Arc simulation method of arc extinguish chamber, electronic equipment, storage medium and program product

Abstract

The invention provides an arc simulation method of an arc extinguish chamber, electronic equipment, a storage medium and a program product. The arc simulation method comprises the following steps: constructing a control equation for arc simulation of the arc extinguish chamber, wherein the control equation comprises a mass conservation equation, a momentum conservation equation and an energy conservation equation; and on the basis of a lattice Boltzmann method, taking a mass conservation equation and a momentum conservation equation as simulation targets, and updating the density and speed of a flow field corresponding to the arc extinguish chamber in each time step in the arc simulation process of the arc extinguish chamber. And solving the energy conservation equation based on a finite difference method, and updating the temperature of the flow field at each time step. And completing arc simulation of the arc extinguish chamber based on the density, the speed and the temperature corresponding to each time step of the flow field. According to the technical scheme, three-dimensional arc simulation of the arc extinguish chamber is achieved, and the simulation speed and precision are improved.

Description

Technical Field

[0001] This application relates to the field of arc simulation in arc-extinguishing chambers, and more particularly to arc simulation methods, electronic devices, storage media, and program products for arc-extinguishing chambers. Background Technology

[0002] Traditional high-voltage switch product design methods involve repeated testing and prototype modifications, which consumes enormous human and material resources, increasing R&D costs and lengthening the development cycle, thus severely impacting market competitiveness. Therefore, to improve product design performance and shorten the development cycle, simulation technology is increasingly being used in high-voltage switch R&D.

[0003] Sulfur hexafluoride (SF6) circuit breakers are used in the electrical industry and employ pressurized SF6 gas to extinguish electric arcs, characterized by high insulation strength and high interruptibility. During current interruption, the arc in an SF6 circuit breaker is strongly accelerated by a pressure gradient, leading to heavy turbulence and extreme temperatures exceeding 15,000 K. Therefore, the arc-extinguishing chamber of the circuit breaker contains a dynamic field of momentum, energy, and mass transfer, and the micro- and meso-scale flow fields and energy transfer within the SF6 circuit breaker remain largely unknown. To gain a clear understanding of the dynamic processes of arc generation and extinction and to grasp the details of various aspects of arc flow, numerical simulation has become an important tool for studying arc flow. Since the 1990s, with the development of field analysis techniques and the improvement of computer performance, numerical simulation methods have been applied to the simulation analysis of high-voltage switchgear both domestically and internationally.

[0004] Toshiba, ABB, GE of Japan, and the University of Liverpool of the UK are at the forefront of arc simulation in circuit breakers, while LG of South Korea is also conducting research in this area. ABB, GE, and the University of Liverpool are able to use parallel computing technology to simulate the airflow field and arc in the arc-extinguishing chamber. In China, parallel computing technology is also currently available for simulating the arc and airflow field in the arc-extinguishing chamber. Major domestic high-voltage switchgear manufacturers are also conducting computer simulation research on the arc breaking of circuit breakers. Early simulation research mainly focused on single-physics characteristic parameters. However, the operating conditions of high-voltage switchgear are complex, involving many physical field issues such as structural mechanical properties, electromagnetic fields, temperature fields, and airflow fields. Single-physics analysis methods cannot comprehensively evaluate the operating conditions of high-voltage switches and may even lead to erroneous conclusions due to overlooking certain aspects. Multiphysics coupled simulation not only provides reliable analytical results but also guides the design of high-voltage switches, allowing for the experimental verification and improvement of optimal solutions. This significantly reduces R&D costs and shortens the development cycle, making it of great significance to high-voltage switchgear research.

[0005] To simulate the arc inside the arc-extinguishing chamber of a high-voltage switch, existing numerical modeling of turbulent arcs is almost entirely based on the traditional two-dimensional (2D) Navier-Stokes equations (NS equations), especially using commercial software. Since 1994, the University of Liverpool has studied axisymmetric turbulent nozzle arcs in gas circuit breakers using the Navier-Stokes equations, finding that the Prandtl mixing length model is suitable for studying turbulent arcs because it is simple and has been successfully applied to turbulent circular jets. Subsequently, researchers both domestically and internationally, based on the compressible 2D Navier-Stokes equations, assumed local thermodynamic equilibrium. This model considers Joule heating, radiation, Lorentz force, arc wall interaction, and actual gas effects, and has been applied to study arc phenomena in high-voltage, medium-voltage, and low-voltage circuit breakers.

[0006] However, on the one hand, the arc characteristics change drastically within hundreds of nanoseconds due to factors such as plasma turbulence, radiation, nozzle ablation, Joule heating, and Lorentz force involved in the interruption process of the high-voltage switch arc-extinguishing chamber. On the other hand, during the interruption of current in an SF6 circuit breaker, the arc can reach extreme temperatures exceeding 15000K, and the SF6 arc is highly compressed during fracture, resulting in high-speed transfer of compressible momentum, energy, and matter within the arc-extinguishing system. Therefore, traditional two-dimensional arc simulation methods are problematic in two ways: firstly, they struggle to accurately describe the complex current phenomena and internal mechanisms of the arc within the arc-extinguishing chamber of such high-voltage switches from generation to extinction; secondly, they cannot perform parallel processing during calculations, leading to low simulation speed and accuracy. Summary of the Invention

[0007] In view of this, this application provides an arc simulation method, electronic device, storage medium, and program product for an arc extinguishing chamber, which can solve the problems of low simulation speed and accuracy of two-dimensional simulation methods.

[0008] This application provides an arc simulation method, electronic device, storage medium, and program product for an arc-extinguishing chamber. The following description covers various aspects of this application, and the embodiments and beneficial effects described below can be referenced interchangeably.

