Free metal particle trajectory simulation method and system based on deformable grid
Through the particle trajectory simulation method based on deformable mesh, the problem of insufficient grid update instability and simulation accuracy in the prior art is solved, and more accurate particle motion simulation is achieved, which is suitable for safety assessment of gas insulating equipment.
Patent Information
- Application Number
- CN202510661139.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-22
- Publication Date
- 2025-09-02
AI Technical Summary
In the prior art, particle motion simulation methods have problems such as instability of grid updates and insufficient simulation accuracy when dealing with complex geometric shapes, especially in long-distance motion, which makes it difficult to maintain the stability and high quality of the grid, resulting in the inability to effectively adapt to the particle motion simulation requirements under concave polygon geometry.
The free metal particle trajectory simulation method based on deformable mesh is adopted. By establishing a density function, updating the grid node position, and local grid reconstruction using Riemann gradient control and frontier propulsion method, the limitations of the point charge model are overcome to achieve more accurate particle motion simulation.
It improves the accuracy and stability of particle motion simulation, provides efficient simulation tools, and provides technical support for the safe operation of gas insulating equipment.
Smart Images
Figure CN120579407A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of electric power, and more particularly to a method and system for simulating free metal particle trajectories based on a deformable grid. Background Art
[0002] Gas-insulated equipment (GIEE) is a key component in power systems. Solid impurity particles within GIEE can trigger gas gap discharges, a significant factor affecting the safe and stable operation of GIEE. Accurately modeling the motion of these particles has important theoretical and engineering applications for fault tracing and equipment safety assessment.
[0003] In the existing technology, particle motion simulation usually uses a point charge model to characterize particles. However, due to the disturbance of the electric field by the particles themselves and the influence of gas resistance, the point charge model may cause distortion in mechanical analysis, thereby reducing the accuracy of the simulation. In addition, the grid-based simulation method has limitations when dealing with complex geometric shapes (such as concave polygons). Existing grid motion methods are limited by grid update and smoothing technology. After the grid is updated, there may be problems such as nodes exceeding the boundary or the quality of the grid deteriorating. Especially in long-distance movement, it is difficult to maintain the stability and high quality of the grid. This makes the existing methods unable to effectively adapt to the needs of particle motion simulation under concave polygonal geometries.
[0004] Therefore, there is an urgent need for a simulation method that can overcome the above-mentioned defects to improve the accuracy and stability of particle motion trajectory simulation and provide technical support for the safe operation of gas-insulated equipment. Summary of the Invention
[0005] To address the deficiencies in the prior art, the present invention provides a method for simulating free metal particle trajectories based on a deformable grid. By using deformable grid technology, the interaction between particles and physical fields is fully considered, the limitations of the point charge model are overcome, and a more accurate simulation of particle motion is achieved.
[0006] The present invention adopts the following technical solutions.
[0007] The first aspect of the present invention relates to a method for simulating the trajectory of free metal particles based on a deformable grid, the method comprising the following steps: Step 1, establishing a particle motion model and establishing a density function with free metal particles as key points; Step 2, when the particle position changes, updating the position and grid of the particle node in the background grid, calculating the grid quality and collecting low-quality grids; Step 3, based on the Riemann gradient control method, establishing a grid size field for each reconstruction range, and then using the frontier advancing method to perform local grid reconstruction; Step 4, simulating the particle motion according to the boundary conditions of the particle motion.
[0008] Establish a particle motion model and a density function with free metal particles as key points, including: obtaining geometric information based on the STL file of the particle motion model and constructing a grid data structure using points, lines, and surfaces.
[0009] Establish a particle motion model and a density function with free metal particles as key points, including: density function ρ with particles as key points p for:
[0010]
[0011] ρ=min(ρ p ,ρ max )
[0012] Where (x, y) is the position of the particle in the Euler coordinate system,
[0013] C is the midpoint of the particle model,
[0014] r is the particle radius,
[0015] (ρ min ,ρ max ) are the specified minimum and maximum mesh densities, and ρ is the mesh density at a certain location in the solution domain.
