Simulation method and device for streamer development process in gas medium, electronic equipment and storage medium

Abstract

The invention provides a simulation method and device for a streamer development process in a gas medium, electronic equipment and a storage medium, and belongs to the technical field of high-voltage streamer generation and emulation.The method comprises the steps that the electron mobility is calculated according to gas components; calculating electric field distribution; according to the electric field distribution and the electron mobility, the average electron velocity is solved; generating a random number as the electron speed of the subdivision grid by using the elastic collision probability distribution; updating an electron position by using a microscopic electron migration equation to obtain electron density, and solving a macroscopic ion drift equation to obtain updated positive ion density and negative ion density; and calculating collision reaction among different particles by using an improved stochastic dynamics analysis method to obtain re-updated electron density, positive ion density and negative ion density, carrying out iterative calculation until the set simulation time is reached, and outputting a result. According to the method, the randomness of the discharge process can be simulated, the time step length is not limited by CFL conditions, and the calculation efficiency is higher.

Description

Technical Field

[0001] The present invention relates to the technical field of high-voltage streamer generation and simulation, and in particular to a simulation method, device, electronic equipment and storage medium for a streamer development process in a gas medium. Background Art

[0002] Streamer discharge is a key form of gas discharge, commonly occurring in gas gaps under high voltage. It is a critical stage in the breakdown process. Lightning, a common phenomenon in nature, is triggered by air streamer discharges caused by the high electric field generated by accumulated charges within thunderclouds. Similarly, power equipment operating at high voltages can easily trigger streamer discharges in gases, such as corona discharges in transmission lines and surface flashovers on transmission line insulators. Understanding the mechanism of streamer discharge is crucial for improving the insulation performance of power equipment.

[0003] Numerical simulation is an effective method for studying streamer development and discharge mechanisms. Common streamer simulation models include fluid models, particle models, and fluid-particle hybrid models. The fluid model is the most commonly used method for streamer simulation. This model treats the plasma as a continuous medium and describes the discharge process by solving the macroscopic transport equations of charged particles. However, the fluid model has the following problems: it ignores the microscopic collision process between particles and cannot simulate the random characteristics of streamer discharge. The time step of the fluid model needs to meet the Courant-Friedrichs-Lewy (CFL) condition, but the electron velocity in the strong electric field region is extremely high, resulting in an extremely short simulation step size, which reduces the computational efficiency of the fluid model. Summary of the Invention

[0004] To address the above issues, the present invention provides a simulation method, device, electronic device and storage medium for the streamer development process in a gas medium, which can simulate the randomness of the discharge process and the time step is not restricted by the CFL conditions, thereby improving the computational efficiency.

[0005] The present invention provides a method for simulating the flow development process in a gas medium, comprising: defining gas components and calculating electron mobility required for simulation based on the gas components; Calculating the electric field distribution in the simulation area, and solving the average electron velocity of all the grids according to the electric field distribution and the electron mobility; Based on the average electron velocity, a random number is generated using an elastic collision probability distribution, and the obtained random number is used as the electron velocity of the grid; Based on the electron velocity, the electron position is updated using a microscopic electron migration equation to obtain an updated electron quantity, the electron density is obtained based on the electron quantity, and a macroscopic ion drift equation is solved to obtain updated positive ion density and negative ion density; Calculating a reaction rate required for the simulation, and calculating collision reactions between different particles based on the reaction rate using an improved stochastic kinetic analysis method to obtain updated numbers of electrons, positive ions, and negative ions, thereby obtaining updated electron density, positive ion density, and negative ion density; The electric field distribution, the electron density, the positive ion density and the negative ion density in the simulation area are iteratively calculated until the set simulation time is reached, and the electric field distribution, electron density, positive ion density and negative ion density results are output to analyze the streamer development process.

[0006] As a further improvement of the present invention, the electric field distribution is calculated by the following formula:

[0007] Where, For the +1 simulation step of the electric field strength vector, Δ t is the time step of the streamer simulation, For the The space charge density of the simulation step is ε is the gas dielectric constant, is the elementary charge, For the The charge number of the particle, For the The particle in the The mobility of the simulation step, For the i The particle in the The density of simulation steps, is the divergence operator.

[0008] As a further improvement of the present invention, based on the calculated electric field distribution and the electron mobility, the average electron velocity of all meshes is solved by the following formula:

[0009] Where, is the average electron velocity, E is the amplitude of the electric field intensity; μ ( E ) is the electron mobility, which is a function of the electric field strength amplitude.

[0010] As a further improvement of the present invention, the method of generating random numbers based on the average electron velocity using the elastic collision probability distribution and using the obtained random numbers as the electron velocity of the grid includes generating random numbers that conform to the gamma distribution. , and then the random number that conforms to the elastic collision probability distribution is calculated by the following formula:

[0011] Where, is the electron speed, β is the coefficient; Among them, the elastic probability distribution of electron velocity is:

[0012]

[0013] Where, is the probability density function of the electron velocity, is the electron velocity, Γ is the Gamma function, is the average electron velocity.