[0009] In a first aspect, this application provides an arc simulation method for an arc-extinguishing chamber, comprising: constructing control equations for arc simulation of the arc-extinguishing chamber, the control equations including mass conservation equations, momentum conservation equations and energy conservation equations;

[0010] Based on the lattice Boltzmann method, and using the mass conservation equation and momentum conservation equation as simulation targets, the density and velocity of the flow field corresponding to the arc-extinguishing chamber at each time step are updated during the arc simulation process in the arc-extinguishing chamber.

[0011] The energy conservation equation is solved using the finite difference method, and the temperature of the flow field is updated at each time step.

[0012] Based on the density, velocity, and temperature of the flow field at each time step, the arc simulation of the arc-extinguishing chamber is completed.

[0013] According to this scheme, on the one hand, the lattice Boltzmann method is used to update the density and velocity of the flow field at each time step. As a mesoscopic numerical simulation tool, the lattice Boltzmann method can achieve three-dimensional electric arc simulation and has significant advantages such as high-fidelity transient calculation, ease of handling complex boundaries, high computational efficiency on GPUs, and parallel computing capability. On the other hand, the finite difference method is used to update the temperature of the flow field at each time step. Compared with the traditional finite integral method, the finite difference method has higher numerical accuracy and can better capture subtle changes in the temperature field. Therefore, by fusing the lattice Boltzmann method and the finite difference method for electric arc simulation, not only is three-dimensional electric arc simulation achieved, but the simulation speed and accuracy are also improved.

[0014] In one possible implementation of the first aspect above, based on the lattice Boltzmann method and with the mass conservation equation and momentum conservation equation as the simulation targets, the density and velocity of the flow field in the arc-extinguishing chamber at each time step during the arc simulation process are updated, including:

[0015] The geometric model of the arc-extinguishing chamber is discretized into grid cells based on the lattice Boltzmann model, and each grid cell includes multiple lattice points.

[0016] Determine the unit conversion factor for each grid point from the physical units of the geometric model to the grid units, and convert the physical quantities of all grid points from physical units to grid units according to the unit conversion factor.

[0017] Local collisions and migrations are performed at each grid point to update the density and velocity of the flow field at each time step.

[0018] According to this scheme, the microscopic particle interaction mechanism of the lattice Boltzmann model is used to efficiently update density and velocity, thereby capturing transient changes in the electric arc flow.

[0019] In one possible implementation of the first aspect above, local collisions and migrations are performed at each grid point to update the density and velocity of the flow field at each time step, including:

[0020] Local collisions are performed at each grid point to obtain the distribution function after the collision.

[0021] Based on the distribution function after the collision, each grid point is migrated to an adjacent grid point along the discrete velocity direction specified by the lattice Boltzmann model, and the migration distribution function is obtained.

[0022] Based on the migrated distribution function, the density and velocity of the flow field are updated at each time step.

[0023] According to this scheme, by updating the distribution function, the density and velocity of the flow field can be efficiently coupled and solved, providing a microscopic physical description of the electric arc dynamics.

[0024] In one possible implementation of the first aspect above, determining the unit conversion coefficients for each lattice point from the physical units of the geometric model to the lattice units includes:

[0025] Based on the Mach number similarity criterion and the Reynolds number similarity criterion, the unit conversion coefficients are determined. The unit conversion coefficients include: characteristic length conversion coefficient, characteristic time conversion coefficient, characteristic mass conversion coefficient, and characteristic temperature conversion coefficient.

[0026] According to this scheme, based on the Mach number similarity criterion and the Reynolds number similarity criterion, the unit conversion coefficient is determined so that the lattice Boltzmann model can adaptively match the high Mach number and high Reynolds number characteristics of the high voltage arc, avoiding simulation deviations caused by scale conversion distortion.

[0027] In one possible implementation of the first aspect above, the energy conservation equation is solved based on the finite difference method, and the temperature of the flow field is updated at each time step, including:

[0028] Discretize the time and space derivatives of the energy conservation equation.

[0029] Solve the discretized energy conservation equations to update the temperature of the flow field at each time step.

[0030] According to this scheme, temperature calculation is facilitated by discretizing the time derivative and space derivative of the energy conservation equation.

[0031] In one possible implementation of the first aspect described above, the time derivative of the energy conservation equation is discretized by using a first-order Euler scheme.

[0032] Discretizing the spatial derivatives of the energy conservation equation includes: using an upwind scheme to handle the convection terms of the energy conservation equation, and using a second-order central difference scheme to handle the heat conduction and viscous dissipation terms of the energy conservation equation.

[0033] In one possible implementation of the first aspect mentioned above, the lattice Boltzmann model employs a pressure-based regularization scheme.

[0034] According to this scheme, the pressure-based regularization scheme can better handle compressible flows (high arc compression) and high Mach number problems, and reduce numerical errors.

[0035] In a second aspect, this application provides an electronic device, which includes a processor and a memory, wherein the memory stores at least one instruction or at least one program, and the at least one instruction or at least one program is loaded and executed by the processor to implement the method disclosed in the first aspect above and any possible implementation thereof.

[0036] Thirdly, this application provides a computer-readable storage medium storing at least one instruction or at least one program, wherein the at least one instruction or at least one program is loaded and executed by a processor to implement the method disclosed in the first aspect above and any possible implementation thereof.

[0037] Fourthly, this application provides a computer program product, including a computer program or instructions, which, when executed by a processor, implement the methods disclosed in the first aspect above and any possible implementation thereof.

