LBM-based method, system and medium for evolution of complex cross-section ice shape of power transmission line

Abstract

The application discloses a power transmission line complex section icing shape evolution method and system based on LBM, and a medium, relates to the technical field of icing model construction, and combines the physical mechanism of icing formation and the classical Makkonen thermodynamic growth model, aims at the assumption defect of uniform distribution of traditional model icing, introduces the lattice Boltzmann method (LBM) to carry out flow field calculation and boundary tracking to realize the evolution of the shape of the icing, calculates the velocity distribution around the power transmission line based on the LBM, disperses the surface of the power transmission line into a plurality of control volumes, and obtains the local collision flux of the control volume; the normal movement of the icing interface is described by using the level set method, the boundary movement is realized by dispersing the level set equation through the upwind difference format, and the dynamic update of the icing interface is completed by combining the grid self-adaptive strategy, and the accurate evolution simulation of the shape evolution characteristics of non-uniform icing such as fan-shaped and crescent-shaped icing under complex wind field is realized.

Description

Technical Field

[0001] This invention relates to the field of icing model construction technology, specifically to a method, system, and medium for the evolution of icing shape of complex cross-sections of transmission lines based on LBM. Background Technology

[0002] Icing on transmission and distribution lines is one of the major natural disasters causing power grid safety malfunctions. Icing accidents can lead to serious incidents such as line breaks, tower collapses, and insulator flashovers, as well as widespread power outages, causing enormous losses to the social economy and people's lives. Therefore, accurately predicting and assessing the development trend of icing on transmission lines is of great engineering significance for power grid disaster prevention and mitigation, safe operation and maintenance, and emergency response.

[0003] From a physical perspective, the formation of icing on transmission lines is a typical complex process involving multiple physical fields, encompassing thermodynamics, fluid mechanics, and phase change kinetics. Specifically, supercooled water droplets collide with and freeze on the conductor surface under the influence of wind. The growth process is affected by multiple factors, including ambient temperature, wind speed, wind direction, liquid water content, and droplet size, resulting in significant non-uniformity and time-varying characteristics in the morphology, density, and mechanical properties of the icing.

[0004] In existing technologies, the classical thermodynamic and mass balance model, represented by the Makkonen model, is commonly used for numerical simulation of icing growth on transmission lines. Based on the principles of thermal balance and mass conservation, the Makkonen model can effectively calculate the icing growth rate on columnar structures by solving the energy balance equation and water droplet capture rate of the icing surface. Due to its clear physical meaning and high computational efficiency, it is widely used in engineering estimation of icing loads and the formulation of related standards.

[0005] However, the Makkonen model relies on a key assumption in its geometric modeling: it treats the conductor as an ideal circular cross-section and assumes that icing grows uniformly along the conductor's circumference. This assumption is applicable to simple, isotropic wind fields where the icing shape approximates a coaxial circular cross-section. However, under real-world complex terrain and variable wind conditions, icing on the conductor surface often exhibits significant shape evolution characteristics. Studies show that factors such as wind direction changes, wind speed fluctuations, and conductor vibrations lead to uneven circumferential distribution of water droplet collision efficiency on the conductor surface, resulting in non-axisymmetric, non-uniform icing morphologies such as fan-shaped, crescent-shaped, and airfoil-shaped icing. These morphologies significantly influence dynamic behaviors such as icing load, wind load, and ice shedding jumps. The Makkonen model, lacking the geometric representation capability for the icing shape evolution process, struggles to accurately describe the spatial distribution characteristics and dynamic growth process of these non-uniform icing morphologies.

[0006] Therefore, how to overcome the limitations of the traditional Makkonen model in geometric modeling, construct a mechanism model that can adapt to the evolution of non-uniform icing shape under complex wind field conditions, and realize dynamic modeling and accurate prediction of icing development trends has become an urgent technical problem to be solved in the field of transmission line icing disaster prevention and control. Summary of the Invention

[0007] To overcome the limitations of the traditional Makkonen model in geometric modeling, this invention aims to construct a numerical model adaptable to the evolution of non-uniform icing shapes under complex wind field conditions, thereby achieving accurate prediction of icing development trends. The purpose of this invention is to provide a method, system, and medium for the evolution of icing shapes in complex cross-sections of transmission lines based on the Lattice Boltzmann Method (LBM). Combining the physical mechanism of icing formation and the classic Makkonen thermodynamic growth model, and addressing the assumption of uniform icing distribution in traditional models, the Lattice Boltzmann Method (LBM) is introduced for flow field calculation and boundary tracking to realize the evolution of icing shapes. Based on LBM, the velocity distribution around the transmission line is calculated, and the transmission line surface is discretized into several control volumes to obtain the local collision flux of the control volumes. The level set method is used to describe the normal movement of the icing interface, and the boundary movement is realized by discretizing the level set equations through the windward difference scheme. A grid adaptive strategy is combined to complete the dynamic updating of the icing interface, achieving accurate simulation of the evolution characteristics of non-uniform icing shapes such as fan-shaped and crescent-shaped icing under complex wind field conditions.

[0008] The above-mentioned technical objective of the present invention is achieved through the following technical solution:

[0009] This solution provides a method for the evolution of icing shapes in complex cross-sections of transmission lines based on LBM (Leadership Modeling). The method includes:

[0010] A Makkonen thermodynamic growth model was constructed to extrapolate the equivalent icing thickness: the icing mass growth rate per unit length of transmission line was decomposed into collision subprocess, adhesion subprocess and freezing subprocess, and an efficiency coefficient calculation model for each subprocess was constructed.