[0014] As a further improvement of the present invention, the gamma distribution is Gamma (0.75, 1).

[0015] As a further improvement of the present invention, the microscopic electron migration equation is:

[0016] Where, For the +1 simulation step of the electron coordinate vector, For the The electron coordinate vector of the simulation step length, For the +1 simulation step of the electric field strength vector, For the +1 simulation step length of the electric field intensity amplitude, is the simulation step size, is the electron velocity of the mesh; The macroscopic ion drift equation is:

[0017] Where, For the k +1 simulation step of ion density, For the k The ion density of the simulation step is For the k The ion source term of simulation steps is For the k +1 simulation step of the electric field strength vector, μ i is the mobility of the ions, is the simulation step size, is the divergence operator.

[0018] As a further improvement of the present invention, the method of calculating the collision reaction between different particles using the improved stochastic dynamics analysis method includes: Setting the simulation time for dynamics analysis t r It is time 0; Computational time step for kinetic analysis ; Time step based on dynamic analysis , generates a binomial distribution ( , ) ,in For the The number of particles, Indicates the The probability of a collision reaction occurring; Based on random numbers , calculate the time step of a dynamic analysis The vector of all particles after ; Set the simulation time for the dynamic analysis to t r Updated to t r = t r + ; Comparing simulation times for dynamics analysis t r and streamer simulation step Δ t , if the simulation time of the dynamic analysis t r Less than the streamer simulation step Δ t , repeat except setting the simulation time of dynamic analysis t r The above steps except time 0; if the simulation time of dynamic analysis t r Not less than streamer simulation step Δ t , then the above iterative process is terminated, and the vector consisting of all the particles finally obtained is X ( t r ) as the updated number of electrons, positive ions and negative ions.

[0019] The present invention provides a simulation device for the flow injection development process in a gas medium, comprising a gas component definition module, an iterative solution module, and a result output module; The gas component definition module is used to define gas components; The iterative solution module is used to iteratively calculate the electric field distribution, electron density, positive ion density and negative ion density in the simulation area according to the gas composition until a set simulation time is reached; The result output module is used to output the electric field distribution, electron density, positive ion density and negative ion density in the simulation area after the simulation time is reached, so as to analyze the streamer development process; The iterative solution module includes a first calculation unit, a second calculation unit, a third calculation unit, a fourth calculation unit, and a fifth calculation unit; The first calculation unit is used to calculate the electron mobility required for simulation according to the gas composition; The second calculation unit is used to calculate the electric field distribution in the simulation area, and solve the average electron velocity of all the grids according to the calculated electric field distribution and the electron mobility; The third calculation unit is configured to generate a random number based on the average electron velocity using an elastic collision probability distribution, and use the obtained random number as the electron velocity for meshing; The fourth calculation unit is configured to update the electron position according to the electron velocity using a microscopic electron migration equation to obtain an updated electron quantity, obtain an electron density based on the electron quantity, and solve a macroscopic ion drift equation to obtain an updated positive ion density and a negative ion density; The fifth calculation unit is used to calculate the reaction rate required for the simulation. Based on the reaction rate, the improved stochastic dynamics analysis method is used to calculate the collision reaction between different particles to obtain the updated number of electrons, positive ions, and negative ions, so as to obtain the updated electron density, the positive ion density, and the negative ion density.

[0020] The present invention provides an electronic device comprising a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the simulation method of the flow development process in the gas medium.

[0021] The present invention provides a storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of the simulation method of the flow development process in the gas medium are realized.

[0022] The present invention provides a simulation method, device, electronic device and storage medium for the streamer development process in a gas medium. The elastic collision probability distribution is used to randomly generate the electron velocities of all subdivided grids, fully considering the randomness of the electron motion process and more in line with the random characteristics of actual discharge. The microscopic electron migration equation is used to describe the electron motion process, solving the problem that the time step of the streamer simulation needs to meet the CFL condition, resulting in an extremely short simulation step and low computational efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 4 is a flow chart of a method for simulating a flow injection development process in a gas medium according to an embodiment of the present invention.

[0024] Figure 2 It is a schematic diagram of a simulation geometric model of Example 1 in the simulation method of the streamer development process in a gas medium according to an embodiment of the present invention.

[0025] Figure 3 This is a schematic diagram of the electron density evolution obtained by simulating the streamer development process in the gas medium according to Example 1 using the simulation method of the embodiment of the present invention.

[0026] Figure 4 This is a schematic diagram of the electron density evolution obtained by fluid model simulation in Example 1.

[0027] Figure 5 This is a schematic diagram of the electron density evolution obtained by simulating the streamer development process in the gas medium according to Example 2 using the simulation method of the embodiment of the present invention.

[0028] Figure 6 This is a schematic diagram of the electron density evolution obtained by fluid model simulation in Example 2.

[0029] Figure 7 3 is a schematic structural diagram of a simulation device for a flow development process in a gas medium according to an embodiment of the present invention.