[0038] It should be understood that the beneficial effects of the second to fourth aspects mentioned above can be referred to the beneficial effects described in the first aspect, and will not be repeated here. Attached Figure Description

[0039] Figure 1 A flowchart illustrating the arc simulation method provided in this application embodiment;

[0040] Figure 2 Another schematic flowchart of the arc simulation method provided in the embodiments of this application;

[0041] Figure 3 Another schematic flowchart of the arc simulation method provided in the embodiments of this application;

[0042] Figure 4 Another schematic flowchart of the arc simulation method provided in the embodiments of this application;

[0043] Figure 5 Another schematic flowchart of the arc simulation method provided in the embodiments of this application;

[0044] Figure 6 A block diagram of an electronic device provided in an embodiment of this application;

[0045] Figure 7 This is a block diagram of a SoC (system on chip) provided in an embodiment of this application. Detailed Implementation

[0046] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0047] As mentioned above, in some embodiments, for simulating the arc inside the arc-extinguishing chamber of a high-voltage switch, existing numerical modeling of turbulent arcs is almost entirely based on the traditional two-dimensional Navier-Stokes equations, and the finite volume method is often used when solving the Navier-Stokes equations. This involves dividing the continuous computational domain into a series of non-overlapping, finite sub-regions, each called a control volume or element. Each control volume is typically associated with a node, which represents the corresponding control volume. Then, the partial differential equations to be solved (usually in conservation form) are integrated over each control volume. This step transforms the equations into integral equations describing the conservation of physical quantities within the control volume. The rate of change of physical quantities within the control volume is equal to the sum of the flux entering through its boundary and the internal source terms, thus solving the mass, momentum, and energy conservation equations in the Navier-Stokes equations.

[0048] However, this two-dimensional arc simulation method has two main drawbacks: first, it is difficult to accurately describe the complex current phenomena and internal mechanisms of the arc inside the arc extinguishing chamber of such high-voltage switches from generation to extinction; second, it cannot be processed in parallel during the calculation process, resulting in low simulation speed and accuracy.

[0049] In addition, in some embodiments, traditional commercial software often uses body-fitted meshes in the calculation of three-dimensional electric arc simulation. This simulation method requires a large number of meshes, and most of the meshes are used to densify the fine structure inside the circuit breaker. This method still has the problem of excessively long simulation time.

[0050] Based on this, embodiments of this application provide an arc simulation method for an arc extinguishing chamber, which can be applied to computer equipment. The following description uses a computer device as the executing entity of this method to illustrate the arc simulation method in detail.

[0051] Reference Figure 1 , Figure 1 This is a schematic flowchart of an arc simulation method provided in an embodiment of this application. Figure 1 As shown, the arc simulation method includes the following steps S110-S140.

[0052] S110: Construct the governing equations for arc simulation in the arc extinguishing chamber. The governing equations include the mass conservation equation, momentum conservation equation, and energy conservation equation.

[0053] Specifically, for compressible flow without mass and momentum sources, the Navier-Stokes equations describing the mass conservation equations and momentum conservation equations can be expressed as:

[0054] (Formula 1)

[0055] (Formula 2)

[0056] Formula 1 is the mass conservation equation, and Formula 2 is the momentum conservation equation.

[0057] In the formula, ρ is density, u β Let β be the component of the velocity along the β direction, where β represents the spatial direction. For example, β = x, y, z represents the three coordinate axes in three-dimensional space. α Let be the component of the velocity in the direction α, where α represents the spatial direction, for example, α = x, y, z. s For the hydrostatic pressure of the fluid, δ αβ The Kronecker function is used, which employs the Einstein summation convention, Π αβ Let t be the viscous stress tensor and t be time.

[0058] Regarding the viscous stress tensor Π in Formula 2 αβ The calculation formula is as follows:

[0059] (Formula 3)

[0060] In the formula, x α Let x be the component of position in the α direction. β The component of position in the β direction, Let γ be the velocity divergence, and γ be the volumetric expansion rate of the fluid (γ is the summation subscript). μ is the dynamic viscosity, and according to Sutherland's law, μ is calculated as follows:

[0061] (Formula 4)

[0062] In the formula, T is the absolute temperature of the gas. ref For reference temperature, μ ref For reference dynamic viscosity.

[0063] The energy conservation equation has multiple equivalent forms. The embodiments in this application use the static temperature T of the fluid. s Furthermore, since there is no expression for a heat source term, the energy conservation equation is expressed as follows:

[0064] (Formula 5)

[0065] In the formula, T s For temperature, C vp is the specific heat capacity at constant volume of the fluid. s Let p be the static pressure of the fluid. s =ρr g T s r g r is the ratio of the gas constant to the molecular weight of the gas. g =R / W, where R is the gas constant and W is the molecular weight of the gas. q α For heat flux, q α =-λ∂T s / ∂x γ λ is the thermal conductivity of the fluid, λ = μC p / Pr, μ is the dynamic viscosity, C p Specific heat capacity at constant pressure, Pr is the Prandtl number, which can be set to, for example, 0.71. The fluid selected is air.

[0066] S120: Based on the lattice Boltzmann method, and using the mass conservation equation and momentum conservation equation as simulation targets, it updates the density and velocity of the flow field corresponding to the arc-extinguishing chamber at each time step during the arc simulation process in the arc-extinguishing chamber.

[0067] S130: Solve the energy conservation equation based on the finite difference method to update the temperature of the flow field at each time step.

[0068] S140: Based on the density, velocity, and temperature of the flow field at each time step, complete the arc simulation of the arc-extinguishing chamber.

[0069] Understandably, based on the density, velocity, and temperature of the flow field at each time step, the arc simulation of the arc extinguishing chamber can be completed as time steps progress, thus fully describing the entire process of complex current changes in the arc inside the high-voltage switch arc extinguishing chamber from generation to extinction.

