A method for evaluating the deflection of a silicone rubber umbrella skirt based on two-way fluid-structure coupling

Abstract

This invention belongs to the field of high voltage and insulation technology, and provides a method for evaluating the deflection of silicone rubber insulator skirts based on bidirectional fluid-structure interaction. The method includes: establishing a model with air as the fluid domain and the insulator as the structural field; simulating the inlet boundary conditions and parameters of the airflow field in the fluid domain, then dividing the fluid domain into a fluid domain mesh and dividing the skirt surface into several moving mesh regions, and reconstructing these moving mesh regions in real time using an automatic mesh reconstruction method; setting the skirt material parameters, skirt and core rod structural parameters in the structural field, then dividing the skirt into a solid domain mesh, and using the skirt edge displacement as the skirt deflection; dynamically exchanging skirt surface pressure and structural deformation data bidirectionally, setting the calculation step size and total time, and iteratively solving the skirt edge deflection data through bidirectional fluid-structure interaction. This invention addresses the problem of insufficient research on the deflection of silicone rubber insulator skirts.

Description

Technical Field

[0001] This invention belongs to the field of high voltage and insulation technology, and provides a method for evaluating the deflection of silicone rubber umbrella skirts based on bidirectional fluid-structure interaction. Background Technology

[0002] The ultra-high voltage (UHV) transmission lines in Northwest China transmit new energy to the southeastern coastal areas. The silicone rubber composite insulators of the 750kV transmission lines supporting UHVDC stations need to withstand strong winds for a long time. Stress concentration occurs at the root of the sheds. Repeated stress concentration at the root and offset of the shed edges will reduce the mechanical strength of the silicone rubber material. In severe cases, crescent-shaped cracks will form at the root of the sheds. The presence of cracks increases the risk of core rod exposure in the vicinity and the formation of discharge channels along the core rod-sheath interface, seriously threatening the operational reliability of the transmission lines.

[0003] Existing methods for optimizing the design parameters of anti-deflection composite insulator skirts mainly rely on experiments and simulation calculations. While wind tunnel tests of skirt deflection performance closely approximate actual working conditions, this process is time-consuming and labor-intensive, and cannot analyze skirt characteristics. Therefore, it is necessary to propose a method for calculating and analyzing the deflection of silicone rubber skirts. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a method for evaluating the deflection of silicone rubber sheds based on bidirectional fluid-structure interaction, which can solve the problem of insufficient research on the deflection of silicone rubber insulator sheds.

[0005] The technical solution of the present invention includes the following steps: A model is established with air as the fluid domain and insulators as the structural field, and the fluid domain encapsulates the structural field.

[0006] The inlet boundary conditions and parameters of the air flow field in the simulated fluid domain are determined. The inlet boundary conditions include wind speed and the windward angle of the insulator skirt. The air parameters include dynamic viscosity and density. Then, the fluid domain is meshed, and the skirt surface is divided into several moving mesh regions. The moving mesh regions are reconstructed in real time using an automatic mesh reconstruction method to update the flow field development and pressure distribution on the skirt surface in real time.

[0007] The material parameters of the insulator skirt, the structural parameters of the skirt and the core rod are set in the structural field. Then, the skirt is meshed in the solid domain. The skirt surface is divided into a system coupling region of fluid domain and structural field. The displacement of the skirt edge is used as the skirt deflection.

[0008] The surface pressure of the umbrella skirt and the amount of structural deformation are dynamically exchanged in two directions. The calculation step size and total time are set by combining the dynamic response characteristics of the umbrella skirt deflection. The edge deflection data of the umbrella skirt under different wind speeds and different windward angles are obtained by iterative solution through two-way coupling of fluid domain and structural field.

[0009] Furthermore, the insulator has fewer than 5 sheds, and the shed structure includes a large shed, a small shed, and a medium shed, with the small shed located between the large shed and the medium shed.

[0010] Furthermore, the inlet boundary conditions include wind speed and the angle of attack of the insulator skirts.

[0011] Furthermore, both the fluid domain mesh and the solid domain mesh are tetrahedral meshes, and their orthogonal mass is greater than 0.25.

[0012] Furthermore, the side length of the fluid domain mesh intersecting with the umbrella skirt is ≤2 mm, and the side length of the solid domain mesh is ≤2 mm.

[0013] Furthermore, the inlet boundary conditions and parameters of wind in the fluid domain were simulated using the RNG k-ε turbulence model.

[0014] Furthermore, the calculation step size is 0.003 seconds, and the total duration is 0.06 seconds.

[0015] Furthermore, the method for bidirectional dynamic data exchange is as follows: Based on the initial umbrella skirt structure, calculate the airflow field distribution in the fluid domain and obtain the aerodynamic pressure acting on the umbrella skirt surface; interpolate and map the aerodynamic pressure onto the umbrella skirt surface to drive the umbrella skirt to bend and deform, thus forming a new umbrella skirt structure; based on the new umbrella skirt structure, recalculate the airflow field distribution in the fluid domain and obtain the aerodynamic pressure acting on the umbrella skirt surface; repeat the above steps until the calculation is completed.

[0016] The technical solution provided by this invention has the following advantages compared with the prior art: 1. A complete fluid-structure interaction analysis framework was constructed by establishing a model with air as the fluid domain and the insulator as the structural field, thus encompassing the structural field within the fluid domain. By simulating the inlet boundary conditions and parameters of the airflow field in the fluid domain, including wind speed and the insulator skirt's windward angle, and air parameters such as dynamic viscosity and density, an accurate simulation of the actual wind environment was achieved. Based on this, the fluid domain was meshed, and the skirt surface was divided into several dynamic mesh regions. An automatic mesh reconstruction method was used to reconstruct the dynamic mesh regions in real time, thereby accurately capturing the dynamic changes of the skirt surface under wind loads and updating the flow field development and pressure distribution on the skirt surface in real time.