[0030] Explanation of the accompanying drawings: 1. Gas component definition module; 2. Iterative solution module; 21. First calculation unit; 22. Second calculation unit; 23. Third calculation unit; 24. Fourth calculation unit; 25. Fifth calculation unit; 3. Result output module. DETAILED DESCRIPTION

[0031] The following is a combination of specific embodiments and appendix Figure 1-7 The invention is described in detail so that those skilled in the art can more fully understand the purpose, features and effects of the invention.

[0032] Unless otherwise defined, all technical and scientific terms used herein have the same meanings as commonly understood by those skilled in the art to which the invention belongs. In the event that the definition of a term in the present invention conflicts with the meaning commonly understood by those skilled in the art to which the invention belongs, the definition in the present invention shall prevail.

[0033] The present invention provides a simulation method, device, electronic device and storage medium for the flow development process in a gas medium, taking into account the microscopic motion process of charged particles and the collision between particles, to solve the technical problems that the fluid model cannot simulate the randomness of the discharge process and the time step is limited by the CFL conditions.

[0034] Example 1 As a specific embodiment of the present invention, this embodiment provides a simulation method for the flow development process in a gas medium, referring to Figure 1 , the specific steps are as follows: S100, defining gas components, and calculating electron mobility required for simulation based on the gas components; S200, calculating the electric field distribution in the simulation area, and solving the average electron velocity of all the grids according to the electric field distribution and the electron mobility; S300, based on the average electron velocity, using elastic collision probability distribution to generate a random number, and using the obtained random number as the electron velocity for grid division; S400, updating the electron position according to the electron velocity using a microscopic electron migration equation to obtain an updated electron quantity, obtaining an electron density based on the electron quantity, and solving a macroscopic ion drift equation to obtain updated positive ion density and negative ion density; S500, calculating a reaction rate required for simulation, and calculating collision reactions between different particles based on the reaction rate using an improved stochastic kinetic analysis method to obtain updated numbers of electrons, positive ions, and negative ions, thereby obtaining updated electron density, positive ion density, and negative ion density; S600, iteratively calculate the electric field distribution, the electron density, the positive ion density and the negative ion density in the simulation area until the set simulation time is reached, and output the electric field distribution, electron density, positive ion density and negative ion density results to analyze the streamer development process.

[0035] In this embodiment, the electric field distribution, the electron density, the positive ion density and the negative ion density in the simulation area are iteratively solved through S200-S500 until the set simulation time is reached, and the evolution results of the electric field distribution and particle density can be obtained, and then the streamer development process can be analyzed.

[0036] The simulation method for the streamer development process in the gas medium of this embodiment uses the elastic collision probability distribution to randomly generate the electron velocity of all subdivided grids, fully considering the randomness of the electron motion process, and is more in line with the random characteristics of actual discharge; the microscopic electron migration equation is used to describe the electron motion process, which solves the problem that the time step of the streamer simulation needs to meet the CFL condition, resulting in an extremely short simulation step and low computational efficiency.

[0037] In addition, the improved random dynamics analysis method is used to batch process the collision reactions between different particles, which solves the problem of extremely large computational complexity caused by the traditional particle model processing the movement and collision reactions of charged particles one by one. The improved random dynamics analysis method takes into account the randomness of the collision reaction, which is consistent with the random characteristics of actual discharge.

[0038] The streamer development process to be simulated in this embodiment can be described as follows: under the action of an external electric field, electrons and ions are affected by the electric field force and accelerated, and during the movement process, they also collide with neutral gas molecules, causing electrons and ions to migrate macroscopically along the direction of the electric field. However, since the mass of ions is much greater than that of electrons, the ion mobility is low, which has little effect on the streamer development process; when the electron speed is high enough, electrons collide with neutral gas molecules to cause impact ionization, generating new electrons and positive ions, and doubling the number of electrons and positive ions. This process is also called electron impact ionization reaction; during the development of the streamer, electron attachment, electron and positive ion recombination reaction, and positive ion and negative ion recombination reaction will also occur. These reactions affect the density of electrons, positive ions, and negative ions. It can be seen that there are several important processes in the development of the streamer, including electron movement, ion movement, and collision reaction, and the streamer simulation needs to take these processes into account. Therefore, in the simulation of this embodiment, the core particles are electrons, positive ions, and negative ions, and the simulation calculation is mainly based on electrons, positive ions, and negative ions.

[0039] Gas discharge involves two processes: electron / ion movement and collision reaction. In this embodiment, S400 and S500 simulate these two processes, respectively. S400 reflects the electron / ion movement process, where changes in electron position cause changes in the number of electrons at different positions. S500 reflects the collision reaction, where electron impact ionization causes an increase in the number of electrons. Therefore, the number of electrons changes again due to collisions. Similarly, the number of ions also changes during the movement and collision processes.