[0016] When the particle position changes, the position and mesh of the particle node in the background mesh are updated, the mesh quality is calculated and the low-quality mesh is collected, including: the mesh quality is:
[0017]
[0018] The vertices A, B, and C of the background grid before the particle position changes form a triangle △ABC;
[0019] AB, AC, and BC are the sides of triangle △ABC.
[0020] Based on the Riemann gradient control method, a grid size field is established for each reconstruction range, and then the frontier advancing method is used to perform local grid reconstruction, including: obtaining a closed polygon composed of low-quality grids, adding adjacent triangles to the low-quality grid set, and obtaining the reconstructed area; calculating the Riemann metric of each node according to the local area boundary, and gradienting the Riemann metric of the reconstructed area; based on the Riemann gradient field, using a discrete method based on bisection to divide the geometric model boundary; and performing local grid reconstruction according to the frontier advancing method.
[0021] The Riemannian metric of each node is calculated according to the local region boundary, and the Riemannian metric of the reconstructed region is gradiented, including: calculating the change gradient h(Q) and h(P) of the Riemannian metric between the two end points (P, Q) in the local region boundary. When ||h(Q)||>||h(P)||, the current gradient is calculated as:
[0022] γ=h(Q) / h(P) 1 / l(PQ,M(Q))
[0023] Where l(PQ,M(Q)) is the Riemann length after updating the Riemann metric M(Q) of point Q.
[0024] The Riemannian metric of each node is calculated according to the local area boundary, and the Riemannian metric of the reconstructed area is gradiented, including: the updating method of the Riemannian metric M(Q) of the Q point is:
[0025] Calculate the correction factor as:
[0026] η=(γ0 / γ) l(PQ)
[0027] Where γ0 is the maximum allowable gradient, and the current gradient γ = h(Q) / h(P) 1 / l(PQ) , l(PQ) is the Riemann length of the line segment PQ with point Q as the reference; the Riemann metric M(Q) of point Q is updated using the correction coefficient:
[0028] M(Q)=M(Q)η -2 .
[0029] The second aspect of the present invention relates to a free metal particle trajectory simulation system based on a deformable grid; the system is implemented using the method described in the first aspect of the present invention; the system includes an establishment unit, an update unit, a reconstruction unit, and a simulation unit; the establishment unit is used to establish a particle motion model and a density function with free metal particles as key points; the update unit is used to update the position and grid of particle nodes in the background grid when the particle position changes, calculate the grid quality and collect low-quality grids; the reconstruction unit is used to establish a grid size field for each reconstruction range based on the Riemann gradient control method, and then use the frontier advancing method to perform local grid reconstruction; the simulation unit is used to simulate particle motion according to the boundary conditions of particle motion.
[0030] A third aspect of the present invention relates to a terminal, comprising a processor and a storage medium; the storage medium is used to store instructions; and the processor is used to operate according to the instructions to execute the steps of the method described in the first aspect of the present invention.
[0031] A fourth aspect of the present invention relates to a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in the first aspect of the present invention.
[0032] The beneficial effect of this invention lies in that, compared with existing technologies, the present method for simulating free-flowing metal particle trajectories based on a deformable grid fully considers the interaction between particles and the physical field through deformable grid technology, overcomes the limitations of point charge models, and achieves more accurate particle motion simulation. This method provides an efficient and stable simulation tool for studying particle motion in gas-insulated equipment.
[0033] The beneficial effects of the present invention also include:
[0034] A marching frontier method is used to generate a density-adaptive initial background mesh to accommodate the size differences between the particle model and the background geometry. For concave polygonal geometries, a Delaunay graph-based mapping technique is proposed to update the mesh node positions and perform local mesh reconstruction using the marching frontier method.
