Method and system for coupling analysis of bubble motion and electric field distortion in transformer oil

Abstract

This invention relates to the field of transformer technology, providing a method and system for coupled analysis of bubble movement and electric field distortion in transformer oil. The method includes: constructing a two-dimensional geometric simulation model of a needle-plate electrode; describing the synergistic effects of electric force, buoyancy, gravity, drag, drag force, and surface tension on bubble deformation, migration, and coalescence behavior within the two-dimensional geometric simulation model using a set of coupled electric field-flow field-phase field equations; and the evolution law of the electric field intensity inside the bubble being dominated by the voltage phase and increasing near the tip electrode; meshing the computational domain and setting the time step and solver; performing numerical calculations on the coupled electric field-flow field-phase field equations; and extracting field quantity data and generating contour maps after post-processing. This method can realistically reflect the intrinsic mechanism of partial discharge caused by the dynamic behavior of bubbles, providing theoretical support for precise prevention and early warning of transformer insulation faults.

Description

Technical Field

[0001] This invention belongs to the field of transformer technology, and in particular relates to a method and system for coupled analysis of bubble movement and electric field distortion in transformer oil. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] Insulating oil, as a key liquid dielectric, is widely used in power equipment, especially large power transformers, due to its excellent electrical breakdown strength, good thermal conductivity, and strong adaptability to complex electrical geometries.

[0004] During actual transformer operation, under long-term thermal stress and electric field effects, free-state bubbles are precipitated in the insulation system due to impurities in the oil and dissolved gas precipitation caused by temperature changes. The precipitation of these bubbles provides conditions for partial discharge, and the sustained energy of this partial discharge accelerates the pyrolysis of the insulating oil, producing hydrocarbon gases. When the gas in the oil is supersaturated, it promotes the formation of more bubbles. These suspended bubbles are not static; they undergo a series of complex dynamic behaviors, including deformation, migration, coalescence, and even rupture, as the oil flows. Because the dielectric constant of gases is usually significantly lower than that of insulating oil, the presence of bubbles severely distorts the electric field distribution in their surrounding space, causing the electric field strength to concentrate inside the bubbles, often much higher than the background field strength in the oil. This electric field distortion effect significantly reduces the overall breakdown voltage of the insulation system, potentially leading to premature breakdown along the gas channels of the bubbles, thus triggering insulation faults. Such insulation failures induced by bubble dynamics pose a severe challenge to the long-term stability and safe operation of transformers.

[0005] Existing research focuses on the effect of a single electric field or a single influencing factor on the migration and movement of bubbles in insulating oil. The synergistic effect of different physical fields and forces at different stages in the entire process of bubble migration and coalescence is not yet clear. Research on the synergistic influence of multiple factors on the bubble migration and coalescence process is not in-depth, and the simulation of non-uniform oil channel environment has not been explored. Summary of the Invention

[0006] To address the technical problems mentioned above, this invention provides a coupled analysis method and system for the movement of air bubbles and electric field distortion in transformer oil. This method can accurately reflect the intrinsic mechanism of partial discharge caused by the dynamic behavior of air bubbles, providing theoretical support for the precise prevention and early warning of transformer insulation faults.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: The first aspect of the present invention provides a method for coupled analysis of bubble movement and electric field distortion in transformer oil, comprising: A two-dimensional geometric simulation model of a needle-plate electrode was constructed. The synergistic effect of electric force, buoyancy, gravity, drag, drag force and surface tension on bubble deformation, migration and coalescence behavior in the two-dimensional geometric simulation model of the needle-plate electrode was described by the electric field-flow field-phase field coupled control equation set. The evolution law of the electric field intensity inside the bubble being dominated by voltage phase and enhanced when it is close to the tip electrode was also described. The computational domain is meshed, and the time step and solver are set. Numerical calculations are performed on the coupled control equations of electric field, flow field and phase field. Field quantity data are extracted and contour maps are generated after post-processing.

[0008] Furthermore, the two-dimensional geometric simulation model of the needle-plate electrode includes a needle electrode, a plate electrode, a bubble, and insulating oil. Spherical bubbles are present in the insulating oil. The needle electrode is a high-voltage electrode with applied power frequency AC high voltage. The plate electrode is grounded. The spherical bubbles are attached to the insulating cardboard behind the needle electrode.

[0009] Furthermore, the two-dimensional geometric simulation model of the needle-plate electrode is configured with oil flow direction, material properties, and safe flow velocity based on the actual operating conditions of the transformer.

[0010] Furthermore, the set of electric field-flow field-phase field coupled control equations includes: ; in, For mobility, For a continuously changing phase field variable, Chemical potential, This represents the velocity of the bubble.

[0011] Furthermore, the mobility is an adaptive adjustment function that varies with the electric field strength and phase field gradient.

[0012] Furthermore, the chemical potential describes the generalized thermodynamic force of a non-uniform multiphase system, representing a scalar field of the driving force for the diffusion of matter in a non-uniform multiphase system, the gradient of which determines the direction and rate of diffusion of matter.

[0013] Furthermore, the set of electric field-flow field-phase field coupled control equations includes: ; ; in, Indicates the velocity of each phase of the fluid. Indicates the density of the fluid. This represents the pressure inside the fluid. The surface tension at the interface between the air bubbles and the insulating oil. For electric field force, This is the acceleration due to gravity.