[0040] Optionally, when meshing the simulation area, a vertical cross meshing method, a triangular meshing method, or an adaptive density meshing method may be used. Optionally, for the vertical cross meshing method, the meshing of the two-dimensional simulation area is square, and the meshing of the three-dimensional simulation area is cubic. The simulation method for the flow development process in a gas medium of this embodiment performs calculations based on the meshing.

[0041] Specifically, in S100, according to the type of insulating gas mainly used in actual power equipment, the gas types corresponding to the flow simulation include air, carbon dioxide CO2 and environmentally friendly insulating gas, and the environmentally friendly insulating gas can be perfluoroisobutyronitrile C4F7N, perfluoroketone C5F 10 Taking air as an example, in stream injection simulation, it can be considered that air is composed of 80% nitrogen N2 and 20% oxygen O2.

[0042] Furthermore, based on the defined gas components and known gas collision cross section data, the electron mobility is obtained by solving the Boltzmann equation. Taking air as an example, the electron mobility can be calculated using the Phelps collision cross section dataset using the BOLSIG+ software.

[0043] Specifically, in S200, the calculation formula of the electric field distribution is as follows:

[0044] Where, For the +1 simulation step of the electric field strength vector, Δ t is the time step of the streamer simulation, For the The space charge density of the simulation step is ε is the gas dielectric constant, is the elementary charge, For the The charge number of the particle, For the The particle in the The mobility of the simulation step, For the The particle in the The density of simulation steps, is the divergence operator.

[0045] In this embodiment, the calculation formula of the electric field distribution is an iterative form with time steps, and is solved using the finite volume method.

[0046] Furthermore, based on the calculated electric field distribution and the electron mobility, the average electron velocity of all meshes is solved by the following formula:

[0047] Where, is the average electron velocity, E is the amplitude of the electric field intensity; μ ( E ) is the electron mobility, which is a function of the electric field strength amplitude.

[0048] In the prior art, the electron velocity is calculated using the following formula:

[0049] Where, is the electron mass, is the electric field strength vector, is the elementary charge, is the electron velocity vector.

[0050] In this embodiment, the electric field distribution and the electron mobility are used to calculate the average electron velocity, which reduces the solution time of the above-mentioned electron velocity equation and can increase the calculation efficiency of the streamer simulation.

[0051] Specifically, in S300, the elastic collision probability distribution of the electron velocity is:

[0052]

[0053] Where, is the probability density function of the electron velocity, is the electron speed, β is the coefficient, Γ is the Gamma function, is the average electron velocity.

[0054] In real-world scenarios, electrons are affected by a variety of factors, including electric field strength, thermal motion, and collision processes. Therefore, electron velocity exhibits a certain degree of randomness. To account for this randomness, this embodiment uses an elastic collision probability distribution to generate a random number as the electron velocity, which better reflects the actual motion of electrons.

[0055] Preferably, generate random numbers that conform to the gamma distribution , and then the random number that conforms to the elastic collision probability distribution is calculated by the following formula:

[0056] Where, is a random number that conforms to the probability distribution of elastic collisions and is used as the electron velocity for meshing. The gamma distribution is Gamma(0.75,1).

[0057] Since the elastic collision probability distribution of electron velocity is a non-standard probability distribution function, it is difficult to directly generate a corresponding random number. Therefore, in this embodiment, based on the transformation method, a random number that conforms to the gamma distribution Gamma (0.75, 1) is first generated. , after using the above transformation, we can get the random number that conforms to the elastic collision probability distribution .

[0058] In this embodiment, in order to simulate the randomness of the streamer discharge process, elastic collision probability distribution is introduced to randomly generate electron velocity.

[0059] Specifically, in S400 , since electron mobility is much higher than ion mobility, electron impact ionization is the main process of streamer discharge. Therefore, the microscopic electron migration equation is used to describe the electron motion process, and the macroscopic ion drift equation is used to describe the ion motion process.

[0060] The electron positions are updated by the following microscopic electron migration equation:

[0061] Where, For the +1 simulation step of the electron coordinate vector, For the The electron coordinate vector of the simulation step length, For the +1 simulation step of the electric field strength vector, For the +1 simulation step length of the electric field intensity amplitude, is the simulation step size, is a random number that conforms to the probability distribution of elastic collisions, that is, the electron velocity of the mesh.

[0062] The electron velocity direction is set to the electric field direction at the mesh to maintain consistency with the fluid model assumptions.

[0063] After determining the position coordinates of all electrons, the grids where all electrons are located can be obtained, and then the number of electrons in all updated grids can be obtained. The electron density corresponds to the number of electrons. The electron density is obtained by converting the number of electrons. If the number of electrons in a grid is known, the number of electrons is divided by the grid volume Δ V is the electron density.

[0064] Furthermore, the macroscopic ion drift equation is:

[0065] Where, For the +1 simulation step of ion density, For the The ion density of the simulation step is For the The ion source term of simulation steps is For the +1 simulation step of the electric field strength vector, μ i is the mobility of the ions, Δ t is the simulation step size, is the divergence operator.

