SF6 gas stream, characterized in that, Includes the following processes: Construct a quantitative photoionization source term integral model based on specific SF6 spectral data; By fitting the pressure-reduced absorption function into an exponential sum form, we obtain the exponential absorption function model. Substituting the exponential absorption function model into the quantitative photoionization source term integral model yields the total photoionization source term model and the Helmholtz-type partial differential equation. Determine the quenching pressure and average photoionization efficiency required in the quantitative photoionization source term integral model; calibrate the ionizing radiation efficiency required in the quantitative photoionization source term integral model through simulation experiments; Within a wide atmospheric pressure range, for each selected pressure point, the exponential absorption function model is fitted to obtain a set of corresponding Helmholtz parameters, thus obtaining the Helmholtz parameters for all pressure points and forming a standard data lookup table. The standard data lookup table is used to find the Helmholtz parameters for a certain pressure point and substitute them into a Helmholtz-type partial differential equation.

2. The method for constructing a photoionization calculation model for a pure SF6 gas stream according to claim 1, characterized in that, The expression for the quantitative photoionization source term integral model is: （1） in, Here, is the absorption function, used to describe the probability that a photon arrives at the observation point without being absorbed; Represents the radiation source point Photon yield at a given location is used to describe the number of effective photons emitted per unit volume per unit time. The space representing the integral; k represents the characteristic wavelength of ionizing radiation.

3. The method for constructing a photoionization calculation model for a pure SF6 gas stream according to claim 1, characterized in that, The expression for the exponential absorption function model is: ; in, The number of exponent terms, and These are Helmholtz parameters; Here, is the absorption function, used to describe the probability that a photon arrives at the observation point without being absorbed; The distance between two points; For the observation point, As the radiation source point; This is the working air pressure.

4. The method for constructing a photoionization calculation model for a pure SF6 gas stream according to claim 1, characterized in that, The expression for the total photoionization source term model is: ; For observation point Photoionization source term at the location, For observation point The first j Photoionization source term; The number of exponent terms; The expression for the Helmholtz-type partial differential equation model is as follows: in, and These are Helmholtz parameters; For observation point Photon yield at the location; For gradient operators; Working air pressure; ； in, This represents the average photoionization efficiency. To excite the frequency, The ionization frequency, For ionizing radiation efficiency; To quench the air pressure; The collisional ionization yield.

5. The method for constructing a photoionization calculation model for a pure SF6 gas stream according to claim 4, characterized in that, The expression for the collisional ionization yield is: ; The ionization coefficient; Electron density; For electron mobility, denoted as electric field strength.

6. The method for constructing a photoionization calculation model for a pure SF6 gas stream according to claim 4, characterized in that, The recommended value for ionizing radiation efficiency is ; .

7. The method for constructing a photoionization calculation model for a pure SF6 gas stream according to claim 1, characterized in that, The operating range is from 1 to 15 atmospheres.

8. A photoionization calculation model for pure SF6 gas streams, characterized in that, This includes a total photoionization source term model, a Helmholtz-type partial differential equation model, a photon yield calculation model, and a standard data lookup table; The expression for the total photoionization source term model is: ; For observation point Photoionization source term at the location, For observation point The first j Photoionization source term; The number of exponent terms; The expression for the Helmholtz-type partial differential equation model is as follows: in, and These are Helmholtz parameters; For observation point Photon yield at the location, For gradient operators; Working air pressure; The expression for the photon yield calculation model is as follows: ； in, This represents the average photoionization efficiency. To excite the frequency, The ionization frequency, For ionizing radiation efficiency; To quench the air pressure; For collisional ionization yield; The standard data lookup table is a table relating pressure points to Helmholtz parameters, used to find the corresponding working pressure. The next set of Helmholtz parameters and .

9. A photoionization calculation model for a pure SF6 gas stream according to claim 8, characterized in that, The expression for the collisional ionization yield is: ; The ionization coefficient; Electron density; For electron mobility, denoted as electric field strength.

10. The application of the photoionization calculation model for pure SF6 gas streams as described in any one of claims 8-9, characterized in that, Includes the following steps: Obtain the working air pressure and find a set of Helmholtz parameters for the corresponding working air pressure according to the standard data lookup table; The average photoionization efficiency, ionizing radiation efficiency, quenching pressure, and collisional ionization yield are obtained and input into the photon yield calculation model to solve for the observation points. Photon yield at the location; observation point The photon yield at the observation point, along with the Helmholtz parameters, is input into a Helmholtz-type partial differential equation model to obtain the results. The first j Photoionization source term; observation point The first j The photoionization source term is input into the total photoionization source term model, and the output observation point is... Photoionization source term at the location.

Images