[0014] Furthermore, the local density and viscosity of each phase fluid in the electric field-flow field-phase field coupled control equation set are interpolated using phase field variables.

[0015] Furthermore, the mesh division follows the following three principles: The larger the gradient of physical quantities, the denser the mesh layout should be in the region. The more gradual the change in physical quantities, the sparser the grid layout should be. Adjust the grid parameters to meet different analytical needs.

[0016] A second aspect of the present invention provides a coupled analysis system for bubble movement and electric field distortion in transformer oil, comprising: The model building module is configured to: build a two-dimensional geometric simulation model of the needle-plate electrode; describe the synergistic effect of electric field force, buoyancy, gravity, drag, drag force and surface tension on bubble deformation, migration and coalescence behavior in the two-dimensional geometric simulation model of the needle-plate electrode through the electric field-flow field-phase field coupled control equation set; and the evolution law of the electric field intensity inside the bubble being dominated by voltage phase and enhanced when it is close to the tip electrode. The solver module is configured to: mesh the computational domain, set the time step and solver, perform numerical calculations on the coupled control equations of electric field-flow field-phase field, and extract field quantity data and generate contour maps after post-processing.

[0017] Compared with the prior art, the beneficial effects of the present invention are: This invention can accurately reflect the migration characteristics of bubbles driven by electric field force, buoyancy, surface tension and viscous drag of oil flow. It clarifies the evolution law that the electric field strength inside the bubble is dominated by voltage phase and significantly enhanced when it is close to the tip electrode. This reveals the edge concentration effect where the electric field strength at the bubble interface is much higher than the background field strength, providing key physical basis for identifying weak points in insulation. Attached Figure Description

[0018] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0019] Figure 1 This is a schematic diagram of the force analysis of a single bubble in Embodiment 1 of the present invention; Figure 2 This is a schematic diagram of the drag force analysis under the horizontal state of the double bubble in Embodiment 1 of the present invention; Figure 3 This is a schematic diagram of the drag force analysis under the tilted state of the double bubble in Embodiment 1 of the present invention; Figure 4This is a flowchart of the coupling analysis method of bubble movement and electric field distortion in transformer oil according to Embodiment 1 of the present invention; Figure 5 This is a schematic diagram of the transformer oil passage model structure of the needle-plate electrode according to Embodiment 1 of the present invention; Figure 6 This is a mesh partitioning diagram of the transformer oil passage model of the needle-plate electrode according to Embodiment 1 of the present invention; Figure 7 This is a single bubble migration trajectory diagram of Embodiment 1 of the present invention; Figure 8 This is a field strength distribution diagram of bubbles and insulating oil in Embodiment 1 of the present invention; Figure 9 This is a schematic diagram of the displacement of the bubble under different voltages in Embodiment 1 of the present invention; Figure 10 This is a schematic diagram of the maximum electric field intensity inside the bubble under different voltages in Embodiment 1 of the present invention; Figure 11 This is a schematic diagram of the displacement of air bubbles under different oil speeds in Embodiment 1 of the present invention; Figure 12 This is a schematic diagram of the maximum electric field intensity inside the bubble under different oil speeds in Embodiment 1 of the present invention; Figure 13 This is a schematic diagram of the initial state of two air bubbles in the insulating oil according to Embodiment 1 of the present invention; Figure 14 This is a schematic diagram of the coalescence process of two bubbles under different voltages in Embodiment 1 of the present invention; Figure 15 This is a schematic diagram of the maximum electric field strength inside the bubble under different voltages in Embodiment 1 of the present invention; Figure 16 This is a schematic diagram of the coalescence process of two bubbles at different initial positions in Embodiment 1 of the present invention; Figure 17 This is a schematic diagram of the maximum electric field strength inside the bubble at different initial positions according to Embodiment 1 of the present invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0021] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0022] Example 1 This embodiment provides a method for coupled analysis of bubble movement and electric field distortion in transformer oil.

[0023] As described in the background section, it is necessary to conduct in-depth research on the coupling modeling method of bubbles in transformer oil under extremely non-uniform electric fields, and to analyze the motion law and dynamic characteristics of bubbles under the influence of multi-physics coupling and multiple factors.

[0024] The coupling analysis method for bubble movement and electric field distortion in transformer oil provided in this embodiment is used to simulate and analyze the movement, deformation, coalescence, and electric field distortion caused by bubbles in transformer oil under extremely non-uniform electric fields.

[0025] This embodiment provides a coupled analysis method for bubble movement and electric field distortion in transformer oil. By constructing a multiphysics coupled simulation model based on needle-plate electrodes, it comprehensively considers the synergistic effect of the electric field and fluid field. Through simulation calculations, it analyzes the influence of factors such as voltage amplitude and oil velocity on bubble migration and the degree of electric field distortion under a highly non-uniform electric field. It also examines the mechanism by which voltage amplitude, bubble quantity, and bubble position affect bubble aggregation and the maximum electric field strength. This method realistically reflects the intrinsic mechanism of partial discharge in power transformer oil caused by the dynamic behavior of bubbles, providing a theoretical basis for precise prevention and early warning of transformer insulation faults.

[0026] I. Force analysis of single bubble motion.