[0017] 2. By setting the material parameters of the insulator's skirt and the structural parameters of the skirt and core rod in the structural field, a solid domain mesh was generated for the skirt. The skirt surface was divided into a system coupling region of the flow field and the structural field, and the displacement of the skirt edge was used as the skirt deflection amount to establish a quantitative evaluation standard for the structural response. Finally, by dynamically exchanging two-way data between the skirt surface pressure and the structural deformation, and by setting the calculation step size and total time based on the dynamic response characteristics of the skirt deflection, a two-way coupled iterative solution of the fluid domain and the structural field was achieved, thereby obtaining the skirt edge deflection data under different wind speeds and windward angles.

[0018] 3. This invention, through a two-way coupling mechanism, accurately reflects the dynamic deflection process of the umbrella skirt under wind load, avoiding the limitation of the one-way coupling method that cannot consider the reaction of structural deformation to the flow field. It achieves high-precision prediction of the umbrella skirt deflection amount, and can comprehensively grasp the umbrella skirt deflection characteristics of silicone rubber composite insulators in strong wind environments, providing a scientific basis for the optimized design of insulator structures.

[0019] Other advantages, objectives and features of the present invention will become apparent in part from the following description, and in part from those skilled in the art through study and practice of the invention. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is an overall flowchart of an embodiment of the present invention; Figure 2 This is a geometric model diagram of an insulator according to an embodiment of the present invention.

[0022] Figure 3 This is a computational geometry model diagram of an embodiment of the present invention.

[0023] Figure 4 This is a schematic diagram of the local coordinate system method according to an embodiment of the present invention.

[0024] Figure 5 This is a streamline diagram of the area around the umbrella skirt in an embodiment of the present invention.

[0025] Figure 6 This is a pressure cloud diagram around the umbrella skirt according to an embodiment of the present invention.

[0026] Figure 7 The images show pressure distribution cloud diagrams on the upper and lower surfaces of the umbrella skirt and pressure distribution curves on the cross-section, representing embodiments of the present invention.

[0027] Figure 8 The figure shows the simulation calculation results of an embodiment of the present invention.

[0028] Figure 9 This is a comparison diagram of the maximum deflection of the umbrella skirt in an embodiment of the present invention. Detailed Implementation

[0029] The following detailed description of a specific embodiment of the present invention is provided in conjunction with the accompanying drawings. However, it should be understood that the scope of protection of the present invention is not limited to the specific embodiment.

[0030] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "axial," "radial," and "circumferential" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing the technical solution of this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0031] In the description of the embodiments of the present invention, unless otherwise stated, "a plurality of" means two or more.

[0032] like Figures 1 to 9 As shown, this invention provides a method for evaluating the deflection of silicone rubber umbrella skirts based on bidirectional fluid-structure interaction, comprising the following steps: A model is established with air as the fluid domain and insulators as the structural field, and the fluid domain encapsulates the structural field.

[0033] The inlet boundary conditions and parameters of the air flow field in the simulated fluid domain are determined. The inlet boundary conditions include wind speed and the windward angle of the insulator skirt. The air parameters include dynamic viscosity and density. Then, the fluid domain is meshed, and the skirt surface is divided into several moving mesh regions. The moving mesh regions are reconstructed in real time using an automatic mesh reconstruction method to update the flow field development and pressure distribution on the skirt surface in real time.

[0034] The material parameters of the insulator skirt, the structural parameters of the skirt and the core rod are set in the structural field. Then, the skirt is meshed in the solid domain. The skirt surface is divided into a system coupling region of fluid domain and structural field. The displacement of the skirt edge is used as the skirt deflection.

[0035] The surface pressure of the umbrella skirt and the amount of structural deformation are dynamically exchanged in two directions. The calculation step size and total time are set by combining the dynamic response characteristics of the umbrella skirt deflection. The edge deflection data of the umbrella skirt under different wind speeds and different windward angles are obtained by iterative solution through two-way coupling of fluid domain and structural field.

[0036] In this modeling approach, "air as the fluid domain" refers to the fluid solution region modeled as a continuous medium in computational fluid dynamics simulations; "insulator as the structural field" refers to the integral insulator configuration, including silicone rubber skirts and fiberglass core rods, being treated as a solid deformation solution object in structural mechanics simulations; and "fluid domain enveloping the structural field" means that the fluid domain geometry completely surrounds the structural field entity, making the skirt surface the physical interface between the fluid and the solid, thus forming a spatial topological relationship for the definable system coupling region. This modeling method provides the geometric basis for subsequent bidirectional data exchange, ensuring that aerodynamic pressure loads can act on the skirt surface, while structural displacements can be fed back to the fluid mesh boundary.