[0070] Through steps S110-S140, the generation and extinction of the electric arc are treated as a fluid simulation. On one hand, the lattice Boltzmann method is used to update the density and velocity of the flow field at each time step. As a mesoscopic numerical simulation tool, the lattice Boltzmann method can effectively simulate airflow fields and turbulence, thereby simulating the three-dimensional supersonic compressible airflow field of the high-voltage switch arc-extinguishing chamber and completing the arc simulation of the arc-extinguishing chamber. Furthermore, the lattice Boltzmann method has significant advantages such as high-fidelity transient calculation, ease of handling complex boundaries, high computational efficiency on GPUs (graphics processing units), and parallel computing capabilities. On the other hand, the finite difference method is used to update the temperature of the flow field at each time step. Compared to the traditional finite integral method, the finite difference method has higher numerical accuracy and can better capture subtle changes in the temperature field. Moreover, the finite integral method can only run on a CPU (central processing unit), while the finite difference method can run efficiently on a GPU. Therefore, this application integrates the lattice Boltzmann method and the finite difference method for arc simulation, which not only realizes the three-dimensional arc simulation of the arc-extinguishing chamber of high-voltage switch, but also improves the speed and accuracy of the simulation.

[0071] The following section provides a detailed explanation of the process by which the density and velocity of the flow field in the arc-extinguishing chamber are updated at each time step in the arc simulation process using the lattice Boltzmann method in S120, with the mass conservation equation and momentum conservation equation as the simulation targets.

[0072] Reference Figure 2 , Figure 2 This is another schematic flowchart illustrating the arc simulation method provided in this application. Figure 2 As shown, the process of updating the density and velocity of the flow field at each time step based on the lattice Boltzmann method includes the following steps S210~S230.

[0073] S210: Based on the lattice Boltzmann model, the geometric model of the arc-extinguishing chamber is discretized into grid elements, and each grid element includes multiple grid points.

[0074] The lattice Boltzmann model can be either a D3Q19 discrete velocity model or a D2Q9 discrete velocity model. Furthermore, the lattice Boltzmann model can employ a pressure-based regularization scheme, which better handles compressible flows (high arc compression) and high Mach number problems, reducing numerical errors.

[0075] It is understandable that the D3Q19 discrete velocity model for compressible flow can generally be divided into two types of schemes: density-based schemes and pressure-based schemes. The embodiments of this application adopt the simpler pressure-based scheme, which can be improved by introducing a corresponding force source term ψ. iTo correct compressibility errors.

[0076] Therefore, the evolution equation of the lattice Boltzmann equation, which describes the conservation of mass and momentum, can be expressed as:

[0077] (Formula 6)

[0078] In the formula, f i Let be the discrete velocity distribution function, and i be the order of the discrete velocity. iα For discrete velocity vectors, δ t τ is the unit time step. τ is the relaxation time, τ=μ / (ρc S 2 )+δ t / 2,δ x =δ y =δ z δ is the unit grid spacing. t c is the unit time step. S For the speed of sound in a lattice, c S 2 The virtual lattice sound velocity used for calculation purposes, c S 2 =1 / 3. R is the regularization operator, acting on the non-equilibrium distribution function, f i neq The non-equilibrium distribution function is defined as f i neq =f i -f i eq +0.5*ψ i f i eq Let ψ be the equilibrium distribution function. i For power source items.

[0079] For example, this application uses the D3Q19 discrete velocity model, and the velocity set and corresponding weight coefficients of the model are defined as follows:

[0080] (Formula 7)

[0081] (Formula 8)

[0082] In the formula, c ix c iy c iz Let δ be a discrete velocity vector in different directions in three-dimensional space. x δ is the unit grid spacing. t The unit time step. These are the weighting coefficients for different discrete directions i.

[0083] In some embodiments, refer to Figure 3 , Figure 3 This is another schematic flowchart illustrating the arc simulation method provided in this application. Figure 3 As shown, in S210, the geometric model of the arc-extinguishing chamber is discretized into mesh elements based on the lattice Boltzmann model, including the following steps S310~S340.

[0084] S310: Obtain the STL file of the arc-extinguishing chamber and obtain the geometric model of the arc-extinguishing chamber based on the STL file.

[0085] S320: Project the geometric model onto the grid space corresponding to the lattice Boltzmann model to obtain the grid points where the geometric model intersects with the grid space. The intersecting grid points are marked as boundary grid points.

[0086] S330: Based on these boundary grid points, reconstruct the outline of the region occupied by the arc-extinguishing chamber in the grid space.

[0087] S340: Based on the contour of the region, determine the type of all grid points in the grid space, and reconstruct the grid element corresponding to the arc-extinguishing chamber in the grid space according to the type of all grid points.

[0088] Specifically, the type of all grid points in the mesh space is determined based on the contour of the region: grid points located inside the contour of the region are marked as solid grid points, and grid points located outside the contour of the region are marked as fluid grid points.

[0089] As is understandable, an STL file is a surface mesh model file. An STL file is a pure geometric file without topology, color, material, or texture. While an STL file can represent the shape of an object, it cannot represent its material, color, surface pattern, or store the topological relationships between vertices. Based on an STL file, the triangular facet information stored in the file can be parsed, including the vertex coordinates and normal vectors of each face. This information can be pieced together to reconstruct the complete 3D object outline, and thus reconstruct the geometric model of the arc-extinguishing chamber.

[0090] Furthermore, when projecting this geometric model onto the mesh space corresponding to the lattice Boltzmann model, projection can be performed from any viewpoint in the x, y, and z directions of the coordinate system. This discrimination method requires less computation and improves the efficiency of boundary point identification.

[0091] This process enables the reconstruction from STL files to mesh cells.

[0092] S220: Determine the unit conversion factor for each grid point from the physical unit to the grid unit in the geometric model, and convert the physical quantities of all grid points from physical units to grid units according to the unit conversion factor.

[0093] The physical quantities of the grid points can include density, velocity, and temperature.

[0094] Specifically, the unit conversion coefficient can be determined based on the Mach number similarity criterion and the Reynolds number similarity criterion, and the unit conversion coefficient includes the characteristic length conversion coefficient ΔL, the characteristic time conversion coefficient ΔT, the characteristic mass conversion coefficient ΔM, and the characteristic temperature conversion coefficient ΔK.