[0066] Since the mobility of ions is much smaller than that of electrons, in this embodiment, in order to speed up the simulation, a macroscopic ion drift equation is used to describe the movement process of ions. The ion source term is obtained by calculating the collision reaction between different particles using an improved random dynamics analysis method.

[0067] Optionally, since the ion mobility is much smaller than the electron mobility, the ion mobility has little effect on the streamer development process and can be set as a constant. The ion mobility in air can be set to 2×10 -4 m 2 (V·s) -1 .

[0068] Specifically, in S500, the reaction rate required for the simulation is calculated, and based on the reaction rate, the collision reactions between different particles are calculated using an improved stochastic kinetic analysis method, wherein the collision reactions considered include electron impact ionization reaction, electron attachment reaction, electron and positive ion recombination reaction, and positive ion and negative ion recombination reaction.

[0069] In this embodiment, the reaction rate is calculated using a reaction frequency method, which sets the reaction frequencies of electron impact ionization reaction, electron attachment reaction, electron and positive ion recombination reaction, and positive ion and negative ion recombination reaction, and then converts the reaction frequencies into the reaction rates.

[0070] Preferably, the reaction rate of the impact ionization reaction is p 1 is calculated by the following formula:

[0071] Where, is the reaction frequency of the impact ionization reaction, in 1 / s, is the number of electrons in each grid.

[0072] Reaction rate of electron attachment reaction p 2 is calculated by the following formula:

[0073] Where, is the reaction frequency of the electron attachment reaction, in 1 / s, is the number of electrons in each grid.

[0074] Reaction rate of electron and positive ion recombination reaction p 3 is calculated by the following formula:

[0075] Where, is the reaction frequency of the electron and positive ion recombination reaction, in m 3 / s, Δ V is the volume of the mesh, is the number of electrons in each grid, is the number of positive ions in each grid.

[0076] The reaction rate of the recombination reaction between positive ions and negative ions p4 is calculated by the following formula:

[0077] Where, is the reaction frequency of the compound reaction between positive ions and negative ions, in m 3 / s; Δ V is the volume of the mesh, is the number of positive ions in each grid, is the number of negative ions in each grid.

[0078] In existing technologies, fluid models typically use reaction frequency to describe the intensity of the reaction between particles. The reaction rate can be converted from the reaction frequency and the amount of particle increase can be calculated using the reaction rate.

[0079] In another feasible embodiment, the reaction rates of the electron impact ionization reaction and the electron attachment reaction are calculated using the collision cross section method. The reaction rate of the electron impact ionization reaction is calculated by the following formula:

[0080] Where, is the density of background gas molecules, in units of 1 / m 3 ; σ i is the collision cross section of the electron impact ionization reaction, in m 2 ; is the electron velocity in m / s.

[0081] The reaction rate of the electron attachment reaction is calculated by the following formula:

[0082] Where, is the density of background gas molecules, in units of 1 / m 3 ; σ a is the collision cross section of the electron attachment reaction, in m 2 , is the electron velocity in m / s.

[0083] If the cross-section data of gas electron impact ionization and electron attachment are known, the reaction rates of the gas electron impact ionization reaction and electron attachment reaction can be directly calculated using the collision cross-section method.

[0084] Furthermore, in S500, the improved stochastic dynamics analysis method is used to calculate the collision reactions between different particles to obtain the updated numbers of electrons, positive ions, and negative ions, including: Setting the simulation time for dynamics analysis tr It is time 0; Computational time step for kinetic analysis ; Time step based on dynamic analysis , generates a binomial distribution ( , ) ,in For the The number of particles, Indicates the The probability of a collision reaction occurring; Based on random numbers , calculate the time step of a dynamic analysis The vector of all particles after ; Set the simulation time for the dynamic analysis to t r Updated to t r = t r + ; Comparing simulation times for dynamics analysis t r and streamer simulation step Δ t , if the simulation time of the dynamic analysis t r Less than the streamer simulation step Δ t , repeat the above steps except the first step; if the simulation time of the dynamic analysis is t r Not less than streamer simulation step Δ t , then the above iterative process is terminated, and the vector consisting of all the particles finally obtained is X ( t r ) as the updated number of electrons, positive ions and negative ions.

[0085] Preferably, the time step of the kinetic analysis is calculated by the following formula :

[0086]

[0087]

[0088] Where, is the time step of the dynamic analysis, e is the error tolerance, For the The number of particles, X is the vector of the number of all particles, For the The collision reaction causes the The change in the amount of particles, For the The reaction rate of a collision reaction.

[0089] Stochastic dynamics analysis methods need to meet the time step The number of particles in the system is approximately constant, so the time step It needs to be small enough. You can use the above method to select an appropriate time step. The error tolerance affects the time step size. The larger the error tolerance, the larger the time step.

[0090] Preferably, The probability of a collision reaction occurring Calculated by the following formula:

[0091] In this embodiment, random numbers are generated to simulate the randomness of the change in the number of particles during the collision reaction. Binomial distribution can be used to prevent the number of particles from becoming negative in the dynamics analysis.