[0027] To improve heat dissipation efficiency, transformers rely on the circulating flow of insulating oil to dissipate heat. During this process, air bubbles in the oil move with the oil flow. Since air bubbles are deformable fluids, they undergo complex physical changes such as deformation and coalescence during migration, necessitating mechanical analysis. Under the combined influence of the electric and fluid fields, air bubbles are primarily affected by electric force, buoyancy, gravity, drag, drag force, and surface tension. Among these, electric force and surface tension are the main causes of air bubble shape changes, while buoyancy, gravity, drag, and drag force collectively influence the air bubble's trajectory and migration behavior. For a single air bubble with a radius of... Force analysis of the bubbles, such as Figure 1 As shown.

[0028] The coupling between the electric field and the fluid field is achieved through the electric force. This is achieved by acting on the fluid unit. Under the influence of an external electric field, polarized charges are induced around the bubble, and the resulting electric field superimposed on the original electric field to form a composite electric field, causing the bubble to experience an electric force. The expression for the electric force per unit volume is as follows: (1); (2); (3); in, For Maxwell's stress tensor, For electric field strength, For unit tensors, For electric potential, The vacuum permittivity, ▽ Gradient; relative permittivity as a whole of the gas-liquid two-phase flow system. Its spatial distribution in a gas-liquid two-phase flow system is represented as: (4); in, and These represent the volume fractions of air bubbles and insulating oil, respectively. and , respectively, are the relative permittivity of the air bubbles and the insulating oil. A volume fraction weighted average is used here to ensure a continuous distribution of the permittivity within the solution domain.

[0029] buoyancy and gravity These are a pair of forces in opposite directions in the vertical direction. For a single bubble, the buoyancy is always greater than the weight. Therefore, the effect of their resultant force is to make the bubble rise vertically in the static insulating oil. Their expressions are shown in equations (5) and (6), respectively: (5); (6); in, and The densities of insulating oil and air bubbles are respectively. This is the acceleration due to gravity.

[0030] resistance and drag force These are a pair of forces in opposite directions in the horizontal direction. The drag force originates from the flow of the insulating oil, and the resistance originates from the viscosity of the insulating oil. Since the viscosity is much greater than that of the oil, the combined effect of these forces causes the bubbles to move in the same direction as the oil velocity in the horizontal direction. Their expressions are shown in equations (7) and (8), respectively: (7); (8); in, and The dynamic viscosity of insulating oil and air bubbles are respectively. For oil speed, The velocity of the bubble. This represents the characteristic length of the insulating oil.

[0031] Surface tension This is used to suppress the deformation of bubbles caused by the electric field, thus affecting the degree of bubble deformation. The specific derivation process is obtained by building a subsequent model to track the force at the gas-liquid two-phase flow interface.

[0032] II. Stress analysis of multi-bubble aggregation.

[0033] When multiple air bubbles exist in insulating oil, their movement will involve coalescing compared to a single bubble. Taking two bubbles as an example for force analysis, their coalescing process is mainly controlled by hydrodynamic effects. Based on the initial state of the two bubbles, they can be divided into horizontal and inclined states, such as... Figure 2 and Figure 3 As shown.

[0034] When two bubbles rise side-by-side horizontally, the fluid velocity in the region between the bubbles is higher than that on the outer side. According to Bernoulli's principle, the pressure in this region is lower than the pressure on the outer side of the bubble, creating an upward-sloping attractive force between the bubbles—a hydrodynamic drag force. This force points from the center of the rear bubble to the center of the front bubble, causing the two bubbles to move closer together. As the distance between the bubbles decreases, reaching the nanoscale, the oil film between the bubbles gradually thins and drains, eventually rupturing and causing the bubbles to coalesce.

[0035] When two bubbles are tilted, one above the other, the coalescence mechanism primarily stems from the wake effect. The lower bubble enters the low-pressure wake region formed at the bottom of the upper bubble, where it is drawn in, causing it to rise faster than the upper bubble, thus drawing closer and coalescing. Furthermore, if an electric field is present, the difference in dielectric constant between the bubbles and the insulating oil polarizes them, forming electric dipoles. Interaction forces arise between the dipoles of adjacent bubbles, the magnitude and direction of which depend on the angle between the line connecting the bubbles and the direction of the electric field. In a highly non-uniform electric field, the electric field gradient force further influences the bubble trajectory, promoting or inhibiting coalescence. After coalescence, the newly formed bubble increases in volume, and its rising velocity, deformation, and internal electric field distortion characteristics all change significantly.

[0036] III. Model Building.

[0037] This embodiment focuses on multiphysics coupling modeling and simulation of air bubbles in transformer oil under a highly non-uniform electric field. The flowchart is as follows: Figure 4 As shown.

[0038] First, a two-dimensional geometric simulation model of the needle-plate electrode is constructed, and parameters such as oil flow direction, material properties, and safe flow velocity are set according to the actual operating conditions of the transformer. Then, for this gas-liquid two-phase flow problem, force tracking at the gas-liquid two-phase interface is achieved, and a set of coupled control equations of electric field, flow field, and phase field is constructed. Based on this, the mesh is generated following the principles of gradient region refinement and internal sparsity. Numerical calculations are then performed with a reasonable time step and solver. After post-processing, field quantity data are extracted and contour maps are generated, ultimately achieving accurate simulation and analysis of the dynamic behavior of bubbles and the law of electric field distortion in transformer oil. This solution process will be discussed in detail below.