[0037] Fluid domain meshing can refer to discretizing a continuous fluid domain into a finite number of computational units (such as tetrahedrons, hexahedrons, etc.) to support numerical solutions to the Navier-Stokes equations. A moving mesh region can refer to a local fluid mesh region whose surface mesh needs to be updated synchronously with the structure's movement when the structure undergoes large displacement or deformation. An automatic mesh reconstruction method can refer to an algorithmic mechanism that adjusts the topology and node positions of adjacent fluid meshes in real time based on the displacement of nodes on the structural surface during the solution process, such as the spring smoothing method, local remapping method, or RBF interpolation deformation method. For example, the moving mesh region can be reconstructed in real time using the spring smoothing method to maintain mesh quality and adapt to curvature changes caused by skirt bending; or the moving mesh region can be reconstructed in real time using the local remapping method, triggering mesh regeneration when the skirt edge displacement exceeds a preset threshold; furthermore, this application can also reconstruct the moving mesh region in real time using the RBF interpolation deformation method, using the structural surface displacement as a control point to drive the entire fluid domain mesh to deform in a coordinated manner according to spatial mapping relationships. This application achieves continuous, stable, and high-fidelity updates of the flow field development and pressure distribution on the umbrella skirt surface based on any of the above methods, avoiding solution divergence or accuracy degradation caused by mesh distortion. For example, such as... Figure 3As shown, this application can be used for a short string model of a 750kV silicone rubber composite insulator, constructing an air cuboid fluid domain with dimensions of 2000mm×500mm×500mm; setting three working conditions for wind speeds of 30m / s, 35m / s, and 40m / s, and five working conditions for windward angles of 30°, 60°, 90°, 120°, and 150°; defining the aerodynamic viscosity according to the temperature-dependent function η(T), and the density according to the pressure-temperature-dependent function ρ(p,T); using tetrahedral meshing for the fluid domain, with an orthogonal mass of not less than 0.2, and refining the mesh on the umbrella skirt surface to a side length ≤2mm; defining all outer surfaces of the umbrella skirts as dynamic mesh regions, and enabling the automatic mesh reconstruction function; completing a transient solution with a total duration of 0.06s at a time step of 0.003s, maintaining the geometric consistency of the flow field and the convergence of the pressure solution throughout the process.

[0038] The material parameters of the umbrella skirt can be the basic constitutive parameters describing the mechanical behavior of the silicone rubber sheath, including density, Young's modulus, and Poisson's ratio; the structural parameters of the umbrella skirt and the mandrel can be physical quantities characterizing their geometric configuration and assembly relationship, including umbrella diameter, umbrella spacing, up / down tilt angle, mandrel diameter, sheath thickness, and mandrel-sheath fit dimensions; solid domain meshing can refer to discretizing the structural field entity into finite element elements to support the solution of the structural static / dynamic equations; the system coupling region can refer to the shared boundary between the fluid domain and the structural field for the transfer of physical quantities (pressure, displacement), which must be strictly consistent with the dynamic mesh region in space; the displacement of the umbrella skirt edge can refer to the spatial displacement vector of the free end of the umbrella skirt (i.e., the outermost edge point away from the mandrel) in a preset coordinate system; the umbrella skirt deflection can refer to the projection component of this displacement in the axial direction of the insulator mandrel as the final output deflection quantification index to eliminate the measurement direction error caused by non-perpendicular wind direction.

[0039] This application may, for example, define the displacement of the skirt edge through a local coordinate system, such as... Figure 4 As shown: A cylindrical coordinate system extending along the mandrel is established with the mandrel's central axis (y-axis). The displacement components of the skirt edge nodes in the y-axis direction are extracted as the deflection amount. Alternatively, this application can also use a global coordinate system combined with a rotation matrix for correction: first, the displacement vectors of the skirt edge nodes in the global rectangular coordinate system are obtained, then multiplied by the rotation matrix corresponding to the windward angle, and projected onto the mandrel axis. Furthermore, this application can also extract the deflection amount using a geometric constraint method: in post-processing of the structure, all nodes on the skirt edge are locked, and the weighted average of their displacement vectors in the mandrel axis is fitted as the deflection amount. This application obtains an unambiguous, reproducible, and engineering-measurable quantitative expression of the skirt deflection state based on any of the above methods.

[0040] For example, this application may set the density of the silicone rubber umbrella skirt material to 1600 kg / m³ and the Young's modulus to 5 × 10⁻⁶. 6Pa and Poisson's ratio are 0.18; the density of the fiberglass core rod material is 2600 kg / m³ and Young's modulus is 1×10¹. 0 Pa and Poisson's ratio are 0.25; the umbrella pair structure field is divided into tetrahedral meshes with an orthogonal mass of not less than 0.25 and a mesh size of 2mm on the umbrella skirt surface; all outer surfaces of the umbrella skirts are defined as the system coupling region; the upper and lower end faces of the fixed core are used as displacement constraint boundaries; after the solution is completed, the displacement components of the outermost nodes of each umbrella skirt in the core axis (y-axis) are extracted, and the maximum value is taken as the edge deflection of the umbrella skirt under this working condition.

[0041] The pressure on the umbrella skirt surface can refer to the pressure load, in Pa, output by the fluid domain solver and acting on the center of each mesh cell on the umbrella skirt surface. The structural deformation can refer to the displacement vector in three-dimensional space of each node on the umbrella skirt surface, in mm, output by the structural field solver. The two-way dynamic data exchange can refer to the closed-loop information interaction process in each time step, where the pressure load is interpolated from the fluid domain to the structural boundary to drive deformation, and the structural displacement is fed back from the structural domain to the fluid boundary to update the mesh geometry. The calculation step size can refer to the time increment corresponding to each coupled iteration, and its setting needs to take into account both numerical stability and dynamic response capture capability. The total duration can refer to the minimum simulation duration required to cover the entire process of umbrella skirt deflection (including initial disturbance, accelerated deflection, and tendency to steady state).

[0042] This application can employ, for example, a pressure transfer method based on interpolation mapping: the surface pressure of the fluid domain skirt is interpolated area-weighted to the corresponding coupled nodes of the structural domain as the surface load for transient structural analysis; this application can also employ a displacement mapping method based on RBF: the displacement of the nodes on the surface of the structural domain skirt is used as control points, and the displacement field of the fluid domain boundary nodes is generated by inversion using the RBF function to drive dynamic mesh updates; furthermore, this application can also employ a data exchange method based on conformal meshes: during the modeling stage, the fluid and structure use the same mesh topology in the coupled region to achieve a one-to-one direct mapping between pressure and displacement. This application obtains physical consistency and numerical robustness of the pressure-displacement bidirectional drive based on any of the above methods.