[0011] Meteorological conditions in the area where the transmission line is located are obtained, and the evolution of icing shape is analyzed using the Makkonen thermodynamic growth model.

[0012] Configure the computational domain, transmission line geometry, and boundary conditions;

[0013] LBM-based calculations of velocity field and icing density around transmission lines;

[0014] By tracking the trajectory of water droplets, the surface of the transmission line is discretized into several control volumes, and the local collision flux is calculated by counting the number of water droplet impacts in each control volume.

[0015] The freezing coefficient of the freezing subprocess was calculated by combining the meteorological conditions and the Makkonen thermodynamic growth model.

[0016] The normal velocity of the icing interface is determined based on the icing density, the efficiency coefficient of the freezing subprocess, and the local collision flux. The normal velocity of the icing interface is substituted into the level set equation to describe the normal movement of the icing interface. The boundary push of the icing interface is realized by the discrete format of the level set equation, and the dynamic update of the icing interface is completed by combining the mesh adaptive strategy.

[0017] A further optimization scheme is proposed, wherein the construction conditions for the Makkonen thermodynamic growth model include:

[0018] Both the ambient air temperature and the surface temperature of the transmission lines were below freezing.

[0019] Supercooled water droplets in liquid state exist in the ambient air, and the diameter of the supercooled water droplets is between 10 μm and 100 μm;

[0020] The supercooled water droplets overcome the influence of ambient airflow under the action of inertial force and impact the surface of the transmission line.

[0021] A further optimization scheme involves constructing the efficiency coefficient calculation model for each subprocess, including:

[0022] The efficiency coefficient of the collision subprocess is determined by the Stokes number of the droplet motion;

[0023] The efficiency coefficient of the adhesion process is determined by the state of the water film on the transmission line surface and the temperature of the transmission line surface;

[0024] The efficiency coefficient of the freezing subprocess is determined by the surface temperature of the transmission line. When the surface temperature of the transmission line is below the freezing point, the efficiency coefficient of the freezing subprocess is 1. When the surface temperature of the transmission line is equal to the freezing point, the efficiency coefficient α3 of the freezing subprocess is determined by the heat balance equation:

[0025] Q f =Q c +Q e +Q w +Q r ;

[0026] ;

[0027] ;

[0028] Among them, Q f Indicates latent heat release; Q c Indicates convection cooling; Q e Indicates evaporative heat dissipation; Q w Indicates sensible heating; Q rIndicates radiative heat dissipation; t represents the icing development time; L f Indicates latent heat of freezing; M w This indicates the mass of liquid water.

[0029] A further optimized scheme is as follows: the configuration method of the computational domain includes: establishing a computational domain centered on the transmission line axis; discretizing the computational domain into a dense structured mesh; taking the transmission line axis direction as the Z-axis; and taking the xy plane section of the computational domain; the dense structured mesh can be uniform or non-uniform.

[0030] The configuration method for the geometric definition of the transmission line includes: defining the cross-section of the transmission line as a circle, configuring the geometric center of the cross-section of the transmission line at the center of the computational domain, and representing the boundary of the transmission line based on the level set function;

[0031] The convenient conditions include speed conditions, pressure conditions, and water droplet conditions at different boundary locations of the transmission line.

[0032] A further optimized scheme is that the calculation methods for the velocity field and icing density include:

[0033] The velocity field around the transmission line was obtained by solving the Navier-Stokes equations using the D2Q9 model. and ice density :

[0034] ;

[0035]

[0036] ;

[0037] in, Represents the particle distribution function; Represents relaxation time, in relation to kinematic viscosity. Related: , This represents the discrete velocity direction, where i represents the index of the i-th discrete velocity direction; Represents the speed of sound in a lattice; Represents the equilibrium distribution function; The position of the water droplet is represented by Lagrange multiplication table tracking; t represents the icing development time. This represents the weighting coefficient.

[0038] A further optimization scheme is that the method for calculating the local collision flux includes:

[0039] For the i-th control volume, the local collision flux F i for:

[0040] Fi =η i ·v imp ·w·LWC;

[0041] η i =N imp，i / N emp，i ;

[0042] Where, η i N represents the local collision efficiency of the i-th control volume; imp，i N represents the number of water droplets that collide with the i-th control volume; emp，i This represents the total number of water droplets emitted from upstream of the i-th control volume; v imp LWC represents the water droplet impact velocity; W represents the liquid water content; and W represents the wind speed, which affects the water droplet impact efficiency and icing morphology.

[0043] A further optimized solution is that the method for achieving the boundary shift of the icing interface includes:

[0044] Substituting the normal velocity of the icing interface into the level set equation, we get:

[0045] ;

[0046] The discrete level set equation obtained by the upwind difference scheme is:

[0047] ;

[0048] ;

[0049] ;

[0050] ;

[0051] ;

[0052] in, Represents the level set function The value at grid point (i+1,j); Represents the level set function The value at the current grid point (i,j); Indicates the grid spacing in the y-direction; Indicates the grid spacing in the x-direction; This indicates forward difference along the y-axis; This represents the backward difference along the y-axis. This represents the forward difference along the x-axis. This represents the backward difference along the x-axis. Indicates the time step; The gradient magnitude of the level set function ϕ is used to describe the rate of change in the interface normal direction; Indicates the density of the ice layer; This represents the local collision flux of the i-th control volume; This represents the level set function value at time n+1; The level set function value at time n, the level set function zero isosurface =0 is used to indicate the location of the icing interface.