[0039] Step 1: Geometric model construction and parameter settings.

[0040] In actual transformers, the inner walls of the insulating oil channels are not completely smooth, but contain various burrs or protrusions. This results in a highly non-uniform electric field distribution within the channels, driving air bubbles in the oil to undergo specific forms of motion. Therefore, this embodiment constructs a geometric simulation model of transformer oil channels with needle-plate electrodes, and uses multiphysics simulation software to simulate the dynamic behavior of air bubbles in the insulating oil under a highly non-uniform electric field.

[0041] The model mainly consists of four parts: needle electrode, plate electrode, bubble, and insulating oil. The specific structure is as follows: Figure 5 As shown. Assume there is a space with a radius of [missing information] inside the transformer's insulating oil. A spherical bubble is used, with a needle electrode as the high-voltage electrode, applying a high-voltage AC power frequency, and a plate electrode grounded. Assuming the bubble and needle electrode are in close contact with the insulating cardboard behind them, a very high electric field gradient is formed in the vicinity of the needle electrode tip due to its small radius of curvature, effectively simulating the highly non-uniform electric field environment inside the transformer oil channels caused by defects. Since the oil channel dimensions vary at different locations within the transformer, this embodiment selects common dimensions. As the electric field calculation region for the needle-plate electrode model, the simulation results are ensured to have universality and general regularity. Considering the geometric symmetry of the transformer oil passage model of the needle-plate electrode, the model ignores the detailed features of the complex three-dimensional structure inside the transformer, and uses a two-dimensional structure for simulation analysis to simplify the model and reduce the amount of calculation.

[0042] During actual transformer operation, the heat generated by the windings and core causes the insulating oil to expand and decrease in density, rising to the top of the tank or radiator. After the transformer cools, the oil temperature decreases, its density increases, and it settles back to the bottom, thus forming a continuous bottom-up natural convection or forced circulation, consistent with the flow direction of oil circulation for heat dissipation and insulation in actual transformer operation. Therefore, the model is designed with the insulating oil flowing from bottom to top.

[0043] Regarding the flow rate of insulating oil in oil-immersed transformers, power industry standards stipulate that, to ensure the long-term safe and stable operation of transformers, the maximum flow rate limit for insulating oil in forced oil circulation systems is [value missing]. This is to effectively suppress the phenomenon of oil flow charging. Oil flow charging refers to the generation and accumulation of static charge when high-speed flowing insulating oil rubs against solid insulating materials. When the charge accumulates to a certain level, it may trigger a discharge, and in severe cases, it may even endanger the integrity of the main insulation. In engineering practice, for the sake of higher safety margins and adaptability to different operating conditions, the actual maximum flow velocity limit of the insulating oil inside the transformer is [value missing]. Therefore, in subsequent simulation analysis, the flow rate of the insulating oil was set at... The following changes will be made, and the flow of transformer oil in the simulation model can now be represented by a laminar flow model.

[0044] In the multiphysics coupling simulation, the material property parameters of the transformer insulating oil and bubbles are set as shown in Table 1, where the insulating oil parameters are taken from common values.

[0045] Table 1. Material Property Parameters

[0046] Step 2: Construction of multiphysics coupling.

[0047] To address the gas-liquid two-phase flow problem involving the co-flow of bubbles and insulating oil, this embodiment constructs a multi-physics field coupled control equation set of electric field, flow field, and phase field to study the motion state and coalescence process of the bubbles. When the geometry of the interface is complex, directly analyzing the deformation of irregular shapes will increase the computational complexity. Therefore, this embodiment adopts a homogenization method, treating each phase as a continuous physical field with an average mass fraction or volume fraction, and the interphase interaction is transformed into additional source and sink terms in the momentum equation of the fluid mixture (Equation (13)). At the same time, by setting the interface layer control parameters, the specific location of the phase interface is determined under the principle of minimizing free energy. To describe the distribution characteristics of different substances in the solution domain, a continuously changing phase field variable is defined. Its value smoothly transitions from 1 to -1, that is, the bubble takes a value of -1, the insulating oil takes a value of 1, and the region where the phase field variable changes steadily takes a value of 1. The spatiotemporal evolution of the phase field variables follows the law shown in equation (9): (9); in, Let be the mobility, representing the rate of evolution of the interface between the two phases. To prevent premature numerical dispersion of the interface under high field strength, the mobility is defined here as an adaptive adjustment function that varies with the electric field strength and phase field gradient, and its expression is shown in equation (10): (10); in, Let the initial mobility be denoted as . ; The electric field coupling weighting coefficient is taken as... to The magnitude will be adjusted based on subsequent simulation voltage amplitudes; To obtain a reference electric field strength, the average field strength near the needle electrode is taken, and the local field strength is normalized.

[0048] The chemical potential is a generalized thermodynamic force describing a non-homogeneous multiphase system. It represents the scalar field of the driving force for the diffusion of matter in the non-homogeneous multiphase system. Its gradient determines the direction and rate of diffusion of matter. Its expression is shown in equation (11): (11); in, Let be the gas-liquid interfacial tension coefficient, and take . ; This is the interface thickness parameter, representing the width of the transition zone between the two intersecting interfaces.