[0035] The design of the present invention fully considers the interaction between particles and physical fields through deformable grid technology, overcomes the limitations of the point charge model, and achieves more accurate particle motion simulation; the adaptive background grid generation method is suitable for concave polygonal geometric shapes, avoiding the problems of nodes exceeding boundaries and grid quality degradation; the local grid reconstruction method effectively repairs low-quality and invalid grid areas, ensuring the stability of long-distance grid motion and the continuity of simulation. BRIEF DESCRIPTION OF THE DRAWINGS
[0036] Figure 1 Schematic diagram of the composition of three basic grid data units of the present invention;
[0037] Figure 2 A schematic diagram of the present invention for generating a Delaunay background grid using particles and selected boundary points;
[0038] Figure 3 Schematic diagram of the metal particle capture model under a flat electrode selected as the research object for the present invention;
[0039] Figure 4 Schematic diagram of the Delaunay background grid of the present invention;
[0040] Figure 5 Schematic diagram of the present invention for calculating the position of a grid node based on the area ratio coefficient of each node determined by the background grid;
[0041] Figure 6 A schematic diagram of updating the Delaunay background grid according to the present invention;
[0042] Figure 7 A schematic diagram of obtaining a low-quality grid set according to the present invention;
[0043] Figure 8Schematic diagram of the present invention calculating the updated grid node position based on the area ratio coefficient of each node determined by the background grid;
[0044] Figure 9 Schematic diagram of the particle movement achieved by the present invention. DETAILED DESCRIPTION
[0045] In order to make the purpose, technical solutions and advantages of the present invention clearer and more accurate, the technical solutions of the present invention are described in detail below through multiple specific embodiments. The embodiments used in the present invention are only used to explain the present invention and are not intended to limit the content of the present invention.
[0046] Due to the complex structure of electrical equipment within substations, the numerous status indicators, and the significant uncertainty in this information, experts often differ significantly when assigning weights to indicators at each level. These differences often lead to extremes, significantly complicating the subsequent weight assignment algorithm. Therefore, a method is needed to optimize the evaluation matrix elements to reduce the undesirable effects of extreme values.
[0047] A first aspect of the present invention relates to a method for simulating free metal particle trajectories based on a deformable grid, the method comprising the following steps:
[0048] Step 1: Establish a particle motion model and a density function with free metal particles as key points.
[0049] First, the initial meshing method of the particle motion model is established based on the frontier advancement method. The geometric information is obtained based on the STL file of the particle motion model, and the mesh data structure is constructed using points, lines, and surfaces. The composition of the three basic mesh data units is as follows: Figure 1 shown.
[0050] Due to the large size gap between the particles and the background geometry, in order to adaptively control the grid density distribution, a density function with the particle geometry as the key point is established as shown in the formula. Based on this formula, the frontier advancing method is used to generate the initial grid.
[0051] Density function ρ with particles as key points p for:
[0052]
[0053] ρ=min(ρ p ,ρ max )
[0054] Where (x, y) is the position of the particle in the Euler coordinate system,
[0055] C is the midpoint of the particle model,
[0056] r is the particle radius,
[0057] (ρ min ,ρ max ) are the specified minimum and maximum mesh densities, and ρ is the mesh density at a certain location in the solution domain.
[0058] Step 2: When the particle position changes, the position and mesh of the particle node in the background mesh are updated, the mesh quality is calculated, and the low-quality meshes are collected.
[0059] like Figure 2 , generate a Delaunay background grid with particles and selected boundary points, and calculate the area coordinates of all grid nodes in the background grid. The relationship between nodes and background grid and the area coordinate calculation formula are as follows:
[0060]
[0061] Where S i is the area of the triangle Ti formed by the node and the background grid, S is the area of the background grid where the node is located, e i is the area coefficient of the grid node p relative to points A, B, and C, and (xi,yi) is the deformed coordinates of the vertices A, B, and C of the triangle unit where the node p is located.
[0062] When the particle position changes, the mesh node position is updated to achieve mesh deformation and movement. To ensure the validity of the deformed mesh, all meshes are traversed, the mesh quality is calculated, and low-quality meshes are collected. By searching for adjacent low-quality meshes, continuous low-quality mesh areas are identified and the reconstruction range of local low-quality meshes is located.