[0053] A further optimization scheme is that the mesh adaptive strategy includes:

[0054] Mesh refactoring is triggered when any of the following occurs:

[0055] Scenario 1: The distance moved by the icing interface exceeds [a certain distance]. of ; Indicates the basic grid size;

[0056] Case 2: The rate of change of the gradient of the level set function exceeds a preset threshold;

[0057] Scenario 3: Upon arrival Each time step.

[0058] This solution also provides an LBM-based system for the evolution of icing shapes on complex cross-sections of transmission lines, used to implement the aforementioned LBM-based method for the evolution of icing shapes on complex cross-sections of transmission lines. The system includes:

[0059] The model building module is used to construct the Makkonen thermodynamic growth model to extrapolate the equivalent icing thickness: it decomposes the icing mass growth rate per unit length of transmission line into collision subprocess, adhesion subprocess and freezing subprocess, and constructs the efficiency coefficient calculation model for each subprocess.

[0060] The data acquisition module is used to obtain meteorological conditions in the area where the transmission line is located.

[0061] An evolution module is used to perform icing shape evolution in conjunction with the Makkonen thermodynamic growth model;

[0062] The evolution module includes:

[0063] The configuration module is used to configure the computational domain, transmission line geometry, and boundary conditions.

[0064] The first calculation module is used to calculate the velocity field and icing density around the transmission line based on LBM.

[0065] The second calculation module is used to track the trajectory of water droplets, discretize the surface of the transmission line into several control volumes, and calculate the local collision flux by counting the number of water droplet impacts in each control volume.

[0066] The third calculation module is used to calculate the freezing coefficient of the freezing subprocess by combining the meteorological conditions and the Makkonen thermodynamic growth model.

[0067] The push-up module is used to determine the normal velocity of the icing interface based on the icing density, the efficiency coefficient of the freezing subprocess, and the local collision flux. The normal velocity of the icing interface is substituted into the level set equation to describe the normal movement of the icing interface. The boundary push of the icing interface is realized in the discrete format of the level set equation, and the dynamic update of the icing interface is completed in combination with the mesh adaptive strategy.

[0068] This solution also provides a computer-readable medium storing a computer program that, when executed by a processor, can implement the LBM-based method for the evolution of icing shapes in complex cross-sections of transmission lines as described above.

[0069] Compared with the prior art, the present invention has the following beneficial effects:

[0070] 1. This invention provides a method, system, and medium for the evolution of icing shape in complex cross-sections of transmission lines based on LBM. Combining the physical mechanism of icing formation and the classic Makkonen thermodynamic growth model, and addressing the shortcomings of the traditional model's assumption of uniform icing distribution, the Lattice Boltzmann Method (LBM) is introduced to perform flow field calculations and boundary tracking to realize the evolution of icing shape. Based on LBM, the velocity distribution around the transmission line is calculated, and the transmission line surface is discretized into several control volumes to obtain the local collision flux of the control volumes. The level set method is used to describe the normal movement of the icing interface, and the boundary movement is realized by discretizing the level set equations through the windward difference scheme. Combined with the grid adaptive strategy, the dynamic update of the icing interface is completed, realizing the accurate evolution simulation of the shape evolution characteristics of non-uniform icing such as fan-shaped and crescent-shaped icing under complex wind fields.

[0071] 2. This invention provides a method, system, and medium for the evolution of icing shape in complex cross-sections of transmission lines based on the LBM model. The Makkonen thermodynamic growth model lays the core physical foundation for icing prediction, while the icing shape evolution method based on the lattice Boltzmann method compensates for the spatial distribution defects of traditional models. The two models support each other and optimize synergistically, forming an icing development trend prediction system. This system provides important theoretical support and technical means for early warning and precise prevention and control of icing disasters in power grids. This prediction system also provides a research direction for further improving the spatiotemporal resolution and accuracy of icing trend prediction by combining more complex meteorological and topographic field characteristics. Attached Figure Description

[0072] To more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly described below. It should be understood that the following drawings only show some embodiments of the present invention and should not be considered as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort. In the drawings:

[0073] Figure 1 A schematic diagram of the process for the evolution of icing shape in complex cross-sections of transmission lines based on LBM;

[0074] Figure 2 A schematic diagram illustrating the evolution of icing shapes;

[0075] Figure 3 This is a schematic diagram of the structure of the LBM-based transmission line complex cross-section icing shape evolution system. Detailed Implementation

[0076] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of this invention are only for explaining this invention and are not intended to limit this invention.

[0077] The traditional Makkonen model assumes that the conductor is circular and the icing grows uniformly, which cannot adapt to the shape evolution characteristics of non-uniform icing such as fan-shaped and crescent-shaped icing under complex wind fields. In order to overcome the limitations of the traditional Makkonen model in geometric modeling, the present invention provides the following embodiments to construct a numerical model that can adapt to the shape evolution of non-uniform icing under complex wind field conditions, so as to achieve accurate prediction of the icing development trend.