[0095] Understandably, in the lattice Boltzmann model, the conversion between physical units and lattice units is primarily based on similarity criteria, where physical quantities are expressed in the International System of Units (SI). In the isothermal LBGK model (lattice bhatnagar-gross-krook model), there is no need to solve the energy equation; this method is only applicable to weakly compressible flows (Mach number Ma < 0.1), meaning that only the Reynolds number similarity criterion needs to be satisfied.

[0096] For simulations of subsonic or supersonic flows, both the Reynolds number similarity criterion and the Mach number similarity criterion must be satisfied. Therefore, in the embodiments of this application, the dimensional conversion of basic physical quantities such as length, time, mass, and temperature needs to be considered when performing unit conversions, i.e., the characteristic length conversion coefficient ΔL, the characteristic time conversion coefficient ΔT, the characteristic mass conversion coefficient ΔM, and the characteristic temperature conversion coefficient ΔK. The unit conversion coefficients can be obtained based on the following formulas:

[0097] (Formula 9)

[0098] (Formula 10)

[0099] (Formula 11)

[0100] (Formula 12)

[0101] (Formula 13)

[0102] In the formula, u α,physical velocity in physical units, u α,lattice P represents the velocity in grid units. physical Pressure in physical units, P lattice ρ represents the pressure per lattice unit. physical Density in physical units, ρ lattice Density in lattice units. μ physical Dynamic viscosity in physical units, μ lattice C represents the dynamic viscosity in lattice units. v,physical C is the specific heat capacity at constant volume in physical units. v,latticeSpecific heat capacity at constant volume in grid units.

[0103] Furthermore, after converting all physical quantities at all lattice points to lattice units using the unit conversion factor, to ensure computational convergence, the convergence of the calculation can be verified by calculating the velocity of sound and the normalized temperature θ at the lattice points to check if they satisfy the Courant-Friedrichs-Lewy condition (CFL condition). The verification formula is as follows:

[0104] (Formula 14)

[0105] In the formula, θ is the normalized temperature, CFL is the Courant-Friedrich-Levi number, Ma is the Mach number, and γ is the normalized temperature. g c is the specific heat ratio of the gas. s For the speed of sound in a grid.

[0106] Therefore, based on the Mach number similarity criterion and the Reynolds number similarity criterion, the unit conversion coefficient is determined so that the lattice Boltzmann model can adaptively match the high Mach number and high Reynolds number characteristics of the high voltage arc, avoiding simulation deviations caused by scale conversion distortion.

[0107] S230: Perform local collisions and migrations at each grid point to update the density and velocity of the flow field at each time step.

[0108] Through steps S210~S230, the microscopic particle interaction mechanism of the lattice Boltzmann model is used to efficiently update density and velocity, capturing transient changes in the electric arc flow.

[0109] The following section provides a detailed explanation of the process in S230 where local collisions and migrations are performed at each grid point to update the density and velocity of the flow field at each time step.

[0110] Reference Figure 4 , Figure 4 This is another schematic flowchart illustrating the arc simulation method provided in this application. Figure 4 As shown, the process of performing local collisions and migrations at each grid point to update the density and velocity of the flow field at each time step includes the following steps S410~S430.

[0111] S410: Perform local collisions at each grid point to obtain the distribution function after the collision.

[0112] Understandably, in the pressure-based regularization method, the numerical solution of the lattice Boltzmann equations can be achieved through a collision-transfer scheme. In this scheme, all physical models are processed in the collision step, eliminating the need for data communication between lattice nodes, while the transfer step only involves data exchange between adjacent nodes. Therefore, the distribution function after the collision is as follows:

[0113] (Formula 15)

[0114] In the formula, Let f be the distribution function after the collision. i eq Let f be the equilibrium distribution function. i neq Let ψ be the non-equilibrium distribution function, R be the regularization operator, and ψ be the inequality distribution function. i For power source items.

[0115] The equilibrium distribution function f in the equation is explained below. i eq Non-equilibrium distribution function f i neq Regularization operator R and force source term ψ i The expression is explained.

[0116] First, let's explain the equilibrium distribution function f. i eq The expression.

[0117] Unlike the second-order Taylor expansion used in the LBGK model, the equilibrium distribution function f in this embodiment is different. i eq A third-order pressure basis formulation is adopted, which is based on a completely orthogonal basis of D3Q19 Gauss-Hermite polynomials, as shown in the following formula:

[0118] (Formula 16)

[0119] In the formula, f i eq,19r This represents the equilibrium distribution function when using the D3Q19 discrete velocity model. Additionally, the coefficients of the Gauss-Hermite polynomial are as follows:

[0120] (Formula 17)

[0121] (Formula 18)

[0122] Furthermore, the equilibrium distribution function f i eq The thermal effects in the equation of state need to be considered. Therefore, the normalized temperature θ = r is defined. g T s / c S 2 From this, the equilibrium distribution function f can be derived. i eq The physical static pressure csp With the physical speed of sound p s The expression is as follows:

[0123] (Formula 19)

[0124] (Formula 20)

[0125] In the formula, d i This is a hot correction term.

[0126] The following explains the non-equilibrium distribution function f. i neq The expression for the regularization operator R.

[0127] The non-equilibrium distribution function f corresponding to the D3Q19 discrete velocity model used in the embodiments of this application is... i neq The regularization operator R can be expressed as follows:

[0128] (Formula 21)

[0129] (Formula 22)

[0130] The following explains the force source term ψ. i The expression.