[0063] When the particle position changes, update the position and mesh of the particle node in the background mesh, calculate the mesh quality and collect low-quality meshes, including:
[0064] The mesh quality is:
[0065]
[0066] The vertices A, B, and C of the background grid before the particle position changes form a triangle △ABC;
[0067] AB, AC, and BC are the sides of triangle △ABC.
[0068] Step 3: Based on the Riemann gradient control method, a grid size field is established for each reconstruction range, and then the frontier advancing method is used to perform local grid reconstruction.
[0069] Based on the Riemann gradient control method, a grid size field is established for each reconstruction range, and then the frontier advancing method is used to perform local grid reconstruction, including: obtaining a closed polygon composed of low-quality grids, adding adjacent triangles to the low-quality grid set, and obtaining the reconstructed area; calculating the Riemann metric of each node according to the local area boundary, and gradienting the Riemann metric of the reconstructed area; based on the Riemann gradient field, using a discrete method based on bisection to divide the geometric model boundary; and performing local grid reconstruction according to the frontier advancing method.
[0070] Based on the Riemann gradient control method, a grid size field is established for each reconstruction range, and then the frontier advancing method is used to perform local grid reconstruction. The specific steps are as follows:
[0071] The Riemannian metric of each node is calculated based on the local region boundary, and the Riemannian metric of the reconstructed region is gradiented, including:
[0072] Calculate the change gradient h(Q) and h(P) of the Riemannian metric between the two endpoints (P, Q) in the local region boundary. When |h(Q)|>|h(P), calculate the current gradient as:
[0073] γ=h(Q) / h(P) 1 / l(PQ,M(Q))
[0074] Where l(PQ,M(Q)) is the Riemann length after updating the Riemann metric M(Q) of point Q.
[0075] The Riemann metric of each node is calculated based on the local region boundary. For a two-dimensional isotropic problem, the Riemann metric at each point is:
[0076]
[0077] Where h is the density value at the grid point.
[0078] The Riemannian metric of each node is calculated based on the local region boundary, and the Riemannian metric of the reconstructed region is gradiented, including:
[0079] The updating method of the Q-point Riemann metric M(Q) is:
[0080] When an edge that does not meet the Riemann gradient requirements is found, assuming ||h(Q)||>||h(P)||, the correction coefficient is calculated as:
[0081] η=(γ0 / γ) l(PQ)
[0082] Where γ0 is the maximum allowable gradient, and the current gradient γ = h(Q) / h(P) 1 / l(PQ) , l(PQ) is the Riemann length of the line segment PQ with point Q as the reference;
[0083] The Q-point Riemann metric M(Q) is updated using the correction coefficient as follows:
[0084] M(Q)=M(Q)η -2 .
[0085] If the Riemann metric of a point on any edge of the current leaf node is updated, all leaf edges connected to this point need to be updated.
[0086] Based on the Riemann gradient field, a discrete method based on bisection is used to divide the boundary.
[0087] Before the discretization algorithm begins, it is necessary to establish a parametric equation for the boundary curve of the geometric model. The parametric equation is in the form of C(t) = (x(t), y(t)). In two-dimensional geometry, three basic elements are mainly distinguished: lines, circles, and curves. The three elements are distinguished by analyzing the characteristics of line segments in polygons: if there is only one line segment constituting the polygon, or the angle between two adjacent line segments is 180° or 0°, the current polygon is considered a line; if any three points in the polygon are used to calculate the possible center and radius, if all points in the polygon are equidistant from the center or the distance from the radius is within an acceptable range, the polygon is considered a circle; if the polygon is neither a line nor a circle, it is considered a multi-segment line, and so on.
[0088] In the embodiment, the reconstruction region boundary is divided into the initial frontier:
[0089]
[0090] The grid is reconstructed according to the frontier advancing method. The specific steps are as follows:
[0091] First, select an edge AB in the initial front as the initial edge of the newly generated triangle. Usually, the selected edge can be the first edge or the shortest edge in Front. The selected edge AB will be deleted from Front.