[0043] For example, this application can call Fluent (fluid module) and Mechanical (structural module) in the ANSYS Workbench platform, and establish a bidirectional coupling interface through the System Coupling component; set the calculation step size to 0.003s, which is less than 1 / 20 of the period of the first bending mode of the umbrella skirt, so as to effectively distinguish the deflection dynamic process; set the total duration to 0.06s, which covers the maximum response time required from the application of wind load to the convergence of deflection; within each 0.003s time step, Fluent first completes the flow field solution under the current configuration and outputs the pressure distribution on the umbrella skirt surface; System Coupling maps the pressure interpolation to the structural coupling boundary of Mechanical; Mechanical performs transient structural analysis accordingly and outputs the nodal displacements on the umbrella skirt surface; System Coupling then feeds the displacements back to Fluent, triggering dynamic mesh reconstruction; after completing 20 iterations within 0.06s, the maximum displacement value of the umbrella skirt edge in the mandrel axis under all working conditions is extracted to form the umbrella skirt edge deflection dataset.

[0044] This application constructs an enveloping two-way coupled model with air as the fluid domain and insulators as the structural field. By combining the setting of inlet boundary conditions including wind speed and windward angle, dynamic mesh region division and automatic reconstruction mechanism, skirt material and structural parameter configuration, system coupling region definition, and core rod axial deflection extraction method, a closed-loop dynamic exchange of skirt surface pressure and structural deformation is realized. Based on this, by using a calculation step size of 0.003 s and a total duration of 0.06 s adapted to the deflection dynamic response characteristics, the two-way coupling iterative solution of fluid domain-structural field is completed. Finally, the skirt edge deflection data under different wind speed (30 / 35 / 40 m / s) and different windward angle (30°–150°) combinations are obtained, which solves the problems of difficulty in accurately quantifying strong wind-induced skirt deflection and the inability to reveal the fluid-structure coupling mechanism in the prior art, and supports the optimized design of silicone rubber composite insulator anti-deflection structure.

[0045] In the embodiments provided by the present invention, the number of sheds in the insulator is less than 5 in order to simplify calculation and improve efficiency. The structure of the sheds includes a large shed, a small shed, and a medium shed, with the small shed located between the large shed and the medium shed.

[0046] like Figure 2 As shown, the structural parameters of the umbrella skirts are as follows: the diameter of the large umbrella D1 is 200mm, the diameter of the small umbrella D2 is 120mm, the diameter of the medium umbrella D3 is 160mm, the structural height H is 313.5mm (taking two umbrella skirts as an example), the upward tilt angle of the umbrella skirt A1 is 10°, the downward tilt angle of the umbrella skirt A2 is 6°, the diameter of the core rod L1 is 34mm, the core rod-sheath mating dimension L2 is 44mm, and the distance between umbrellas C is 17.5mm.

[0047] Large umbrella, small umbrella, and medium umbrella are three basic structural forms of silicone rubber composite insulator skirts, classified by diameter. They correspond to umbrella-shaped geometries of different sizes and are arranged along the core rod axis in space. The small umbrella being located between the large umbrella and the medium umbrella can refer to the position of the small umbrella being downstream of the large umbrella and upstream of the medium umbrella in the axial sequence, forming an alternating hierarchical configuration of large umbrella-small umbrella-medium umbrella. In this embodiment, this arrangement is used to reproduce the airflow guiding characteristics of a real 750kV insulator skirt group.

[0048] In the embodiments provided by the present invention, the inlet boundary conditions include wind speed and the windward angle of the insulator's skirts.

[0049] Wind speed refers to the average flow velocity of air in the fluid domain along a set direction at the inlet section, with the unit being m / s. It characterizes the magnitude of the dynamic pressure load exerted by the airflow on the umbrella skirt. The umbrella skirt windward angle refers to the angle between the insulator axis and the incoming wind direction, with the unit being degrees (°). It characterizes the angle of attack of the airflow relative to the geometric profile of the umbrella skirt.

[0050] In this embodiment, wind speed is used to determine the velocity boundary value at the fluid domain inlet, serving as a key input parameter for solving the initial flow field distribution in the RNG k-ε turbulence model. This directly affects the peak pressure on the umbrella skirt surface, the separation zone range, and the vortex shedding frequency. In this embodiment, the umbrella skirt windward angle is used to define the spatial orientation relationship between the fluid domain coordinate system and the insulator local coordinate system. This determines the differences in the flow path around the surfaces of the large, small, and medium umbrellas, as well as the asymmetric pressure distribution characteristics, thereby affecting the directionality and amplitude nonlinearity of the umbrella skirt edge displacement response. This application can, for example, generate multiple sets of boundary condition configuration files based on preset wind speed settings (30m / s, 35m / s, 40m / s) and preset windward angle settings (30°, 60°, 90°, 120°, 150°), and load them into the inlet boundary module of the fluid solver; this application can also, for example, dynamically generate a continuous sequence of wind speed and windward angle changes through a parameterized script, driving the transient coupled solver to update the inlet boundary conditions step by step; furthermore, this application can also read wind speed and wind direction information in real time based on the measured meteorological data interface, and map it to the corresponding umbrella skirt windward angle after coordinate transformation, so as to realize the simulation evaluation driven by the field working conditions.

[0051] This application explicitly defines the inlet boundary conditions as two core variables—wind speed and the umbrella skirt's windward angle—that are physically measurable, engineering-adjustable, and simulation-reproducible. This gives the fluid domain modeling a clear input dimension and traversability. Combined with the bidirectional coupling model established in this application, wind speed and windward angle jointly drive the dynamic evolution of pressure on the umbrella skirt surface and the feedback of structural deformation. Thus, without relying on empirical formulas or simplification assumptions, it realistically reflects the spatiotemporal response mechanism of the umbrella skirt deflection under strong wind conditions. This limitation not only enhances the legal certainty of the scope of protection of this application but also provides a clear technical interface for subsequent parameter sensitivity analysis, critical instability criterion construction, and wind-resistant optimization design.