[0078] Example 1

[0079] This embodiment provides a method for the evolution of icing shapes in complex cross-sections of transmission lines based on LBM, such as... Figure 1 and Figure 2 As shown, the specific process includes:

[0080] Step 1: Construct the Makkonen thermodynamic growth model: Decompose the growth rate of icing mass per unit length of transmission line into collision subprocess, adhesion subprocess and freezing subprocess, and construct the efficiency coefficient calculation model for each subprocess.

[0081] In step one, the conditions for constructing the Makkonen thermodynamic growth model include:

[0082] The ambient temperature and the surface temperature of the transmission lines are both below freezing point, providing a low-temperature environment for water droplets to freeze.

[0083] Supercooled water droplets exist in the ambient air, with diameters ranging from 10 μm to 100 μm.

[0084] Supercooled water droplets overcome the influence of ambient airflow under the action of inertial force and impact the surface of the power transmission line.

[0085] In step one, the method for constructing the efficiency coefficient calculation model for each subprocess includes:

[0086] The efficiency coefficient of the collision subprocess is determined by the Stokes number of the droplet motion; specifically, due to the airflow, the small water droplets deflect with the streamlines, reducing the actual collision rate, thus changing the efficiency coefficient of the droplet motion from the Stokes number. Characterization:

[0087] ;

[0088] in, This indicates the density of the water droplet (kg / m³). Indicates the diameter of the water droplet (m); Indicates the incoming flow velocity (m / s); Indicates aerodynamic viscosity (Pa·s); Indicates the equivalent diameter (m) of the transmission line;

[0089] For cylindrical transmission lines, when the Stokes number At that time, the efficiency coefficient of the collision subprocess The approximate formula is:

[0090] ;

[0091] When Stokes number When the value is small, the efficiency coefficient of the collision subprocess is With Stokes number Increase ; where → indicates approaching.

[0092] The efficiency coefficient of the adhesion sub-process is determined by the state of the water film on the transmission line surface and the surface temperature of the transmission line; specifically, whether water droplets adhere after impacting the conductor depends on the state of the surface water film and temperature conditions.

[0093] When the surface temperature of the transmission line is below freezing (i.e., in the dry growth state), the efficiency coefficient of the adhesion subprocess is... The efficiency coefficient of the adhesion subprocess when the surface temperature of the transmission line is equal to the freezing point (i.e., in the wet growth state). ;

[0094] The efficiency coefficient of the freezing subprocess is determined by the surface temperature of the transmission line. When the surface temperature of the transmission line is below the freezing point, the efficiency coefficient of the freezing subprocess is 1. When the surface temperature of the transmission line is equal to the freezing point, the efficiency coefficient α3 of the freezing subprocess is determined by the heat balance equation:

[0095] Q f =Q c +Q e +Q w +Q r ;

[0096] ;

[0097] ;

[0098] Among them, Q f Indicates latent heat release; Q c Indicates convection cooling; Q e Indicates evaporative heat dissipation; Q w Indicates sensible heating; Q r Indicates radiative heat dissipation; t represents the icing development time; L f Indicates latent heat of freezing. Mw represents the mass of liquid water.

[0099] Specifically, the mass of water collected per unit length of transmission line per unit time is: ;in, represents the liquid water content (LWC); v represents the ambient wind speed.

[0100] When the surface temperature of the transmission line is below the freezing point (0°C) (i.e., in the dry growth state), all the collected water freezes immediately. The efficiency coefficient of this freezing subprocess is... The total mass growth rate is: ;

[0101] When the surface temperature of the transmission line equals the freezing point (0°C) (i.e., the wet growth state), only some water freezes, and the rest flows away along the conductor; the efficiency coefficient of the freezing subprocess at this time is... It is determined by the heat balance equation.

[0102] Specifically,

[0103] ;

[0104] ;

[0105] ;

[0106] ;

[0107] ;

[0108] ;

[0109] ;

[0110] in, The value represents the surface area per unit length of the transmission line (m² / m); D represents the equivalent diameter of the transmission line. Ts represents the surface saturated vapor pressure of the transmission line (Pa); Ts represents the surface temperature of the transmission line; Ta represents the ambient air temperature. Indicates the mass transfer coefficient; This indicates the specific heat capacity of air (J / (kg·K)). This represents the Lewis number (approximately 0.85 for air). This represents the convective heat transfer coefficient (W / (m²·K)). This represents the thermal conductivity of air (W / (m·K)). The Nusselt number is determined based on the Hilpert formula described above. v represents the Reynolds number, and vD represents the characteristic length; Indicates the kinematic viscosity of air (m² / s); This represents the Prandtl number (approximately 0.71 for air). Indicates ambient water vapor pressure (Pa); It is a Lewis number (approximately 0.85 for air). This is the specific heat capacity of water.

[0111] In icing calculations, radiative heat loss is usually a small percentage, so we can ignore radiative heat loss Qr. Based on the above equation, we get:

[0112] ;

[0113] Under wet growth conditions Substituting, we get:

[0114] ;

[0115] The constraints are: ;

[0116] in, express The saturated water vapor pressure at that time.

[0117] The process of estimating equivalent icing thickness includes:

[0118] Let the density of the ice be... (Hoarfrost: 200–600 kg / m³; Ice glaze: approximately 900 kg / m³); Define equivalent radial thickness The differential equation is:

[0119] ;

[0120] This equation is an ordinary differential equation (ODE), which is numerically integrated based on the fourth-order Runge-Kutta method:

[0121] Time step is , No. The icing thickness at each time step is ,but:

[0122] ; ;

[0123] Where k1 represents the first-order Runge-Kutta solution; k2 represents the second-order Runge-Kutta solution; k3 represents the third-order Runge-Kutta solution; k4 represents the fourth-order Runge-Kutta solution; R n+1 Indicates the first Ice thickness at each time step.