[0092] Calculate the value of the density function DF at the midpoint of AB, search for points near AB on the Front, requiring that the distance between the point and the midpoint of AB is less than DF and form a triangle (the triangle is required not to intersect the front), calculate the quality of each triangle, and select high-quality △ABD as the candidate.
[0093] Calculate the required point position C of the triangle.
[0094] Compare the quality factors of △ABC and △ABD, and add the one with higher quality to S.
[0095] If △ABD is added to the face set, determine whether edges AD and BD are included in Front. If AD is included in Front, delete AD from Front and add BD to Front. If AD is not included in Front, add AD to Front, and similarly for BD. If △ABC is added to face set S, add edges AC and BC to Front. For edges added to Front, calculate their internal normals and simultaneously add Fn. Determine whether Front is an empty set. If so, remesh. Otherwise, select a new front and repeat the above process.
[0096] Step 4: simulate the particle motion according to the boundary conditions of the particle motion.
[0097] In one embodiment, in order to simulate the movement of particles in a gas-insulated device under the action of a non-uniform electric field, a metal particle capture model under a flat electrode is selected as a research object, such as Figure 3 As shown. When the particle position changes, the position of the particle node in the background grid is generated, and then the Delaunay background grid is generated. The background grid before and after the movement is as follows Figure 4 As shown. The updated grid node position is calculated based on the area ratio coefficient of each node determined by the background grid. The updated grid is as follows Figure 5 shown.
[0098] For the mesh after movement Figure 6 , calculate the quality of all meshes, traverse all meshes to collect all low-quality meshes, and obtain a low-quality mesh set, such as Figure 7 As shown. According to the requirements of the frontier advancing method, a closed polygon composed of low-quality meshes is obtained. All triangles connected to the node are added to the low-quality mesh set and reconstructed together with the rest of the low-quality meshes using the frontier advancing method. Figure 7 As an example of the low-quality mesh shown in the figure, the mesh reconstruction result is as follows Figure 8 According to the boundary conditions of particle motion, the particle motion is simulated. Under the current boundary condition settings, the particle motion that can be achieved is as follows Figure 9 shown.
[0099] The second aspect of the present invention relates to a free metal particle trajectory simulation system based on a deformable grid; the system is implemented using the method described in the first aspect of the present invention; the system includes an establishment unit, an update unit, a reconstruction unit, and a simulation unit; the establishment unit is used to establish a particle motion model and a density function with free metal particles as key points; the update unit is used to update the position and grid of particle nodes in the background grid when the particle position changes, calculate the grid quality and collect low-quality grids; the reconstruction unit is used to establish a grid size field for each reconstruction range based on the Riemann gradient control method, and then use the frontier advancing method to perform local grid reconstruction; the simulation unit is used to simulate particle motion according to the boundary conditions of particle motion.
[0100] A third aspect of the present invention relates to a terminal, comprising a processor and a storage medium; the storage medium is used to store instructions; and the processor is used to operate according to the instructions to execute the steps of the method described in the first aspect of the present invention.
[0101] A fourth aspect of the present invention relates to a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in the first aspect of the present invention.
[0102] Finally, it should be noted that the above embodiments are intended only to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art will appreciate that the technical solutions of the present invention still include modifications or equivalent substitutions that may be made to the specific embodiments of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention are intended to be covered by the claims of the present invention.
Claims
1. A method for simulating free metal particle trajectories based on a deformable grid, characterized in that: The method comprises the following steps: Step 1: Establish a particle motion model and a density function with free metal particles as key points; Step 2: When the particle position changes, the position and mesh of the particle node in the background mesh are updated, the mesh quality is calculated, and the low-quality meshes are collected; Step 3: Based on the Riemann gradient control method, a grid size field is established for each reconstruction range, and then the frontier advancing method is used to perform local grid reconstruction; Step 4: simulate the particle motion according to the boundary conditions of the particle motion.