[0092] Preferably, the vector consisting of all particle numbers Calculated by the following formula:

[0093] Particle density corresponds to the number of particles. Particle density is obtained by converting the number of particles. If the number of particles in a certain grid is known, the number of particles is divided by the grid volume Δ V is the particle density.

[0094] The particle model in the streamer simulation model tracks the motion of individual charged particles and uses the Monte Carlo collision (MCC) method to simulate interparticle collisions. However, the particle model's computational complexity and high collision processing complexity have severely limited its development and application. This embodiment employs an improved stochastic dynamics analysis method, enabling efficient batch processing of collision reactions between different particles. This solves the technical problem of the computationally intensive processing of charged particle motion and collision reactions individually.

[0095] Ultimately, through iterative solutions of the electric field distribution, electron and ion motion equations, and particle collision reactions, we can obtain the time evolution results of the electric field distribution and particle density, and then analyze the streamer development process.

[0096] In addition, in the fluid model, particles are regarded as continuous media, and the particle velocity and density show average characteristics within a certain area. When averaging small-scale structures, large errors are easily generated. Therefore, the fluid model is not suitable for the simulation of small-scale structures. This embodiment processes the movement and reaction process of electrons through particle motion, uses the microscopic electron migration equation to calculate the movement process of all electrons one by one, and takes into account the randomness of electron velocity by adopting the elastic collision probability distribution. It is suitable for the streamer simulation of small-scale structures, solving the problem that the fluid model is based on the continuous medium assumption and is not suitable for the simulation of small-scale structures. This embodiment regards electrons as independent individuals, overcomes the problem of analyzing the movement process of all electrons one by one, and overcomes the problems caused by the average characteristics of the continuous medium.

[0097] In order to more clearly demonstrate the effect of the simulation method of the flow development process in the gas medium of this embodiment, the following is a detailed description through Example 1 and Example 2.

[0098] Example 1 Use needle-plate electrodes to carry out streamer simulation, such as Figure 2 As shown in the figure, the size of the simulation area is 80mm×80mm, the distance between the needle electrode and the plate electrode is 40mm, and a positive polarity voltage of 100kV is applied to the needle electrode. The gas composition is air, that is, 80% N2 and 20% O2. Parameters such as electron mobility and reaction frequency are calculated using the Phelps collision cross section data set using the BOLSIG+ software, and the reaction rate is calculated using the reaction frequency method. The electron density distribution at different simulation times is obtained as shown in the figure. Figure 3 As shown in the figure, the electron density distribution obtained by fluid model simulation is as follows Figure 4 As shown in the figure, since the electric field intensity is highest near the needle electrode, the streamer originates from the needle electrode and gradually develops downward. Comparing the results of this example with the fluid model, it can be seen that the streamer development lengths of the two models at different times are very similar, verifying the accuracy of the streamer simulation method of the present invention.

[0099] Example 2 A surface flow simulation of solid media was carried out using a porous solid medium. The size of the simulation area is 1mm×0.5mm, the length and width of the porous solid medium are 1mm and 0.25mm respectively, the gas medium in the upper half of the model is air, and the medium in the air gap inside the porous solid medium is also air. Parameters such as electron mobility and reaction frequency are calculated using the Phelps collision cross section data set using the BOLSIG+ software, and the reaction rate is calculated using the reaction frequency method. The length of the rod electrode is 0.05mm and the diameter is 0.01mm. The boundary conditions of the rod electrode and the left boundary are set to 15kV potential, the right boundary condition is set to grounding, and the upper and lower boundary conditions are set to Neumann boundary conditions. The electron density distribution at different simulation times is obtained as follows Figure 5 As shown in the figure, the electron density distribution obtained by fluid model simulation is as follows Figure 6 As shown. It can be seen that the streamer development process obtained by the two simulation models is basically the same, that is, the streamers all start from the inside of the pore and gradually merge with the external streamers to cause breakdown. Using a 20-core computer for simulation, the streamer simulation of this embodiment takes about 35 minutes, and the fluid model simulation takes about 1 hour and 45 minutes. It can be seen that the streamer simulation method of this embodiment has higher computational efficiency. Due to the small size of the pore structure and the small size of the subdivision grid, the simulation time step used by the fluid model needs to meet the CFL condition, so the simulation time step is very small, which significantly increases the simulation time; while the simulation of this embodiment is not restricted by the CFL condition, the simulation time step is still large, and the simulation efficiency is higher.

[0100] Example 2 As another specific embodiment of the present invention, this embodiment provides a simulation device for the flow development process in a gas medium, referring to Figure 7 , including gas component definition module 1, iterative solution module 2, and result output module 3.

[0101] The gas component definition module 1 is used to define gas components; The iterative solution module 2 is used to iteratively calculate the electric field distribution, electron density, positive ion density and negative ion density in the simulation area according to the gas composition until the set simulation time is reached; The result output module 3 is used to output the electric field distribution, electron density, positive ion density and negative ion density in the simulation area after the simulation time is reached, so as to analyze the streamer development process.