[0131] For the pressure-based regularized lattice Boltzmann method, the force source term ψ i By the correction term Ψ αβ The second-order Hermitian expansion yields the correction term Ψ. αβ Consider three types of error components: the third moment Ψ αβ,1 Viscous stress tensor Ψ αβ,2 and the error term Ψ related to the mass conservation equation αβ,3 Therefore, the force source term ψ i The expression is as follows:

[0132] (Formula 23)

[0133] In the formula, Ψ αβ,1 Ψ αβ,2 and Ψ αβ,3 The expression is:

[0134] (Formula 24)

[0135] (Formula 25)

[0136] (Formula 26)

[0137] In the formula, Let be the spatial derivative of the third moment of the equilibrium distribution function.

[0138] S420: Based on the distribution function after the collision, each grid point is migrated to an adjacent grid point along the discrete velocity direction specified by the lattice Boltzmann model, and the migrated distribution function is obtained.

[0139] Specifically, the expression for the distribution function after migration is:

[0140] (Formula 27)

[0141] S430: Based on the migrated distribution function, update the density and velocity of the flow field at each time step.

[0142] Specifically, based on the migrated distribution function, the density ρ and velocity u can be updated by taking moments. α That is, density ρ and velocity u α These can be derived from the zeroth and first moments of the migrated distribution function, respectively. Based on this, the density ρ and velocity u are updated. α The calculation formula is as follows:

[0143] (Formula 28)

[0144] Based on steps S410~S430, the density and velocity of the flow field are efficiently coupled and solved by updating the distribution function, providing a microscopic physical description of the electric arc dynamics.

[0145] Furthermore, most traditional models used to describe electric arc turbulence employ Prandtl mixing length models or determine turbulent viscosity by solving two transport equations describing turbulent characteristics, thereby closing the Reynolds-averaged equations (RANS equations), such as the k-ε model and k-ω model. This method performs time averaging of the flow, solving only the stable average flow field, approximating all turbulent fluctuations through the model, abandoning the pursuit of turbulent details, and only concerned with the final overall statistical effect, resulting in poor handling of details. Therefore, in some embodiments of this application, the lattice Boltzmann method can use a large eddy simulation (LES) model to solve for turbulence. Specifically, the LES model uses the Smagorinsky sublattice stress model to simulate the influence of small-scale eddies. In this way, the LES model can capture transient turbulent structures with higher accuracy than the RANS equations. The LES model can resolve transient eddy structures that RANS cannot capture, providing more accurate predictions of flow field details.

[0146] The calculation formula for the subgrid stress model is as follows:

[0147] (Formula 29)

[0148] In the formula, τ eff Let τ be the effective relaxation time, and C be the relaxation time. sm δ is the Smagorinsky constant. t c is the unit time step. S For the speed of sound in a lattice, δ x The unit grid spacing, It is the correlation quantity of the second invariant of the strain rate tensor.

[0149] The following section provides a detailed explanation of the process by which S130 solves the energy conservation equation using the finite difference method and updates the temperature of the flow field at each time step.

[0150] Reference Figure 5 , Figure 5 This is another schematic flowchart illustrating the arc simulation method provided in this application. Figure 5 As shown, the process of solving the energy conservation equation based on the finite difference method and updating the temperature of the flow field at each time step includes the following steps S510~S520.

[0151] S510: Discretize the time derivative and space derivative of the energy conservation equation.

[0152] S520: Solve the discretized energy conservation equations to update the temperature of the flow field at each time step.

[0153] Specifically, the discretization of the time derivative of the energy conservation equation in S510 includes: discretizing the time derivative of the energy conservation equation using a first-order Euler scheme. The discretization of the spatial derivative of the energy conservation equation in S510 includes: using an upwind scheme to handle the convection term of the energy conservation equation, and using a second-order central difference scheme to handle the heat conduction term and the viscous dissipation term of the energy conservation equation.

[0154] Based on steps S510~S520, the time derivative and space derivative of the energy conservation equation are discretized to facilitate temperature calculation.

[0155] Specifically, the time derivative of the energy conservation equation is discretized using a first-order Euler scheme, and the formula used is as follows:

[0156] (Formula 30)

[0157] In the formula, The general variable represents the physical quantity that needs to be solved, and in Formula 30, it represents temperature T. s .

[0158] The formula for the convection term of the energy conservation equation using the upwind approach is as follows:

[0159] (Formula 31)

[0160] In formula 31, temperature T is represented. s .

[0161] The formula for handling the heat conduction term in the energy conservation equation using a second-order central difference scheme is as follows:

[0162] (Formula 32)

[0163] The formula for handling the viscous dissipation term of the energy conservation equation using a second-order central difference scheme is as follows:

[0164] (Formula 33)

[0165] In formula 33, temperature T is represented. s .

[0166] This application also provides an electronic device, which includes a processor and a memory. The memory stores at least one instruction or at least one program segment. The processor loads and executes the instruction or program segment to implement the arc simulation method described in the above embodiments. The specific functions and corresponding technical effects of the electronic device can be found in the above embodiments. Figures 1-5 The methods explained will not be elaborated here.

[0167] Now for reference Figure 6 The diagram shown is a block diagram of an electronic device 1200 according to an embodiment of this application. The electronic device 1200 may include one or more processors (corresponding to...) coupled to a controller hub 1203. Figure 6 The first processor 1201 is described above. In at least one embodiment, the controller hub 1203 communicates with the first processor 1201 via a multi-branch bus such as a front-side bus (FSB), a point-to-point interface such as a quick path interconnect (QPI), or a similar connection. The first processor 1201 executes instructions that control general types of data processing operations. In one embodiment, the controller hub 1203 includes, but is not limited to, a graphics memory controller hub (GMCH) (not shown) and an input / output hub (IOH) (which may be on a separate chip) (not shown), wherein the GMCH includes memory and a graphics controller and is coupled to the IOH.