2. The method for simulating free metal particle trajectories based on a deformable grid according to claim 1, characterized in that: The method of establishing a particle motion model and a density function with free metal particles as key points includes: The geometric information is obtained based on the STL file of the particle motion model, and the grid data structure is constructed using points, lines and surfaces.
3. The method for simulating free metal particle trajectories based on a deformable grid according to claim 2, characterized in that: The method of establishing a particle motion model and a density function with free metal particles as key points includes: The density function ρ with the particle as the key point p for: ρ=min(ρ p ,r max ) Where (x, y) is the position of the particle in the Euler coordinate system, C is the midpoint of the particle model, r is the particle radius, (ρ min ,ρ max ) are the specified minimum and maximum mesh densities, and ρ is the mesh density at a certain location in the solution domain.
4. The method for simulating free metal particle trajectories based on a deformable grid according to claim 3, characterized in that: When the particle position changes, the position and mesh of the particle node in the background mesh are updated, the mesh quality is calculated, and low-quality meshes are collected, including: The mesh quality is: The vertices A, B, and C of the background grid before the particle position changes form a triangle △ABC; AB, AC, and BC are the sides of triangle △ABC.
5. The method for simulating free metal particle trajectories based on a deformable grid according to claim 4, characterized in that: The Riemann gradient control method is based on establishing a grid size field for each reconstruction range, and then the frontier advancing method is used to perform local grid reconstruction, including: Obtain a closed polygon composed of low-quality meshes, add adjacent triangles to the low-quality mesh set, and obtain the reconstructed area; Calculate the Riemannian metric of each node according to the local region boundary and gradient the Riemannian metric of the reconstructed region; Based on the Riemann gradient field, a discrete method based on bisection is used to divide the boundary of the geometric model; Local grid reconstruction is performed based on the frontier advancing method.
6. The method for simulating free metal particle trajectories based on a deformable grid according to claim 5, characterized in that: The step of calculating the Riemannian metric of each node according to the local region boundary and gradient-forming the Riemannian metric of the reconstructed region includes: Calculate the change gradient h(Q) and h(P) of the Riemannian metric between the two endpoints (P, Q) in the local region boundary. When ||h(Q)||>||h(P)||, calculate the current gradient as: γ=h(Q) / h(P) 1 / l(PQ,M(Q)) Where l(PQ,M(Q)) is the Riemann length after updating the Riemann metric M(Q) of point Q.
7. The method for simulating free metal particle trajectories based on a deformable grid according to claim 6, characterized in that: The step of calculating the Riemannian metric of each node according to the local region boundary and gradient-forming the Riemannian metric of the reconstructed region includes: The updating method of the Q-point Riemann metric M(Q) is: Calculate the correction factor as: η=(γ0 / γ) l(PQ) Where γ0 is the maximum allowable gradient, and the current gradient γ = h(Q) / h(P) 1 / l(PQ) , l(PQ) is the Riemann length of the line segment PQ with point Q as the reference; The Q-point Riemann metric M(Q) is updated using the correction coefficient as follows: M(Q)=M(Q)η -2 。 8. A free metal particle trajectory simulation system based on a deformable grid; characterized by: The system is implemented by the method according to any one of claims 1 to 7; The system includes a creation unit, an update unit, a reconstruction unit, and a simulation unit; The establishment unit is used to establish a particle motion model and a density function with free metal particles as key points; The updating unit is used to update the position and mesh of the particle nodes in the background mesh when the particle position changes, calculate the mesh quality and collect low-quality meshes; The reconstruction unit is used to establish a grid size field for each reconstruction range based on the Riemann gradient control method, and then use the frontier advancing method to perform local grid reconstruction; The simulation unit is used to simulate the movement of particles according to the boundary conditions of the particle movement.
9. A terminal comprising a processor and a storage medium; characterized in that: The storage medium is used to store instructions; The processor is configured to operate according to the instructions to execute the steps of the method according to any one of claims 1 to 7.
10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.