[0049] Therefore, the surface tension at the interface between the bubble and the insulating oil is defined as shown in equation (12): (12); To achieve coupling between the phase field and the flow field, the following equation is introduced: (13); (14); in, This indicates the velocity of each phase of the fluid within the system; Indicates the density of the fluid. This represents the pressure inside the fluid. t Time is represented. The local density and viscosity of each phase fluid in the system are interpolated using phase field variables, and their expressions are shown in equations (15) and (16), respectively: (15); (16); In summary, the simulation model uses phase field variables... Flow field velocity Fluid internal pressure and electric potential As the basic solution variables, a set of multi-physics field coupled control equations of electric field, flow field and phase field was constructed.

[0050] Step 3: Mesh generation and solver selection.

[0051] Mesh generation, or discretization of the computational domain into individual cells, directly determines the size of the system of equations to be solved. While finer meshes typically improve numerical accuracy, they also increase computational complexity. Excessive mesh refinement can induce numerical singularities, making convergence difficult. Therefore, mesh design requires a reasonable trade-off between computational accuracy and solution cost; higher density is not always better.

[0052] Therefore, the implementation of grid generation should follow the following three basic principles: (1) In areas with large gradients in physical quantities, such as the edges of components or the junctions of different media, a finer grid layout should be used to ensure calculation accuracy and suppress error accumulation. (2) In regions where physical quantities change relatively smoothly, such as inside components, the mesh size can be appropriately widened to reduce computational overhead and improve overall solution efficiency. (3) Mesh parameters can be flexibly adjusted to meet different analysis needs, covering aspects such as element size, curvature adaptation, and growth rate control, in order to achieve more refined mesh control. In addition, mesh generation is not limited to the discretization of geometric space; appropriate mesh densities can also be set according to different physical fields or solution modules to optimize computational performance.

[0053] The mesh generation results of the transformer oil passage model under the needle-plate electrode structure are as follows: Figure 6 As shown. Given the large computational cost of multiphysics coupling, a denser mesh configuration is used at the component boundaries, while a relatively sparse mesh is used inside the components. For areas with significant geometric differences, the mesh needs to be further refined to keep computational errors within acceptable limits.

[0054] Determining the time step for simulation calculations is the final step in model building. Corresponding to the spatial discretization of mesh generation, the time step achieves approximate discretization of the computation process in the temporal dimension. However, in actual physical processes, the changes in various field quantities are continuous. Therefore, in numerical simulations, based on the ideas of calculus, the continuous time history is divided into several small time increments. It is assumed that the field quantities remain constant or change linearly within each time step, thereby sequentially solving for the distribution of each physical field in the model.

[0055] For the cone-plate electrode oil passage model established in this embodiment, considering both computational accuracy and solution efficiency, the simulation step size is set to... Because the period of the processed high-frequency AC voltage is Setting this time step allows for sampling 20 points within each cycle, which can accurately describe the continuous changes in the voltage waveform. Meanwhile, the motion, deformation, and coalescence of the bubble under the coupling of the electric and flow fields occur on the order of milliseconds. Setting this simulation step size is sufficient to capture the key evolution stages of the bubble's dynamic behavior, avoiding numerical distortion caused by an excessively large step size, and also preventing a significant increase in computational burden due to an excessively small step size.

[0056] Once the model is built and parameters are set, numerical solution can be started. After convergence, the post-processing analysis stage begins. Probe tools are used to extract key locations along the bubble's trajectory, allowing for the quantitative characterization of field changes during bubble motion. Furthermore, the post-processing module generates two-dimensional cloud maps at different time points, visually displaying the spatial distribution characteristics of various field quantities within the solution domain. This allows for the examination of the relationships between physical quantities and spatial location and time, revealing the dynamic behaviors of bubbles such as migration and coalescence under highly non-uniform electric fields, as well as their perturbation mechanisms on the electric field distribution.

[0057] IV. Analysis of Simulation Results

[0058] 1. Motion behavior and field strength distribution of a single bubble.

[0059] With a bubble radius of 1 mm, initially positioned below and to the left of the needle electrode, the simulation yielded the migration trajectory of a single bubble under the influence of a power frequency AC voltage, as shown below. Figure 7 As shown.

[0060] Depend on Figure 7 As shown in the bubble trajectory, under the influence of AC voltage at power frequency, the bubble generally rises diagonally upwards and to the left. During its migration from its initial position towards the top of the computational domain, the bubble simultaneously rises vertically and shifts horizontally to the left, gradually moving away from the tip of the needle electrode. Due to the tip effect of the needle electrode, a highly non-uniform electric field is formed around it. The bubble, with its low dielectric constant, experiences a dielectric force pointing towards the weak electric field region in the non-uniform AC electric field, driving the bubble to generate a horizontal force to the left. Vertically, the bubble experiences an upward buoyancy force in the insulating oil, driving its vertical upward motion, while the viscous resistance of the oil is opposite to the direction of bubble movement. In summary, this motion characteristic can be attributed to the combined effect of multiple forces in the non-uniform electric field.

[0061] During the bubble's motion, the electric field distribution is as follows: Figure 8 As shown.