[0168] Electronic device 1200 may also include a coprocessor coupled to controller hub 1203 (corresponding to...) Figure 6 The processor 1202 and memory 1204 are integrated within the processor (as described in this application). Alternatively, one or both of the memory and GMCH can be integrated within the processor (as described in this application), with memory 1204 and the first coprocessor 1202 directly coupled to the first processor 1201 and the controller hub 1203, which is located on a single chip with the IOH. Memory 1204 can be, for example, dynamic random access memory (DRAM), phase change memory (PCM), or a combination of both. In one embodiment, the first coprocessor 1202 is a dedicated processor, such as a high-throughput MIC processor (many integerized core, MIC), a network or communication processor, a compression engine, a graphics processor, a general-purpose computing on GPU (GPGPU), or an embedded processor, etc. Optional properties of the first coprocessor 1202 are indicated by dashed lines. Figure 6 middle.

[0169] As a computer-readable storage medium, memory 1204 may include one or more tangible, non-transitory computer-readable media for storing data and / or instructions. For example, memory 1204 may include any suitable non-volatile memory such as flash memory and / or any suitable non-volatile storage device such as one or more hard-disk drives (HDDs), one or more compact disc (CD) drives, and / or one or more digital versatile disc (DVD) drives.

[0170] In one embodiment, electronic device 1200 may further include a network interface controller (NIC) 1206. Network interface 1206 may include a transceiver for providing a radio interface for electronic device 1200 to communicate with any other suitable device, such as a front-end module, antenna, etc. In various embodiments, network interface 1206 may be integrated with other components of electronic device 1200. Network interface 1206 can implement the functions of the communication unit in the above embodiments.

[0171] Electronic device 1200 may further include input / output (I / O) device 1205. I / O device 1205 may include: a user interface designed to enable a user to interact with electronic device 1200; a peripheral component interface designed to enable peripheral components to also interact with electronic device 1200; and / or sensors designed to determine environmental conditions and / or location information related to electronic device 1200.

[0172] It is worth noting that, Figure 6 This is merely an example. That is, although... Figure 6 The electronic device 1200 shown includes multiple devices such as a first processor 1201, a first coprocessor 1202, a controller hub 1203, and a memory 1204. However, in actual applications, devices using the methods of this application may include only a portion of the devices in the electronic device 1200. For example, it may include only the first processor 1201 and the network interface 1206. Figure 6 The properties of the optional devices are shown in dashed lines. According to some embodiments of this application, the memory 1204, which is a computer-readable storage medium, stores instructions that, when executed on a computer, cause the electronic device 1200 to perform the arc simulation method according to the above embodiments. Specific details can be found in the methods described in the above embodiments, and will not be repeated here.

[0173] Now for reference Figure 7 The diagram shown is a block diagram of a SoC (system on chip) 1300 according to an embodiment of this application. Figure 7 In the diagram, similar components share the same reference numerals. Additionally, dashed boxes are an optional feature for more advanced SoCs. Figure 7 In the SoC1300, interconnect unit 1350 is coupled to the processor (corresponding to...). Figure 7 The system includes a second processor 1310, a system agent unit 1380, a bus controller unit 1390, an integrated memory controller unit 1340, and one or more coprocessors (corresponding to...). Figure 7 The second coprocessor 1320 may include integrated graphics logic, an image processor, an audio processor, and a video processor; a static random access memory (SRAM) unit 1330; and a direct memory access (DMA) unit 1360. In one embodiment, the second coprocessor 1320 includes a dedicated processor, such as a network or communication processor, a compression engine, a GPGPU, a high-throughput MIC processor, or an embedded processor.

[0174] The static random access memory (SRAM) cell 1330 may include one or more computer-readable media for storing data and / or instructions. The computer-readable storage medium may store instructions, specifically, temporary and permanent copies of those instructions. These instructions may include, when executed by at least one unit in the processor, causing the SoC 1300 to perform the arc simulation method according to the above embodiments, as detailed in the methods described above, which will not be repeated here.

[0175] Various embodiments of the mechanisms disclosed in this application can be implemented in hardware, software, firmware, or combinations of these implementation methods. Embodiments of this application can be implemented as computer programs or program code executable on a programmable system, the programmable system including at least one processor, a storage system (including volatile and non-volatile memory and / or storage elements), at least one input device, and at least one output device.

[0176] Program code can be applied to input instructions to execute the functions described in this application and generate output information. The output information can be applied to one or more output devices in a known manner. For the purposes of this application, the processing system includes any system having a processor such as a digital signal processor (DSP), microcontroller, application-specific integrated circuit (ASIC), or microprocessor.

[0177] The program code can be implemented using a high-level procedural language or an object-oriented programming language to communicate with the processing system. Assembly language or machine language can also be used when needed. In fact, the mechanisms described in this application are not limited to any particular programming language. In either case, the language can be a compiled language or an interpreted language.

[0178] In some cases, the disclosed embodiments may be implemented in hardware, firmware, software, or any combination thereof. The disclosed embodiments may also be implemented as instructions carried or stored thereon on one or more temporary or non-temporary machine-readable (e.g., computer-readable) storage media, which may be read and executed by one or more processors. For example, the instructions may be distributed via a network or through other computer-readable media. Therefore, machine-readable media may include any mechanism for storing or transmitting information in a machine-readable (e.g., computer-readable) form, including but not limited to floppy disks, optical disks, CD-ROMs, compact disc read-only memory (CD-ROMs), magneto-optical disks, read-only memory (ROM), random access memory (RAM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), magnetic cards or optical cards, flash memory, or tangible machine-readable storage for transmitting information (e.g., carrier waves, infrared signals, digital signals, etc.) using the Internet in the form of electrical, optical, acoustic, or other forms of propagated signals. Therefore, machine-readable media include any type of machine-readable medium suitable for storing or transmitting electronic instructions or information in a machine-readable (e.g., computer-readable) form.

[0179] In the accompanying drawings, some structural or methodological features may be shown in a specific arrangement and / or order. However, it should be understood that such a specific arrangement and / or order may not be necessary. Rather, in some embodiments, these features may be arranged in a manner and / or order different from that shown in the accompanying drawings. Furthermore, including structural or methodological features in a particular figure does not imply that such features are required in all embodiments, and in some embodiments, these features may be omitted or may be combined with other features.