[0124] The traditional Makkonen model assumes a circular conductor and uniform icing growth, but under complex wind fields, icing often exhibits a fan-shaped or crescent-shaped distribution. To extrapolate the shape evolution, flow field calculations and boundary tracing need to be coupled.

[0125] Step 2: Obtain meteorological conditions in the area where the transmission line is located, and analyze the icing shape evolution using the Makkonen thermodynamic growth model:

[0126] S21, configure the computational domain, transmission line geometry definition, and boundary conditions;

[0127] Specifically, the configuration method of the computational domain includes: establishing a computational domain centered on the transmission line axis; discretizing the computational domain into a fine-grained structured mesh; taking the direction of the transmission line axis as the Z-axis; and taking the xy-plane cross section of the computational domain; the fine-grained structured mesh can be uniform or non-uniform.

[0128] The configuration method for the geometric definition of transmission lines includes: defining the cross-section of the transmission line as a circle, configuring the geometric center of the cross-section of the transmission line at the center of the computational domain, and representing the boundary of the transmission line based on the horizontal set function;

[0129] Convenient conditions include speed conditions, pressure conditions, and water droplet conditions at different boundary locations of the transmission line.

[0130] Specifically, the boundary locations of the transmission line include the inlet side, the outlet side, the upper and lower boundaries, and the conductor surface; in this embodiment, the velocity condition at the inlet side is a uniform inflow. , The pressure condition is zero gradient; the water droplet condition is uniform release of water droplets; the velocity condition at the outlet side is zero gradient; and the pressure condition is constant pressure. The water droplet condition is free flow; the pressure condition at the upper and lower boundaries is either symmetrical or slip boundary; the pressure condition is symmetrical; the water droplet condition is no water droplet entry; the velocity condition on the conductor surface is no slip. The pressure condition is zero gradient; the water droplet condition is that the water droplet is removed after impact.

[0131] S22, based on LBM calculations, calculates the velocity field and icing density around transmission lines; specifically,

[0132] The velocity field around the transmission line was obtained by solving the Navier-Stokes equations using the D2Q9 model. and ice density :

[0133] ;

[0134]

[0135] ;

[0136] in, Represents the particle distribution function; Represents relaxation time, in relation to kinematic viscosity. Related: , This represents the discrete velocity direction, where i represents the index of the i-th discrete velocity direction; Represents the speed of sound in a lattice; Represents the equilibrium distribution function; The position of the water droplet is represented by Lagrange multiplication table tracking; t represents the icing development time. This represents the weighting coefficient; in this embodiment... ; ; .

[0137] S23, track the water droplet trajectory, discretize the power transmission line surface into several control volumes, and calculate the local collision flux by counting the number of water droplet impacts in each control volume.

[0138] The method for tracking the trajectory of the water droplets in step S23 includes:

[0139] The equation of motion of the water droplet is:

[0140] ;

[0141] in, This represents the velocity vector of the water droplet (m / s). Represents the fluid velocity vector (m / s); This represents the acceleration due to gravity (m / s²). This represents the relaxation time of the water droplet (s). ; d represents the dynamic viscosity of air. p Indicates the diameter of the water droplet;

[0142] Based on the discretization solution obtained using the forward Euler method:

[0143] ;

[0144] in, This represents the velocity vector of the water droplet at the (n+1)th time step; This represents the velocity vector of the water droplet at the (n+1)th time step; This represents the fluid velocity vector at the (n+1)th time step;

[0145] At time step n+1, the droplet position is updated as follows: ;

[0146] In step S23, the method for calculating the local collision flux includes:

[0147] For the i-th control volume, the local collision flux F i for:

[0148] F i =η i ·v imp ·w·LWC;

[0149] η i =N imp，i / N emp，i ;

[0150] Where, η i N represents the local collision efficiency of the i-th control volume; imp，i N represents the number of water droplets that collide with the i-th control volume; emp，i This represents the total number of water droplets emitted from upstream of the i-th control volume; v imp LWC represents the water droplet impact velocity; W represents the liquid water content; and W represents the wind speed, which affects the water droplet impact efficiency and icing morphology.

[0151] S24, combining meteorological conditions and the Makkonen thermodynamic growth model, calculates the freezing coefficient of the freezing subprocess;

[0152] S25. The normal velocity of the icing interface is determined based on the icing density, the efficiency coefficient of the freezing subprocess, and the local collision flux. The normal velocity of the icing interface is substituted into the level set equation to describe the normal movement of the icing interface. The boundary push of the icing interface is realized by the discrete format of the level set equation, and the dynamic update of the icing interface is completed by combining the mesh adaptive strategy.