[0062] Depend on Figure 8 Analysis reveals that the needle electrode generates a non-uniform electric field, with the strongest electric field strength at the needle tip. As the distance from the needle tip increases, the corresponding field strength gradually decreases and diverges outwards, with the lowest field strength located at the top of the left and right sides of the computational domain. The electric field strength in the insulating oil adjacent to the top and bottom of the bubble is lower than that of most of the insulating oil, while the electric field strength in the insulating oil adjacent to the left and right sides is higher than that of most of the insulating oil, exhibiting a significant edge concentration effect. The dielectric constant of the gas inside the bubble is much lower than that of the surrounding insulating oil, causing the electric field lines to refract at the interface and converge towards the interior of the bubble. This results in a uniformly distributed electric field inside the bubble, but with a value much higher than that outside, becoming a weak point for inducing partial discharge.

[0063] (1) Effects of different voltages on bubble motion and electric field distribution: To investigate the effect of different voltages on the migration trajectory of a bubble, the effective voltage values ​​of the needle electrodes were set to 15kV, 25kV, and 35kV. A coordinate system was established with the needle tip as the origin, the left side as the positive X-axis, and the top side as the positive Y-axis. The displacement of the bubble during its migration is shown in the figure. Figure 9 As shown.

[0064] Depend on Figure 9 It can be seen that under different voltage conditions, the trajectory curves of the bubbles all exhibit a monotonically increasing trend from the lower right to the upper left, indicating that under the influence of a non-uniform power frequency AC electric field, the bubbles generally migrate towards the upper left. Comparing the bubble displacement relationship under different voltages, it can be seen that as the applied voltage gradually increases, the Y coordinate value corresponding to the same X coordinate position increases accordingly. That is, the higher the voltage, the more obvious the vertical displacement of the bubble, and the slope of the trajectory also increases significantly with the increase of voltage. As the voltage increases, the electric field strength is significantly enhanced, which increases the effect of the electric field force in the vertical direction. At the same time, the bubbles are subjected to upward buoyancy in the insulating oil, which dominates their vertical upward floating process, while the viscous resistance of the oil itself inhibits the movement of the bubbles. Under higher voltage, the electric field distortion is further aggravated, resulting in an increase in the force field gradient experienced by the bubbles. When buoyancy and viscous resistance are dynamically balanced, the upward speed of the bubbles in the vertical direction increases with the increase of voltage during the horizontal migration to the left. Therefore, the higher the voltage, the greater the slope of the trajectory.

[0065] To investigate the specific mechanism by which different voltages affect the electric field distortion during bubble motion, a domain probe was used to track the maximum electric field intensity inside the bubble, obtaining the maximum electric field intensity inside the bubble as follows: Figure 10 As shown.

[0066] Depend on Figure 10 It can be seen that the bubble vibrates periodically at a frequency of 100Hz in the power frequency AC electric field, and as the power frequency voltage reaches its peak or zero point, the electric field strength inside the bubble also reaches its peak or zero point in its periodic fluctuation. Comparing the maximum electric field strength inside the bubble under different voltages, it can be seen that the overall electric field strength inside the bubble increases with the increase of the applied voltage.

[0067] (2) The effect of different oil velocities on bubble motion and field intensity distribution: To investigate the effect of different insulating oil flow velocities on the migration trajectory of air bubbles, oil velocities of 0.12 m / s, 0.16 m / s, and 0.20 m / s were set. Under the same coordinate system, the displacement of the air bubble during its migration is shown below. Figure 11 As shown.

[0068] Depend on Figure 11It can be seen that the overall trajectory of the bubble still migrates diagonally upward and to the left. Comparing the displacement relationship of the bubble motion at different oil speeds, it can be seen that as the oil speed increases, the absolute value of the X coordinate corresponding to the same Y coordinate is larger, and the Y coordinate value corresponding to the same X coordinate is larger. This indicates that the higher the oil speed, the greater the displacement of the bubble in the vertical and horizontal directions, and the slope of the trajectory increases significantly with increasing oil speed. That is, the higher the oil flow velocity, the greater the viscous drag force on the bubble surface, which enhances the shear effect of the oil in the horizontal direction and improves the bubble's following ability in the oil flow, resulting in a stronger horizontal driving force; in the vertical direction, it works synergistically with the bubble's own buoyancy, resulting in a stronger vertical driving force.

[0069] To investigate the specific influence mechanism of bubble motion on electric field distortion at different oil velocities, a domain probe was also used to track the maximum electric field intensity inside the bubble. The maximum electric field intensity inside the bubble during its migration process is shown in the figure. Figure 12 As shown.

[0070] Depend on Figure 12 It can be seen that the overall electric field strength of the bubble still changes at a frequency of 100Hz, and the value varies with the voltage. Comparing the peak values, it was found that the maximum electric field strength inside the bubble remains basically the same under different oil speeds. This indicates that changing the oil speed only affects the force on the bubble, while the electric field remains almost the same.

[0071] 2. Bubble aggregation behavior and electric field changes.

[0072] The simulation analysis is carried out using the coalescence behavior of two bubbles as an example. The initial state is as follows: Figure 13 As shown.

[0073] (1) Effect of different voltages on bubble aggregation and field strength distribution: To investigate the effect of different voltages on the bubble coalescence process, the effective voltage values ​​of the needle electrodes were set to 15kV, 25kV, and 35kV, respectively. The bubble coalescence process is as follows: Figure 14 As shown.