[0052] In the embodiments provided by the present invention, both the fluid domain mesh and the solid domain mesh are tetrahedral meshes, and their orthogonal masses are greater than 0.25.

[0053] Tetrahedral meshes are polyhedral elements composed of four triangular faces in three-dimensional space, widely used for automatic mesh generation of complex geometric boundaries. Orthogonality quality is a dimensionless index that measures the degree to which the angle between the normal of a mesh element face and the line connecting adjacent nodes deviates from orthogonality. Its value ranges from 0 to 1; the closer the value is to 1, the more regular the shape of the mesh element and the smaller the numerical discretization error. This provides a geometric basis for finite volume discretization of airflow fields in fluid domains and finite element discretization of skirt deformation in structural fields, ensuring that highly adaptable and distortion-controllable computational meshes can still be generated in high-curvature regions such as skirt corrugated surfaces, sharp edges of the umbrella rim, and the core-sheath transition zone. Simultaneously, the threshold setting of orthogonality quality greater than 0.25 satisfies the stability requirements of industrial-grade CFD / CAE solvers for unstructured meshes while also considering modeling efficiency under computational resource constraints, avoiding difficulties in coupled iteration convergence due to excessive mesh refinement.

[0054] An orthogonal mass greater than 0.25 means that in the mesh quality assessment, the orthogonal mass values ​​of all tetrahedral elements are strictly higher than the 0.25 threshold, excluding elements equal to or lower than this value. This index is directly related to the numerical format truncation error and the condition number of the stiffness matrix, especially affecting the accuracy of physical quantity reproduction in areas of abrupt pressure gradient changes on the umbrella skirt surface (such as the leading edge on the windward side and the vortex shedding zone on the leeward side) and stress concentration areas at the root (such as the connection between the umbrella skirt and the sheath). This ensures spatial consistency when mapping aerodynamic pressure loads from the fluid domain to the structural field, preventing pressure interpolation distortion due to mesh distortion; simultaneously, it ensures that the bending deformation response of the umbrella skirt in the structural field does not generate spurious stress oscillations due to element distortion during the finite element solution process, thereby supporting the physical reliability and iterative convergence of the bidirectional dynamic data exchange defined in this application.

[0055] This application adopts a unified tetrahedral mesh type for both the fluid and solid domains, and strictly limits the orthogonal mass to be greater than 0.25. This ensures that the mesh can fit the complex corrugated surface geometry of the silicone rubber umbrella skirt and has sufficient numerical robustness. Based on this, combined with the dynamic mesh reconstruction mechanism and bidirectional data exchange logic defined in this application, the flow field distortion and structural stress drift caused by mesh distortion during large deformation are effectively suppressed. This ensures the engineering credibility and repeatability of the evaluation results of the skirt edge deflection under different wind speeds and windward angles.

[0056] In the embodiments provided by the present invention, the side length of the fluid domain mesh intersecting with the umbrella skirt is ≤2 mm, and the side length of the solid domain mesh is ≤2 mm.

[0057] The fluid domain mesh of the umbrella skirt intersection can refer to a tetrahedral mesh element in the fluid domain where at least one vertex or one edge is located on the geometric boundary of the umbrella skirt surface, or where the projection of its element center falls within a triangular element on the umbrella skirt surface; the solid domain mesh can refer to a tetrahedral finite element mesh element in the structural field used to discretize the solid geometry of the umbrella skirt; the edge length can refer to the length of the longest edge in the tetrahedral mesh element.

[0058] The technical feature is that during the fluid domain mesh generation stage, local size control constraints are applied to the surface of the skirt and its adjacent areas (within a thickness direction of 10 mm) to ensure that the generated tetrahedral mesh has a maximum side length of no more than 2 mm. This feature also utilizes a curvature adaptive refinement strategy to automatically trigger mesh refinement in corrugated sections with a curvature radius of less than 5 mm at the skirt edge, the stagnation point area at the leading edge of the skirt, and the separation area at the trailing edge, ensuring that the side length of the fluid domain mesh in the corresponding areas is ≤2 mm. In this embodiment, this technical feature ensures that the spatial distribution of fluid domain pressure loads on the skirt surface has sufficient resolution, thereby enabling high-fidelity interpolation mapping of aerodynamic pressure to structural field nodes during subsequent bidirectional data exchange. This avoids the underestimation of local load intensity due to the averaging of high-pressure areas at the leading edge (such as stagnation point pressure peaks) caused by mesh coarsening.

[0059] This application generates a fluid domain mesh that meets accuracy requirements by defining a local size function on the umbrella skirt surface and setting the maximum element side length to 2 mm; it also generates a fluid domain mesh that meets accuracy requirements by identifying locations of abrupt changes in the geometric curvature of the umbrella skirt and forcibly inserting denser seed points at such locations; further, it generates a fluid domain mesh that meets accuracy requirements by dynamically adjusting the mesh density of adjacent fluid domains based on the predicted normal pressure gradient of the umbrella skirt surface. Based on any of the above methods, this application obtains reliable analytical capabilities for key flow field features (such as stagnation points, separation bubbles, and reattachment zones) on the umbrella skirt surface, supporting the physical realism of subsequent pressure-displacement bidirectional coupling iterations.