[0153] In step S25, the method for pushing the boundary of the icing interface includes:

[0154] Substituting the normal velocity of the icing interface into the level set equation, we get:

[0155] ;

[0156] The discrete level set equation obtained by the upwind difference scheme is:

[0157] ;

[0158] ;

[0159] ;

[0160] ;

[0161] ;

[0162] in, Represents the level set function The value at grid point (i+1,j); Represents the level set function The value at the current grid point (i,j); Indicates the grid spacing in the y-direction; Indicates the grid spacing in the x-direction; This indicates forward difference along the y-axis; This represents the backward difference along the y-axis. This represents the forward difference along the x-axis. This represents the backward difference along the x-axis. Indicates the time step; Represents the level set function The gradient magnitude is used to describe the rate of change in the interface normal direction; Indicates the density of the ice layer; This represents the local collision flux of the i-th control volume; This represents the level set function value at time n+1; The level set function value at time n, the level set function zero isosurface =0 is used to indicate the location of the icing interface.

[0163] In step S25, the mesh adaptive strategy includes:

[0164] Mesh refactoring is triggered when any of the following occurs:

[0165] Scenario 1: The distance moved by the icing interface exceeds [a certain distance]. of ; Indicates the basic grid size;

[0166] Case 2: The rate of change of the gradient of the level set function exceeds a preset threshold;

[0167] Scenario 3: Upon arrival Each time step.

[0168] Example 2

[0169] This embodiment provides a LBM-based system for the evolution of icing shapes on complex cross-sections of transmission lines, such as... Figure 3 As shown, the system used to implement the LBM-based method for the evolution of icing shapes on complex cross-sections of transmission lines as described in Example 1 includes:

[0170] The model building module is used to construct the Makkonen thermodynamic growth model: decompose the growth rate of icing mass per unit length of transmission line into collision subprocess, adhesion subprocess and freezing subprocess, and construct the efficiency coefficient calculation model for each subprocess.

[0171] The data acquisition module is used to obtain meteorological conditions in the area where the transmission line is located;

[0172] An evolution module is used to perform icing shape evolution in conjunction with the Makkonen thermodynamic growth model;

[0173] The evolution module includes:

[0174] The configuration module is used to configure the computational domain, transmission line geometry, and boundary conditions.

[0175] The first calculation module is used to calculate the velocity field and icing density around the transmission line based on LBM.

[0176] The second calculation module is used to track the trajectory of water droplets, discretize the surface of the transmission line into several control volumes, and calculate the local collision flux by counting the number of water droplet impacts in each control volume.

[0177] The third calculation module is used to calculate the freezing coefficient of the freezing subprocess by combining the meteorological conditions and the Makkonen thermodynamic growth model.

[0178] The push-up module is used to determine the normal velocity of the icing interface based on the icing density, the efficiency coefficient of the freezing subprocess, and the local collision flux. The normal velocity of the icing interface is substituted into the level set equation to describe the normal movement of the icing interface. The boundary push of the icing interface is realized in the discrete format of the level set equation, and the dynamic update of the icing interface is completed in combination with the mesh adaptive strategy.

[0179] Example 3

[0180] This embodiment provides a computer-readable medium storing a computer program. The computer program, when executed by a processor, can implement the LBM-based method for the evolution of icing shapes on complex cross-sections of transmission lines as described in Embodiment 1; specifically, it performs the following steps:

[0181] Step 1: Construct the Makkonen thermodynamic growth model: Decompose the growth rate of icing mass per unit length of transmission line into collision subprocess, adhesion subprocess and freezing subprocess, and construct the efficiency coefficient calculation model for each subprocess.

[0182] Step two: Obtain the meteorological conditions of the area where the transmission line is located, and use the Makkonen thermodynamic growth model to analyze the evolution of icing shape.

[0183] S21, configure the computational domain, transmission line geometry definition, and boundary conditions;

[0184] Specifically, a two-dimensional rectangular computational domain is established with the conductor axis as the center. The width of the computational domain is 20-30 times the diameter of the conductor, and the height of the computational domain is 15-25 times the diameter of the conductor, to ensure that the influence of the far-field boundary conditions on the flow field around the conductor is negligible.

[0185] Based on uniform or non-uniform structured meshes, local refinement is applied to the surface region of transmission lines to capture velocity gradients and water droplet impact characteristics within the boundary layer; the mesh resolution of the structured mesh is... Must meet ,in, This indicates the diameter of the power transmission line.

[0186] The direction of the transmission line axis is the z-axis, and the calculation domain is the xy plane section.

[0187] Based on level set function Initialization, satisfying:

[0188] ;

[0189] in, Point to the surface of the transmission line The shortest distance, the initial interface is the outer surface of the transmission line.

[0190] Based on interface distance function As the basis for encryption, the encrypted area is defined as follows:

[0191] ;

[0192] in, This indicates the encryption bandwidth, which is 3-5 times the background grid size.

[0193] For encrypted areas The internal mesh is subdivided level by level, with the mesh size halved at each level, resulting in a maximum number of mesh refinement levels. Regions far from the interface are kept with a coarse mesh to reduce computational overhead; meanwhile, the minimum mesh size is constrained to be... This ensures the geometric resolution of complex cross-sectional shapes (such as crescent and sector shapes).

[0194] S22, based on LBM calculation of velocity field and icing density around transmission lines;

[0195] S23, track the water droplet trajectory, discretize the power transmission line surface into several control volumes, and calculate the local collision flux by counting the number of water droplet impacts in each control volume.

[0196] S24, combining meteorological conditions and the Makkonen thermodynamic growth model, calculates the freezing coefficient of the freezing subprocess;

[0197] S25. The normal velocity of the icing interface is determined based on the icing density, the efficiency coefficient of the freezing subprocess, and the local collision flux. The normal velocity of the icing interface is substituted into the level set equation to describe the normal movement of the icing interface. The boundary push of the icing interface is realized by the discrete format of the level set equation, and the dynamic update of the icing interface is completed by combining the mesh adaptive strategy.