[0074] Depend on Figure 14 It is evident that the coalescence process of bubbles accelerates significantly with increasing voltage applied to the needle electrode. In insulating oil, bubbles are subjected to an electric field; the higher the voltage, the stronger the electric field, and the stronger the driving force for bubble deformation and coalescence. High voltage conditions cause the liquid film between bubbles to thin and rupture more quickly, allowing bubbles to contact and fuse earlier. Therefore, with increasing voltage, the coalescence rate of bubbles increases, and the degree of fusion is more complete.

[0075] To investigate the specific influence mechanism of bubble coalescence on electric field distortion under different voltages, a domain probe was also used to track the maximum electric field intensity inside the bubble. The maximum electric field intensity inside the bubble during the coalescence process is shown in the figure. Figure 15 As shown.

[0076] Depend on Figure 15 It can be seen that, under different voltage conditions, the maximum electric field intensity inside the bubble still exhibits periodic oscillations synchronized with the power frequency AC voltage. Comparing the maximum electric field intensity inside the bubble at different voltage levels reveals that the field intensity waveform becomes steeper as the voltage increases, indicating that the dynamic changes in the bubble morphology have a more pronounced effect on enhancing the local electric field under high voltage conditions. Since the relative permittivity inside the bubble is much lower than that of transformer oil, significant electric field distortion and concentration effects occur at the interface. The greater the voltage between the electrodes, the more significant the electric field concentration phenomenon at the interface, thus increasing the maximum electric field intensity inside the bubble.

[0077] (2) The influence of different initial positions on bubble aggregation and field strength distribution: To investigate the influence of different initial positions on the bubble coalescence process, initial position models were established with angles of 0°, 20°, and 40° between the line connecting the centers of two bubbles and the horizontal direction. The bubble coalescence process is as follows: Figure 16 As shown.

[0078] Depend on Figure 16 It can be seen that the larger the initial angle between the two bubbles, the shorter the bubble coalescing time and the faster the completion rate. As the initial angle increases, the vertical component of the bubble makes the synergistic effect of buoyancy and electric field force more significant, enhancing the superposition effect of electric field gradient between bubbles, resulting in higher electric field intensity in the contact area and faster interface fusion. At the same time, the vertical component of buoyancy shortens the effective movement path of the bubbles, accelerating the collision and coalescing process.

[0079] To investigate the specific impact mechanism of bubble coalescence on electric field distortion at different initial positions, a domain probe was also used to track the maximum electric field intensity inside the bubble. The maximum electric field intensity inside the bubble during the coalescence process is shown in the figure. Figure 17 As shown.

[0080] Depend on Figure 17 It can be seen that, under different initial positions, the maximum electric field intensity inside the bubble still maintains a periodic fluctuation synchronized with the power frequency AC voltage. Comparing the maximum electric field intensity inside the bubble at each initial position reveals that the larger the initial angle between the two bubbles, the more drastic the change in the electric field waveform, but the difference is not very significant. When the initial angle of the bubble is 0°, the driving force it experiences is singular, consisting only of the horizontal dielectric force, resulting in a relatively gentle coalescence process and minimal change in interface curvature. As the initial angle gradually increases, the vertical component of the bubble introduces the combined effect of buoyancy and electric field force. This not only makes the superposition effect of the electric field gradient between the bubbles more prominent, accelerating the collision and coalescence process, but also, due to the asymmetry of forces, increases the interface curvature of the final fused bubble, thereby further enhancing the distortion of the electric field.

[0081] This embodiment constructs a multi-physics coupled model of electric field, flow field, and phase field to accurately capture the dynamic behavior of bubbles and the induced electric field distortion under extremely non-uniform electric fields, effectively solving the problem of unclear synergistic effects of multiple factors in existing studies. This method can realistically reflect the migration characteristics of bubbles driven by electric force, buoyancy, surface tension, and viscous drag of oil flow. It clarifies the evolution law that the electric field intensity inside the bubble is dominated by voltage phase and significantly enhances near the tip electrode, thus revealing the edge concentration effect where the electric field intensity at the bubble interface is much higher than the background field strength, providing key physical evidence for identifying weak points in insulation. Regarding multi-bubble coalescence, this embodiment, through simulation analysis of different voltages and initial positions, elucidates that the enhanced coupling effect of electrophoretic force and buoyancy is the core mechanism for shortening coalescence time and exacerbating interface distortion. In particular, it discovers the significant dominant role of oil flow velocity on longitudinal motion and the regulation mechanism of the initial angle on the coalescence rate, providing theoretical reference for optimizing the design of internal oil channels in transformers. In addition, the model employs a gradient region-based mesh and a microsecond-level computation step size, which effectively balances the accuracy and efficiency of numerical computation while ensuring the capture of key evolutionary details of bubbles at the millisecond level, making the simulation results highly universal and of great engineering reference value.

[0082] The coupled analysis method for bubble motion and electric field distortion in transformer oil provided in this embodiment first constructs a two-dimensional geometric simulation model of needle-plate electrodes to simulate the highly non-uniform electric field environment inside the transformer. Based on the gas-liquid two-phase flow problem, it tracks the force and evolution process at the gas-liquid interface and establishes a set of multi-physics coupled control equations covering the electric field, flow field, and phase field. It comprehensively considers the synergistic effects of electric force, buoyancy, surface tension, and oil flow drag on bubble deformation, migration, and coalescence behavior. Through simulation calculations, it analyzes the influence of different voltage amplitudes, oil velocities, and initial bubble positions on the bubble dynamic trajectory and the degree of electric field distortion. This method can realistically reflect the intrinsic mechanism of partial discharge caused by bubble dynamic behavior, providing theoretical support for precise prevention and early warning of transformer insulation faults.