[0102] The iterative solution module 2 includes a first calculation unit 21, a second calculation unit 22, a third calculation unit 23, a fourth calculation unit 24, and a fifth calculation unit 25; The first calculation unit 21 is used to calculate the electron mobility required for simulation according to the gas composition; The second calculation unit 22 is used to calculate the electric field distribution in the simulation area, and solve the average electron velocity of all the grids according to the calculated electric field distribution and the electron mobility; The third calculation unit 23 is configured to generate a random number based on the average electron velocity using elastic collision probability distribution, and use the obtained random number as the electron velocity for meshing; The fourth calculation unit 24 is configured to update the electron position according to the electron velocity using a microscopic electron migration equation to obtain an updated electron quantity, obtain an electron density based on the electron quantity, and solve a macroscopic ion drift equation to obtain an updated positive ion density and a negative ion density; The fifth calculation unit 25 is used to calculate the reaction rate required for the simulation. According to the reaction rate, the improved stochastic dynamics analysis method is used to calculate the collision reaction between different particles to obtain the updated number of electrons, positive ions, and negative ions, so as to obtain the updated electron density, the positive ion density, and the negative ion density.

[0103] Example 3 As another specific embodiment of the present invention, this embodiment provides an electronic device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method for simulating the flow development process in the gas medium described in Example 1: S100, defining gas components, and calculating electron mobility required for simulation based on the gas components; S200, calculating the electric field distribution in the simulation area, and solving the average electron velocity of all the grids according to the electric field distribution and the electron mobility; S300, based on the average electron velocity, using elastic collision probability distribution to generate a random number, and using the obtained random number as the electron velocity for grid division; S400, updating the electron position according to the electron velocity using a microscopic electron migration equation to obtain an updated electron quantity, obtaining an electron density based on the electron quantity, and solving a macroscopic ion drift equation to obtain updated positive ion density and negative ion density; S500, calculating a reaction rate required for simulation, and calculating collision reactions between different particles based on the reaction rate using an improved stochastic kinetic analysis method to obtain updated numbers of electrons, positive ions, and negative ions, thereby obtaining updated electron density, positive ion density, and negative ion density; S600, iteratively calculate the electric field distribution, the electron density, the positive ion density and the negative ion density in the simulation area until the set simulation time is reached, and output the electric field distribution, electron density, positive ion density and negative ion density results to analyze the streamer development process.

[0104] Example 4 As another specific embodiment of the present invention, this embodiment provides a storage medium having a computer program stored thereon. When the computer program is executed by a processor, the steps of the method for simulating the flow development process in the gas medium described in Example 1 are implemented: S100, defining gas components, and calculating electron mobility required for simulation based on the gas components; S200, calculating the electric field distribution in the simulation area, and solving the average electron velocity of all the grids according to the electric field distribution and the electron mobility; S300, based on the average electron velocity, using elastic collision probability distribution to generate a random number, and using the obtained random number as the electron velocity for grid division; S400, updating the electron position according to the electron velocity using a microscopic electron migration equation to obtain an updated electron quantity, obtaining an electron density based on the electron quantity, and solving a macroscopic ion drift equation to obtain updated positive ion density and negative ion density; S500, calculating a reaction rate required for simulation, and calculating collision reactions between different particles based on the reaction rate using an improved stochastic kinetic analysis method to obtain updated numbers of electrons, positive ions, and negative ions, thereby obtaining updated electron density, positive ion density, and negative ion density; S600, iteratively calculate the electric field distribution, the electron density, the positive ion density and the negative ion density in the simulation area until the set simulation time is reached, and output the electric field distribution, electron density, positive ion density and negative ion density results to analyze the streamer development process.

[0105] The above description is merely a preferred embodiment of the present invention and does not constitute any other form of limitation to the present invention. Any modification or equivalent variation based on the technical essence of the present invention shall still fall within the scope of protection claimed by the present invention.

Claims

1. A method for simulating the flow development process in a gas medium, characterized in that: The method comprises: defining gas components and calculating electron mobility required for simulation based on the gas components; Calculating the electric field distribution in the simulation area, and solving the average electron velocity of all the grids according to the electric field distribution and the electron mobility; Based on the average electron velocity, a random number is generated using an elastic collision probability distribution, and the obtained random number is used as the electron velocity of the grid; Based on the electron velocity, the electron position is updated using a microscopic electron migration equation to obtain an updated electron quantity, the electron density is obtained based on the electron quantity, and a macroscopic ion drift equation is solved to obtain updated positive ion density and negative ion density; Calculating a reaction rate required for the simulation, and calculating collision reactions between different particles based on the reaction rate using an improved stochastic kinetic analysis method to obtain updated numbers of electrons, positive ions, and negative ions, thereby obtaining updated electron density, positive ion density, and negative ion density; The electric field distribution, the electron density, the positive ion density and the negative ion density in the simulation area are iteratively calculated until the set simulation time is reached, and the electric field distribution, electron density, positive ion density and negative ion density results are output to analyze the streamer development process.