[0198] Mesh refactoring is triggered when any of the following occurs:

[0199] Scenario 1: The distance moved by the icing interface exceeds [a certain distance]. of ; Indicates the basic grid size;

[0200] Case 2: The rate of change of the gradient of the level set function exceeds a preset threshold;

[0201] Scenario 3: Upon arrival Each time step.

[0202] After mesh reconstruction, the physical quantities (velocity field) on the original mesh need to be... Level set function Ice density The data is mapped to a new grid, specifically based on volume-weighted interpolation to ensure the conservation of mass and momentum; based on high-precision interpolation (such as trilinear or WENO) to maintain the accuracy of interface position; and based on bilinear or bicubic interpolation to maintain the smoothness of the flow field.

[0203] Example 4

[0204] For Examples 1-3, in the absence of key inputs, a Long Short-Term Memory (LSTM) network model can be constructed, using historical weather and load sequences as inputs, to predict future ice thickness;

[0205] The input sequence is: ;

[0206] The update process of the Long Short-Term Memory network model is as follows:

[0207] ;

[0208] in, , , These represent the input gate, forget gate, and output gate, respectively. This represents the cell state at time t; This represents the cell state at time t-1; This represents the hidden state at time t; This represents the sigmoid activation function; This represents element-wise multiplication; Represents the hidden state h in the input gate t−1 The weight matrix; Represents the hidden state h in the forget gate t−1 The weight matrix; Indicates the hidden state h in the output gate t−1 The weight matrix; The hidden state h represents the candidate cell state. t−1 The weight matrix; This represents the bias term of the input gate; The bias term representing the forget gate; This represents the bias term of the output gate; Bias terms representing the state of candidate cells; This represents the candidate cell state at time t; This represents the weight matrix of the input xt in the forget gate; This represents the weight matrix of the input xt in the input gate; This represents the weight matrix of the input xt in the output gate; This represents the weight matrix of the input xt in the candidate cell state.

[0209] Output the predicted future icing thickness:

[0210] ;

[0211] Constructing a composite loss function Simultaneously, it fits the observed data and satisfies the physical equation constraints:

[0212] ;

[0213] in, This indicates the measured ice thickness; This indicates the model's predicted thickness; This represents the rate of change of thickness given by the Makkonen thermodynamic growth model; This represents the physical constraint weight coefficient.

[0214] The method provided in this embodiment can effectively suppress sensor noise, prevent pure data-driven models from producing non-physical extrapolation results, and improve the model's generalization ability and reliability.

[0215] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. 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 for the evolution of icing shape in complex cross-sections of transmission lines based on LBM, characterized in that, The method includes: A Makkonen thermodynamic growth model was constructed to extrapolate the equivalent icing thickness: the icing mass growth rate per unit length of transmission line was decomposed into collision subprocess, adhesion subprocess and freezing subprocess, and an efficiency coefficient calculation model for each subprocess was constructed. Meteorological conditions in the area where the transmission line is located are obtained, and the evolution of icing shape is analyzed using the Makkonen thermodynamic growth model. Configure the computational domain, transmission line geometry, and boundary conditions; LBM-based calculations of velocity field and icing density around transmission lines; By tracking the trajectory of water droplets, the surface of the transmission line is discretized into several control volumes, and the local collision flux is calculated by counting the number of water droplet impacts in each control volume. The freezing coefficient of the freezing subprocess was calculated by combining the meteorological conditions and the Makkonen thermodynamic growth model. The normal velocity of the icing interface is determined based on the icing density, the efficiency coefficient of the freezing subprocess, and the local collision flux. The normal velocity of the icing interface is substituted into the level set equation to describe the normal movement of the icing interface. The boundary push of the icing interface is realized by the discrete format of the level set equation, and the dynamic update of the icing interface is completed by combining the mesh adaptive strategy.

2. The method for the evolution of icing shape of complex cross-sections of transmission lines based on LBM according to claim 1, characterized in that, The conditions for constructing the Makkonen thermodynamic growth model include: Both the ambient air temperature and the surface temperature of the transmission lines were below freezing. The ambient air contains supercooled water droplets in a liquid state, the diameter of which is between 10 μm and 100 μm; The supercooled water droplets overcome the influence of ambient airflow under the action of inertial force and impact the surface of the transmission line.

3. The method for the evolution of icing shape of complex cross-sections of transmission lines based on LBM according to claim 2, characterized in that, The methods for constructing the efficiency coefficient calculation model for each subprocess include: The efficiency coefficient of the collision subprocess is determined by the Stokes number of the droplet motion; The efficiency coefficient of the adhesion process is determined by the state of the water film on the transmission line surface and the temperature of the transmission line surface; The efficiency coefficient of the freezing subprocess is determined by the surface temperature of the transmission line. When the surface temperature of the transmission line is below the freezing point, the efficiency coefficient of the freezing subprocess is 1. When the surface temperature of the transmission line is equal to the freezing point, the efficiency coefficient α3 of the freezing subprocess is determined by the heat balance equation: Q f =Q c +Q e +Q w +Q r ; ； ； Among them, Q f Indicates latent heat release; Q c Indicates convection cooling; Q e Indicates evaporative heat dissipation; Q w Indicates sensible heating; Q r Indicates radiative heat dissipation; t represents the icing development time; L f Indicates latent heat of freezing; M w This indicates the mass of liquid water.