[0083] Example 2 The coupled analysis system for bubble movement and electric field distortion in transformer oil provided in this embodiment includes: The model building module is configured to: build a two-dimensional geometric simulation model of the needle-plate electrode; describe the synergistic effect of electric field force, buoyancy, gravity, drag, drag force and surface tension on bubble deformation, migration and coalescence behavior in the two-dimensional geometric simulation model of the needle-plate electrode through the electric field-flow field-phase field coupled control equation set; and the evolution law of the electric field intensity inside the bubble being dominated by voltage phase and enhanced when it is close to the tip electrode. The solver module is configured to: mesh the computational domain, set the time step and solver, perform numerical calculations on the coupled control equations of electric field-flow field-phase field, and extract field quantity data and generate contour maps after post-processing.

[0084] It should be noted that each module in this embodiment corresponds one-to-one with each step in Embodiment 1, and their specific implementation processes are the same, so they will not be repeated here.

[0085] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method of analyzing coupling of bubble motion and electric field distortion in transformer oil, characterized by, include: A two-dimensional geometric simulation model of a needle-plate electrode was constructed. The synergistic effect of electric force, buoyancy, gravity, drag, drag force and surface tension on bubble deformation, migration and coalescence behavior in the two-dimensional geometric simulation model of the needle-plate electrode was described by the electric field-flow field-phase field coupled control equation set. The evolution law of the electric field intensity inside the bubble being dominated by voltage phase and enhanced when it is close to the tip electrode was also described. The computational domain is meshed, and the time step and solver are set. Numerical calculations are performed on the coupled control equations of electric field, flow field and phase field. Field quantity data are extracted and contour maps are generated after post-processing.

2. The coupling analysis method for bubble movement and electric field distortion in transformer oil as described in claim 1, characterized in that, The two-dimensional geometric simulation model of the needle-plate electrode includes a needle electrode, a plate electrode, a bubble, and insulating oil. There are spherical bubbles in the insulating oil. The needle electrode is a high-voltage electrode with applied power frequency AC high voltage. The plate electrode is grounded. The spherical bubbles are attached to the insulating cardboard behind the needle electrode.

3. The coupling analysis method for bubble movement and electric field distortion in transformer oil as described in claim 1, characterized in that, The two-dimensional geometric simulation model of the needle-plate electrode is set according to the actual operating conditions of the transformer, including the oil flow direction, material properties, and safe flow velocity.

4. The coupling analysis method for bubble movement and electric field distortion in transformer oil as described in claim 1, characterized in that, The set of electric field-flow field-phase field coupling control equations includes: ； in, For mobility, For a continuously changing phase field variable, Chemical potential, This represents the velocity of the bubble.

5. The coupling analysis method for bubble movement and electric field distortion in transformer oil as described in claim 4, characterized in that, The mobility is an adaptive adjustment function that varies with the electric field strength and phase field gradient.

6. The coupling analysis method for bubble movement and electric field distortion in transformer oil as described in claim 4, characterized in that, The chemical potential describes the generalized thermodynamic force of a non-uniform multiphase system, representing a scalar field of the driving force for the diffusion of matter in the non-uniform multiphase system, and its gradient determines the direction and rate of diffusion of matter.

7. The coupling analysis method for bubble movement and electric field distortion in transformer oil as described in claim 1, characterized in that, The set of electric field-flow field-phase field coupling control equations includes: ； ； in, Indicates the velocity of each phase of the fluid. Indicates the density of the fluid. This represents the pressure inside the fluid. The surface tension at the interface between the air bubbles and the insulating oil. For electric field force, This is the acceleration due to gravity.

8. The coupling analysis method for bubble movement and electric field distortion in transformer oil as described in claim 1, characterized in that, The local density and viscosity of each phase fluid in the electric field-flow field-phase field coupled control equation set are interpolated using phase field variables.

9. The coupling analysis method for bubble movement and electric field distortion in transformer oil as described in claim 1, characterized in that, The grid division follows the following three principles: The larger the gradient of physical quantities, the denser the mesh layout should be in the region. The more gradual the change in physical quantities, the sparser the grid layout should be. Adjust the grid parameters to meet different analytical needs.

10. A coupled analysis system for bubble movement and electric field distortion in transformer oil, characterized in that, include: The model building module is configured to: build a two-dimensional geometric simulation model of the needle-plate electrode; describe the synergistic effect of electric field force, buoyancy, gravity, drag, drag force and surface tension on bubble deformation, migration and coalescence behavior in the two-dimensional geometric simulation model of the needle-plate electrode through the electric field-flow field-phase field coupled control equation set; and the evolution law of the electric field intensity inside the bubble being dominated by voltage phase and enhanced when it is close to the tip electrode. The solver module is configured to: mesh the computational domain, set the time step and solver, perform numerical calculations on the coupled control equations of electric field-flow field-phase field, and extract field quantity data and generate contour maps after post-processing.

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