2. The method for simulating the flow development process in a gas medium according to claim 1, characterized in that: The electric field distribution is calculated by the following formula: Where, For the +1 simulation step of the electric field strength vector, Δ t is the time step of the streamer simulation, For the The space charge density of the simulation step is ε is the gas dielectric constant, is the elementary charge, For the The charge number of the particle, For the The particle in the The mobility of the simulation step, For the The particle in the The density of simulation steps, is the divergence operator.

3. The method for simulating the flow development process in a gas medium according to claim 2, characterized in that: According to the electric field distribution and the electron mobility, the average electron velocity of all meshes is solved by the following formula: Where, is the average electron velocity, E is the amplitude of the electric field intensity; μ ( E ) is the electron mobility, which is a function of the electric field strength amplitude.

4. The method for simulating the flow development process in a gas medium according to claim 1, characterized in that: The method of generating random numbers based on the average electron velocity using elastic collision probability distribution and using the obtained random numbers as the electron velocity of the grid includes generating random numbers that conform to the gamma distribution. , and then the random number that conforms to the elastic collision probability distribution is calculated by the following formula: Where, is the electron speed, β is the coefficient; Among them, the elastic probability distribution of electron velocity is: Where, is the probability density function of the electron velocity, is the electron velocity, Γ is the Gamma function, is the average electron velocity.

5. The method for simulating the flow development process in a gas medium according to claim 4, characterized in that: The gamma distribution is Gamma(0.75,1).

6. The method for simulating the flow development process in a gas medium according to claim 1, characterized in that: The microscopic electron migration equation is: Where, For the +1 simulation step of the electron coordinate vector, For the The electron coordinate vector of the simulation step length, For the +1 simulation step of the electric field strength vector, For the +1 simulation step of the electric field intensity amplitude, is the simulation step size, is the electron velocity of the mesh; The macroscopic ion drift equation is: Where, For the +1 simulation step of ion density, For the The ion density of the simulation step is For the The ion source term of simulation steps is For the +1 simulation step of the electric field strength vector, μ i is the mobility of the ions, Δ t is the simulation step size, is the divergence operator.

7. The method for simulating the flow development process in a gas medium according to claim 6, characterized in that: The method of calculating the collision reaction between different particles by using the improved random dynamics analysis method includes: Setting the simulation time for dynamics analysis t r It is time 0; Computational time step for kinetic analysis ; Time step based on dynamic analysis , generates a binomial distribution ( , ) ,in For the The number of particles, Indicates the The probability of a collision reaction occurring; Based on random numbers , calculate the time step of a dynamic analysis The vector of all particles after ; Set the simulation time for dynamic analysis to t r Updated to t r = t r + ; Comparing simulation times for dynamics analysis t r and streamer simulation step Δ t , if the simulation time of the dynamic analysis t r Less than the streamer simulation step Δ t , repeat except setting the simulation time of dynamic analysis t r The above steps except time 0; if the simulation time of dynamic analysis t r Not less than streamer simulation step Δ t , then the above iterative process is terminated, and the vector consisting of all the particles finally obtained is X ( t r ) as the updated number of electrons, positive ions and negative ions.

8. A device for simulating the flow development process in a gas medium, characterized in that: The device comprises a gas component definition module (1), an iterative solution module (2), and a result output module (3); The gas component definition module (1) is used to define gas components; The iterative solution module (2) is used to iteratively calculate the electric field distribution, electron density, positive ion density and negative ion density in the simulation area according to the gas composition until a set simulation time is reached; The result output module (3) is used to output the electric field distribution, electron density, positive ion density and negative ion density in the simulation area after the simulation time is reached, so as to analyze the streamer development process; The iterative solution module (2) includes a first calculation unit (21), a second calculation unit (22), a third calculation unit (23), a fourth calculation unit (24), and a fifth calculation unit (25); The first calculation unit (21) is used to calculate the electron mobility required for simulation according to the gas composition; The second calculation unit (22) is used to calculate the electric field distribution in the simulation area, and solve the average electron velocity of all the grids according to the calculated electric field distribution and the electron mobility; The third calculation unit (23) is used to generate a random number based on the average electron velocity using the elastic collision probability distribution, and use the obtained random number as the electron velocity of the grid; The fourth calculation unit (24) is used to update the electron position according to the electron velocity using a microscopic electron migration equation to obtain an updated electron quantity, obtain an electron density based on the electron quantity, and solve a macroscopic ion drift equation to obtain an updated positive ion density and a negative ion density; The fifth calculation unit (25) is used to calculate the reaction rate required for the simulation, and according to the reaction rate, the improved random dynamics analysis method is used to calculate the collision reaction between different particles to obtain the updated number of electrons, positive ions, and negative ions, so as to obtain the updated electron density, the positive ion density, and the negative ion density.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory, wherein: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 7.

10. A storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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