[0180] This application also provides a computer-readable storage medium storing at least one instruction or at least one program segment, which is loaded and executed by a processor to implement the arc simulation method in the above embodiments. Its specific functions and corresponding technical effects can be found in the above embodiments. Figures 1-5 The methods explained will not be elaborated here.

[0181] This application also provides a computer program product, which includes a computer program or instructions. When executed by a processor, the computer program or instructions implement the arc simulation method described in the above embodiments. Its specific functions and corresponding technical effects can be found in the above embodiments. Figures 1-5 The methods explained will not be elaborated here.

[0182] It should be noted that the order of the embodiments described above is merely for descriptive purposes and does not represent the superiority or inferiority of the embodiments. Furthermore, specific embodiments have been described above. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps described in the claims can be performed in a different order than that shown in the embodiments and still achieve the desired result. Additionally, the processes depicted in the drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0183] It should be noted that all units / modules mentioned in the device embodiments of this application are logical units / modules. Physically, a logical unit / module can be a physical unit / module, a part of a physical unit / module, or a combination of multiple physical units / modules. The physical implementation of these logical units / modules themselves is not the most important factor; the combination of functions implemented by these logical units / modules is the key to solving the technical problems proposed in this application. Furthermore, to highlight the innovative aspects of this application, the above-described device embodiments of this application have not introduced units / modules that are not closely related to solving the technical problems proposed in this application. This does not mean that the above-described device embodiments do not contain other units / modules.

[0184] It should be noted that in the examples and description of this application, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one" does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0185] Although this application has been illustrated and described with reference to certain preferred embodiments thereof, those skilled in the art should understand that various changes in form and detail may be made thereto without departing from the spirit and scope of this application.

Claims

1. A method for simulating electric arc in an arc-extinguishing chamber, characterized in that, include: The governing equations for simulating the arc in the arc-extinguishing chamber are constructed, and the governing equations include the mass conservation equation, the momentum conservation equation, and the energy conservation equation. Based on the lattice Boltzmann method, and taking the mass conservation equation and the momentum conservation equation as simulation targets, the density and velocity of the flow field corresponding to the arc-extinguishing chamber at each time step are updated during the arc simulation process in the arc-extinguishing chamber. The energy conservation equation is solved using the finite difference method, and the temperature of the flow field is updated at each time step. The arc simulation of the arc-extinguishing chamber is completed based on the density, velocity, and temperature of the flow field at each time step.

2. The arc simulation method for the arc-extinguishing chamber according to claim 1, characterized in that, The method based on the lattice Boltzmann, using the mass conservation equation and the momentum conservation equation as simulation targets, updates the density and velocity of the flow field in the arc-extinguishing chamber at each time step during the arc simulation process, including: The geometric model of the arc-extinguishing chamber is discretized into grid cells based on the lattice Boltzmann model, and each grid cell includes multiple grid points; Determine the unit conversion factor for each grid point from the physical unit to the grid unit of the geometric model, and convert the physical quantities of all grid points from the physical unit to the grid unit according to the unit conversion factor; Local collisions and migrations are performed at each of the grid points to update the density and velocity of the flow field at each time step.

3. The arc simulation method for the arc-extinguishing chamber according to claim 2, characterized in that, The process of performing local collisions and migrations at each of the grid points to update the density and velocity of the flow field at each time step includes: Local collisions are performed at each of the grid points to obtain the distribution function after the collisions. Based on the distribution function after the collision, each grid point is migrated to an adjacent grid point along the discrete velocity direction specified by the lattice Boltzmann model, and the migrated distribution function is obtained. Based on the migrated distribution function, the density and velocity of the flow field at each time step are updated.

4. The arc simulation method for the arc-extinguishing chamber according to claim 2, characterized in that, The determination of the unit conversion coefficients for each of the grid points from the physical units of the geometric model to the grid units includes: The unit conversion coefficients are determined based on the Mach number similarity criterion and the Reynolds number similarity criterion; the unit conversion coefficients include: characteristic length conversion coefficient, characteristic time conversion coefficient, characteristic mass conversion coefficient, and characteristic temperature conversion coefficient.

5. The arc simulation method for the arc-extinguishing chamber according to claim 1, characterized in that, The process of solving the energy conservation equation based on the finite difference method and updating the temperature of the flow field at each time step includes: Discretize the time and space derivatives of the energy conservation equation; Solve the discretized energy conservation equation to update the temperature of the flow field at each time step.

6. The arc simulation method for the arc-extinguishing chamber according to claim 5, characterized in that, Discretizing the time derivative of the energy conservation equation includes: discretizing the time derivative of the energy conservation equation using a first-order Euler scheme; Discretizing the spatial derivative of the energy conservation equation includes: using an upwind scheme to process the convection term of the energy conservation equation, and using a second-order central difference scheme to process the heat conduction term and the viscous dissipation term of the energy conservation equation.

7. The arc simulation method for the arc-extinguishing chamber according to claim 2, characterized in that, The lattice Boltzmann model employs a pressure-based regularization scheme.

8. An electronic device, characterized in that, The electronic device includes a processor and a memory, wherein the memory stores at least one instruction or at least one program, and the at least one instruction or the at least one program is loaded and executed by the processor to implement the arc simulation method of the arc extinguishing chamber as described in any one of claims 1-7.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores at least one instruction or at least one program, which is loaded and executed by a processor to implement the arc simulation method for the arc extinguishing chamber as described in any one of claims 1-7.

10. A computer program product, comprising a computer program or instructions, characterized in that, When the computer program or instructions are executed by the processor, they implement the arc simulation method for the arc extinguishing chamber as described in any one of claims 1-7.

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