[0060] For example, this application involves: after constructing the fluid domain geometric model, creating a local size control surface on the umbrella skirt surface and setting the maximum element side length parameter to 2mm; then calling the automatic mesh generation module to perform side length re-evaluation and re-division on all fluid domain mesh elements that intersect with the control surface or are less than 10mm away from it, based on the global tetrahedral mesh, ultimately generating a fluid domain mesh adjacent to the umbrella skirt with side lengths ≤2mm; simultaneously, when meshing the umbrella skirt entity in the structural field, setting 3 layers of elements along the umbrella skirt thickness direction, with the tangential side length of each layer of elements also controlled to ≤2mm, ensuring that the solid domain mesh forms a discrete foundation on the umbrella skirt surface that matches the scale of the fluid domain mesh, providing a geometrically consistent coupling interface for bidirectional data exchange.

[0061] By simultaneously limiting the side lengths of the fluid domain mesh and the solid domain mesh intersecting the umbrella skirt to ≤2 mm, a strict spatial matching of the two types of meshes at the fluid-structure interaction interface was achieved. This dimensional constraint ensured both the fluid domain's accurate capture of local pressure gradients on the umbrella skirt surface (such as the pressure difference of up to 2616.43 Pa between the leading edge stagnation point and the trailing edge negative pressure zone) and the fidelity of the structural field's spatial response to the resulting minute bending deformations (typical deflection of 1.2–4.8 mm). Furthermore, the mapping error between pressure load and displacement feedback during bidirectional dynamic data exchange was significantly reduced, thereby improving the accuracy of predicting the deflection of the umbrella skirt edge under different wind speeds (30–40 m / s) and windward angles (30°–150°). This kept the deviation between the simulation results and wind tunnel tests within 7.3%, meeting the accuracy requirements for engineering evaluation.

[0062] In the embodiments provided by the present invention, the inlet boundary conditions and parameters of wind in the fluid domain are simulated by the RNG k-ε turbulence model.

[0063] The RNG k-ε turbulence model is a two-equation turbulence model derived from renormalization group theory. It modifies the turbulent viscosity transport term and eddy viscosity coefficient in the standard k-ε model, enhancing the model's applicability in medium-to-high Reynolds numbers, strong shear, strong curvature, and fast-strain flow fields. The RNG k-ε model is a turbulence modeling method suitable for regions with significant flow separation, reattachment, three-dimensional vortex structures, and strong adverse pressure gradients. Its governing equations introduce analytical terms reflecting small-scale turbulence effects, making the model's prediction accuracy for complex geometries (such as insulator skirt gaps) better than the standard k-ε model. The RNG k-ε model is used to solve the numerical simulation of the inlet boundary conditions and parameters of the airflow field in the fluid domain in a closed loop. That is, given input conditions such as wind speed, windward angle, dynamic viscosity and density, it solves the transport equations of turbulent kinetic energy k and its dissipation rate ε, thereby obtaining the turbulent viscosity, velocity distribution and pressure distribution at each grid node in the fluid domain, providing accurate aerodynamic load boundaries for subsequent two-way coupling. This model directly acts on the fluid domain grid, and its output results form the basis for calculating the pressure load on the umbrella skirt surface, which is a key modeling step to accurately capture the dynamic response characteristics of the umbrella skirt deflection.

[0064] The application proposes to improve the simulation capability of strongly separated flow and three-dimensional vortex structures in the gap between umbrella skirts by adopting the RNG k-ε turbulence model. This model is well-suited to the inlet boundary conditions and parameters of the air flow field in the fluid domain, making the obtained pressure load on the umbrella skirt surface closer to the real physical state. On this basis, combined with bidirectional dynamic data exchange and real-time reconstruction of dynamic mesh, it can accurately reflect the continuous influence of flow field feedback on structural response during large deformation, thereby ensuring the engineering usability and prediction confidence of the umbrella skirt edge deflection data under different wind speeds and windward angles.

[0065] In the embodiments provided by this invention, the method for bidirectional dynamic data exchange is as follows: Based on the initial umbrella skirt structure, calculate the airflow field distribution in the fluid domain and obtain the aerodynamic pressure acting on the umbrella skirt surface; interpolate and map the aerodynamic pressure onto the umbrella skirt surface to drive the umbrella skirt to bend and deform, thus forming a new umbrella skirt structure; based on the new umbrella skirt structure, recalculate the airflow field distribution in the fluid domain and obtain the aerodynamic pressure acting on the umbrella skirt surface; repeat the above steps until the calculation is completed.

[0066] The initial umbrella skirt structure can refer to the umbrella skirt geometry before the start of the coupled iteration, which has not undergone any wind-induced deformation. It is determined by the model building steps and includes the spatial position, curvature, thickness, and connection relationship with the mandrel. This structure serves as the reference geometry for fluid domain mesh generation and boundary condition application, and does not change over time, only being updated in subsequent iterations. The airflow field distribution can refer to the velocity vector field and pressure scalar field at each spatial point in the fluid domain obtained by numerically solving the Navier-Stokes equations under set inlet boundary conditions (wind speed, angle of attack), fluid property parameters (dynamic viscosity, density), and turbulence model (RNG k-ε). Aerodynamic pressure is the set of discrete values ​​of this pressure scalar field on the mesh nodes of the umbrella skirt surface, representing the normal load exerted by the air on a unit area of ​​the umbrella skirt surface. Its physical unit is Pascal (Pa), and it is the direct mechanical input driving structural deformation. This application can, for example, solve the steady-state initial field on the initial geometry according to the fluid control equations to obtain a convergent initial flow field pressure distribution; it can also, for example, perform single-step time advancement on the initial geometry at t=0 using a transient flow field solver to output the initial pressure field; further, this application can also call the built-in solver of commercial CFD software (such as ANSYS Fluent) to automatically complete mesh adaptation, equation discretization, and pressure field solving on the initial umbrella skirt structure. This application obtains the initial aerodynamic pressure data used to drive structural deformation based on any of the above methods. For example, using the cuboid air domain covered by the insulator constructed in this application as the computational domain, setting the inlet wind speed to 35 m / s and the windward angle to 90°, the initial flow field calculation is completed using the RNG k-ε model, and the maximum surface pressure on the windward side of the umbrella skirt is found to be 2616.43 Pa, with a low-pressure zone formed on the leeward side, and the pressure gradient driving the umbrella skirt to deflect towards the leeward side.