4. The method for the evolution of icing shape of complex cross-sections of transmission lines based on LBM according to claim 1, characterized in that, The configuration method of the computational domain includes: establishing a computational domain centered on the transmission line axis; discretizing the computational domain into a dense structured mesh; taking the direction of the transmission line axis as the Z-axis; and taking the xy plane section of the computational domain; the dense structured mesh can be uniform or non-uniform. The configuration method for the geometric definition of the transmission line includes: defining the cross-section of the transmission line as a circle, configuring the geometric center of the cross-section of the transmission line at the center of the computational domain, and representing the boundary of the transmission line based on the level set function; The convenient conditions include speed conditions, pressure conditions, and water droplet conditions at different boundary locations of the transmission line.

5. The method for the evolution of icing shape of complex cross-sections of transmission lines based on LBM according to claim 1, characterized in that, The methods for calculating the velocity field and icing density include: The velocity field around the transmission line was obtained by solving the Navier-Stokes equations using the D2Q9 model. and ice density : ； ； ； in, Represents the particle distribution function; Indicates relaxation time, relative to kinematic viscosity Related: △t represents the time step; This represents the discrete velocity direction, where i represents the index of the i-th discrete velocity direction; Represents the speed of sound in a lattice; Represents the equilibrium distribution function; The position of the water droplet is represented by Lagrange multiplication table tracking; t represents the icing development time. This represents the weighting coefficient.

6. The method for the evolution of icing shape of complex cross-sections of transmission lines based on LBM according to claim 1, characterized in that, The method for calculating the local collision flux includes: For the i-th control volume, the local collision flux F i for: F i =η i v imp ·w·LUCK; or i =N imp，i / N emp，i ; Where, η i N represents the local collision efficiency of the i-th control volume; imp，i N represents the number of water droplets that collide with the i-th control volume; emp，i This represents the total number of water droplets emitted from upstream of the i-th control volume; v imp LWC represents the water droplet impact velocity; W represents the liquid water content; and W represents the wind speed, which affects the water droplet impact efficiency and icing morphology.

7. The method for the evolution of icing shape of complex cross-sections of transmission lines based on LBM according to claim 1, characterized in that, The method for achieving the boundary shift of the icing interface includes: Substituting the normal velocity of the icing interface into the level set equation, we get: ； The discrete level set equation obtained by the upwind difference scheme is: ； ； ； ； ； in, Level set function The value at grid point (i+1,j); Level set function The value at the current grid point (i,j); Indicates the grid spacing in the y-direction; Indicates the grid spacing in the x-direction; This indicates forward difference along the y-axis; This represents the backward difference along the y-axis. This represents the forward difference along the x-axis. This represents the backward difference along the x-axis. Indicates the time step; Level set function The gradient magnitude is used to describe the rate of change in the interface normal direction; Indicates the density of the ice layer; This represents the local collision flux of the i-th control volume; This represents the level set function value at time n+1; The level set function value at time n, the level set function zero isosurface =0 is used to indicate the location of the icing interface.

8. The method for the evolution of icing shape of complex cross-sections of transmission lines based on LBM according to claim 4, characterized in that, The mesh adaptive strategy includes: Mesh refactoring is triggered when any of the following occurs: Scenario 1: The distance moved by the icing interface exceeds [a certain distance]. of ; Indicates the basic grid size; Case 2: The rate of change of the gradient of the level set function exceeds a preset threshold; Scenario 3: Upon arrival Each time step.

9. A LBM-based system for the evolution of icing shapes on complex cross-sections of transmission lines, characterized in that, The system is used to implement the LBM-based method for the evolution of icing shapes in complex cross-sections of transmission lines according to any one of claims 1-8, the system comprising: The model building module is used to construct the Makkonen thermodynamic growth model to extrapolate the equivalent icing thickness: it decomposes the icing mass growth rate per unit length of transmission line into collision subprocess, adhesion subprocess and freezing subprocess, and constructs the efficiency coefficient calculation model for each subprocess. The data acquisition module is used to obtain meteorological conditions in the area where the transmission line is located. An evolution module is used to perform icing shape evolution in conjunction with the Makkonen thermodynamic growth model; The evolution module includes: The configuration module is used to configure the computational domain, transmission line geometry, and boundary conditions. The first calculation module is used to calculate the velocity field and icing density around the transmission line based on LBM. The second calculation module is used to track the trajectory of water droplets, discretize the surface of the transmission line into several control volumes, and calculate the local collision flux by counting the number of water droplet impacts in each control volume. The third calculation module is used to calculate the freezing coefficient of the freezing subprocess by combining the meteorological conditions and the Makkonen thermodynamic growth model. The push-up module is used to determine the normal velocity of the icing interface based on the icing density, the efficiency coefficient of the freezing subprocess, and the local collision flux. The normal velocity of the icing interface is substituted into the level set equation to describe the normal movement of the icing interface. The boundary push of the icing interface is realized in the discrete format of the level set equation, and the dynamic update of the icing interface is completed in combination with the mesh adaptive strategy.

10. A computer-readable medium having a computer program stored thereon, characterized in that, The computer program, when executed by a processor, can implement the LBM-based method for the evolution of icing shapes in complex cross-sections of transmission lines as described in any one of claims 1-8.

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