[0067] Dynamic pressure interpolation mapping refers to the process of converting the numerical values ​​of the pressure field calculated in the fluid domain at the nodes on the umbrella skirt surface into the load values ​​borne by the corresponding nodes in the structural field through spatial interpolation algorithms (such as nearest neighbor interpolation, linear interpolation, or radial basis function interpolation). This process must satisfy force balance and geometric consistency constraints to ensure that the pressure load is accurately transmitted to the structural mesh nodes. The bending deformation of the umbrella skirt refers to the non-rigid deformation of the silicone rubber material under aerodynamic pressure load due to its elastic modulus and Poisson's ratio characteristics. This is manifested as a displacement response of the umbrella skirt edge along the direction perpendicular to the mandrel. Its deformation mode includes cantilever beam bending and local membrane stretching coupling effects. Updating the umbrella skirt structure refers to superimposing the nodal displacements after bending deformation onto the initial geometric coordinates to generate a new three-dimensional configuration of the umbrella skirt that reflects the true shape at the current moment. This configuration will serve as the fluid domain geometric boundary for the next iteration. This application can, for example, map aerodynamic pressure to structural nodes using a weighted average interpolation method based on the spatial topological relationship between the nodes on the umbrella skirt surface and the nodes on the fluid domain surface in the structural finite element model; it can also decompose the fluid pressure into structural node force components according to the projection relationship based on the normal direction of the umbrella skirt surface, and complete the mapping by combining the node area weight; furthermore, this application can also call the pressure mapping function built into the System Coupling module in ANSYS Workbench to automatically complete the pressure data transfer and unit system unification at the fluid-solid interface. This application obtains the structural load input required to drive the bending deformation of the umbrella skirt based on any of the above methods. The obtained umbrella skirt surface pressure data is imported into the Transient Structural module, and pressure interpolation mapping is automatically completed through the coupling interface; under the action of local high pressure of 2616.43 Pa, the edge of the large umbrella produces a lateral displacement of 0.87 mm towards the leeward side, and the small umbrella exhibits higher curvature deformation due to its smaller size, forming the first-order updated umbrella skirt structure.

[0068] The new umbrella-skirt structure can refer to the umbrella-skirt geometry generated after bending deformation, in which the surface curvature, gap width, and windward projected area have all changed. This structure serves as the geometric basis for updating the fluid domain mesh, directly affecting the vortex generation location, separation point migration, and pressure redistribution characteristics in the flow field. Recalculating the airflow field distribution in the fluid domain can refer to adjusting the fluid domain mesh topology in real time based on the updated umbrella-skirt surface position under the premise of activated dynamic mesh mechanism, and then solving the fluid control equations again on the new mesh to reflect the dynamic reaction of structural deformation to the flow field. This process differs from the fixed geometric assumption in unidirectional coupling and reflects the essence of fluid-solid bidirectional physical feedback. This application, for example, may use the Spring Analogy method to locally remesh the fluid domain mesh based on the dynamic mesh region definition (i.e., the umbrella skirt surface), maintaining mesh quality while adapting to umbrella skirt displacement; this application may also enable a hybrid strategy of local remeshing and smoothing, inserting new mesh elements in areas of significant umbrella skirt deflection while maintaining the original topology in other areas; furthermore, this application may call the Dynamic Mesh module in ANSYS Fluent to automatically trigger mesh updates and flow field recalculation upon receiving structural displacement data. This application obtains updated aerodynamic pressure reflecting the structural deformation feedback effect based on any of the above methods. For example, this application may be... Figure 2 In the process shown, the updated structure obtained above reduces the gap between the large umbrella and the medium umbrella from the initial 17.5 mm to 16.2 mm. Fluent recalculated after the dynamic mesh update and found that the gap vortex intensity increased and the low-pressure area on the leeward side expanded, causing the aerodynamic pressure at the edge of the umbrella skirt to drop from 2616.43 Pa to 2481.35 Pa. However, the absolute value of the pressure gradient increased, further aggravating the deflection trend.

[0069] Repeating the above steps can refer to using the updated aerodynamic pressure obtained above as the input for a new round of mapping, entering the deformation driving stage mentioned above, thereby generating the second-order updated structure and triggering the flow field recalculation mentioned above, forming a closed-loop iterative chain of pressure → deformation → geometric update → pressure; this loop continues to execute, each round corresponding to one time step (limited to 0.003 seconds in this application), and the total number of iterations is determined by the total duration (limited to 0.06 seconds in this application), for a total of 20 steps. Completion of the calculation can refer to reaching the preset total duration, or satisfying the convergence criterion (such as the change in skirt edge displacement between two adjacent steps being less than 1×10⁻). 5 (mm), at which point the iteration terminates and outputs the sequence of skirt edge deflection for all time steps.

[0070] This application calculates the aerodynamic pressure on the initial umbrella structure, then uses interpolation mapping to drive bending deformation to generate an updated structure. The aerodynamic pressure is then recalculated based on this updated structure, and this closed-loop process is repeated cyclically. This achieves a two-way dynamic coupling between fluid load and structural response, ensuring physical consistency, temporal synchronization, and data fidelity. Furthermore, by combining the dynamic mesh reconstruction mechanism and the defined calculation step size and total duration specified in this application, the deflection assessment process is ensured to have a clear executable path and engineering reproducibility, thus effectively supporting the reliability analysis and structural optimization design of 750kV silicone rubber composite insulators in strong wind environments.

[0071] like Figure 5 The diagram shown is the streamline distribution around the umbrella skirt when the deflection is at its maximum, calculated through the above steps. At this time, t = 0.039s. A distinct vortex structure can be clearly seen in the gap between the umbrella skirts, indicating that the vortex structure in the gap between the umbrella skirts is an important cause of the deflection of the umbrella skirts.

[0072] like Figure 6 As shown, when the skirt deflection is at its maximum, the pressure cloud diagram around the skirt is as follows: at this time, t = 0.039s. It can be seen that the upper surface area of ​​the skirt is a red positive pressure area, and the lower surface is a blue negative pressure area. The pressure difference between the upper and lower surfaces is the direct cause of the skirt deflection.

[0073] like Figure 7 The figure shows the pressure distribution contour map and the pressure distribution curve of the umbrella skirt cross section when the skirt deflection is at its maximum. 1# represents the upper surface, and 2# represents the lower surface. The upper surface (1#) is mainly under positive pressure, while the lower surface (2#) is mainly under negative pressure. The pressure curves of the upper and lower surface cross sections show that the maximum pressure difference reaches 2616.43 Pa. It is this imbalance in pressure distribution that causes the umbrella skirt to deflect downwards.

[0074] like Figure 8 and Figure 9 As shown in the diagram, under a wind angle of 30° and a wind speed of 40 m / s, the maximum deflection of the shed skirt in simulation and experiment are compared. It can be seen that the maximum deflection of the silicone rubber insulator shed skirt in the experiment is 21.9 mm, while the maximum deflection in the simulation calculation is 23.516 mm. The deviation in the maximum deflection of the silicone rubber insulator shed skirt between the two methods is 7.3%, which meets the actual engineering requirements.

[0075] It should be noted that any parts not disclosed or specifically described in this invention are existing technology or conventional configurations, and their specific structures and working principles will not be elaborated further. In this document, 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 that element.

[0076] Although embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. It can be applied to various fields suitable for the present invention. Other modifications can be readily implemented by those skilled in the art. Therefore, without departing from the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details and examples shown and described herein.

Claims

1. A method for evaluating the deflection of silicone rubber umbrella skirts based on bidirectional fluid-structure interaction, characterized in that, Includes the following steps: A model is established with air as the fluid domain and insulators as the structural field, wherein the fluid domain encompasses the structural field. The inlet boundary conditions and parameters of the air flow field in the simulated fluid domain are then divided into a fluid domain mesh, and the umbrella skirt surface is divided into several moving mesh regions. The moving mesh regions are reconstructed in real time using an automatic mesh reconstruction method to update the flow field development and pressure distribution on the umbrella skirt surface in real time. Set the material parameters of the insulator's shed, the structural parameters of the shed and the core rod in the structural field, then perform solid domain meshing on the shed, divide the shed surface into a system coupling region of fluid domain and structural field, and use the displacement of the shed edge as the shed deflection amount; The surface pressure of the umbrella skirt and the amount of structural deformation are dynamically exchanged in two directions. The calculation step size and total time are set by combining the dynamic response characteristics of the umbrella skirt deflection. The edge deflection data of the umbrella skirt under different wind speeds and different windward angles are obtained by iterative solution through two-way coupling of fluid domain and structural field.

2. The method for evaluating the deflection of silicone rubber umbrella skirts based on bidirectional fluid-structure interaction according to claim 1, characterized in that, The insulator has fewer than 5 sheds, and the sheds have a structure including a large shed, a small shed, and a medium shed, with the small shed located between the large shed and the medium shed.

3. The method for evaluating the deflection of silicone rubber umbrella skirts based on bidirectional fluid-structure interaction according to claim 1, characterized in that, The inlet boundary conditions include wind speed and the windward angle of the insulator's skirts.

4. The method for evaluating the deflection of silicone rubber umbrella skirts based on bidirectional fluid-structure interaction according to claim 1, characterized in that, Both the fluid domain mesh and the solid domain mesh are tetrahedral meshes, and their orthogonal mass is greater than 0.

25.

5. The method for evaluating the deflection of silicone rubber umbrella skirts based on bidirectional fluid-structure interaction according to claim 4, characterized in that, The side length of the fluid domain mesh intersecting the umbrella skirt is ≤2 mm, and the side length of the solid domain mesh is ≤2 mm.

6. The method for evaluating the deflection of a silicone rubber umbrella skirt based on bidirectional fluid-structure interaction according to claim 1, characterized in that, The inlet boundary conditions and parameters of wind in the fluid domain were simulated using the RNG k-ε turbulence model.

7. The method for evaluating the deflection of silicone rubber umbrella skirts based on bidirectional fluid-structure interaction according to claim 1, characterized in that, The calculation step size is 0.003 seconds, and the total duration is 0.06 seconds.

8. The method for evaluating the deflection of silicone rubber umbrella skirts based on bidirectional fluid-structure interaction according to claim 1, characterized in that, The method for bidirectional dynamic data exchange is as follows: Based on the initial umbrella skirt structure, the air flow field distribution in the fluid domain is calculated to obtain the aerodynamic pressure acting on the umbrella skirt surface; Pneumatic pressure interpolation is mapped onto the surface of the umbrella skirt, driving the umbrella skirt to bend and deform, thus creating a new umbrella skirt structure. Based on the new umbrella skirt structure, the air flow field distribution in the fluid domain is recalculated to obtain the aerodynamic pressure acting on the umbrella skirt surface; Repeat the above steps until the calculation is complete.

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