An electron beam cold hearth furnace smelting inclusion migration distribution analysis method, storage medium and equipment

Abstract

This invention discloses a method, storage medium, and device for analyzing the migration and distribution of inclusions in electron beam cold hearth furnace melting, belonging to the technical field of metal smelting simulation. It acquires actual operating data of the electron beam cold hearth furnace and constructs a cold hearth unit model based on numerical simulation. Then, it sequentially sets the electron beam energy input, metal solidification and melting, and the heat transfer settings of the cold hearth unit based on a convection heat transfer model. Steady-state simulation is performed on the cold hearth unit. When the physical field reaches a steady state, a discrete random trajectory model is used to simulate the movement of inclusions in the melt. The motion trajectory of inclusions under different operating conditions is simulated, tracking the migration process of inclusions to obtain the migration distribution of inclusions. This invention accurately simulates the migration behavior of different types of inclusions within the cold hearth unit through numerical simulation, ensuring that as few inclusions as possible flow into the crystallizer, improving the overall efficiency of the melting process and the quality of the final product.

Description

Technical Field

[0001] This invention belongs to the technical field of metal smelting simulation, specifically relating to a method, storage medium, and equipment for analyzing the migration and distribution of inclusions in electron beam cold hearth furnace smelting. Background Technology

[0002] In metal smelting, especially in electron beam cold hearth furnace melting, the presence of inclusions significantly affects smelting quality, reducing the purity and performance of the final product. Common inclusions include metal oxides, sulfides, and bubbles. These inclusions not only affect the fluidity and melting efficiency of the molten pool but may also adversely impact the mechanical properties of the product. With the large-scale development of industrial production, the use of recycled materials has become an important economic measure. However, recycled materials typically contain a significant number of inclusions, posing a greater challenge to the smelting process.

[0003] In existing technologies, for example, Chinese patent CN115758928A discloses a numerical simulation method for inclusion distribution during electron beam cold hearth melting. Based on ANSYS finite element numerical simulation software, it injects inclusions of varying sizes and densities into the model and obtains the inclusion distribution in the ingot by analyzing the inclusion distribution profile and calculating the number of inclusions escaping from the outlet. Specifically, this method focuses on analyzing the inclusion distribution in the crystallizer unit, using numerical simulation technology to analyze and predict the inclusion distribution in the crystallizer. However, the crystallizer unit and the cold hearth unit perform completely different functions in the melting process. The cold hearth unit is responsible for inclusion removal and is a crucial stage in the melting process. If inclusions are not effectively removed in the cold hearth unit, they will continue to flow into the crystallizer unit. At this point, even if the distribution of inclusions in the crystallizer is understood, effective removal is no longer possible. Therefore, although this technology can analyze the inclusion distribution in the crystallizer, it does not solve the problem of inclusions not being removed in the cold hearth unit. Summary of the Invention

[0004] The purpose of this invention is to provide a method, storage medium, and device for analyzing the migration and distribution of inclusions in electron beam cold hearth furnace melting, aiming to solve the above-mentioned problems, analyze the migration behavior of inclusions inside the cold hearth unit, and ensure that inclusions flow into the crystallizer as little as possible, thereby improving the overall efficiency of the melting process and the quality of the final product.

[0005] This invention is mainly achieved through the following technical solutions:

[0006] A method for analyzing the migration and distribution of inclusions in electron beam cold hearth furnace melting includes the following steps:

[0007] Step S1: Obtain actual operating data of the electron beam cold hearth furnace and construct a cold hearth unit model based on numerical simulation; then, set the parameters of the cold hearth unit model.

[0008] A1: Set the electron beam energy input, where the heat flux control equation for the electron beam energy is:

[0009] ;

[0010] in: Let t be the instantaneous heat flux of the electron beam at position (x,y) on the surface of the molten pool at time t;

[0011] The absorption rate of the electron beam;

[0012] The current of the electron beam;

[0013] The accelerating voltage of the electron beam;

[0014] σ is the radius of the electron beam spot;

[0015] A is the area of ​​the region affected by the electron beam;

[0016] ω is the scanning frequency of the electron beam;

[0017] (x, y) are the position coordinates of the molten pool surface;

[0018] t represents time;

[0019] A2: Set up the metal solidification and melting process, and the control equation is:

[0020] ;

[0021] in, The liquid phase fraction at the (n+1)th iteration;

[0022] The liquid phase fraction at the nth iteration;

[0023] Specific heat capacity;

[0024] The initial temperature;

[0025] T represents temperature;

[0026] This is the final temperature;

[0027] Given the initial enthalpy;

[0028] Porosity is the porosity of the porous medium.

[0029] This represents the volume of the liquid portion at the current temperature.

[0030] The total volume at the current temperature;

[0031] α This is the temperature dependence coefficient;

[0032] This refers to the enthalpy value during the phase transition process.

[0033] β This is the heat flux gain factor;

[0034] This represents the current local temperature.

[0035] A3: Heat transfer settings for the cold bed unit based on a convection heat transfer model;

[0036] Step S2: Based on the cold bed unit model, perform steady-state simulation on the cold bed unit to bring the melt inside the cold bed unit to a steady state, and then obtain the various physical fields inside the cold bed unit;

[0037] Step S3: When the field of the physical field reaches a steady state, based on numerical simulation, a discrete random trajectory model is used to simulate the motion of inclusions in the melt; the motion trajectory of inclusions under different operating conditions is simulated, the migration process of inclusions is tracked, and the migration distribution of inclusions is obtained.

[0038] To better realize the present invention, further, in step S3, when simulating the movement of inclusions in the melt, the role of inclusions in the cooling bed unit is analyzed based on the interactions between inclusions, between inclusions and the melt, and between inclusions and the semi-solid phase.

[0039] (1) The interaction between inclusions and melt is as follows:

[0040] ;

[0041] in: The acceleration of the inclusions;

[0042] v The velocity of the inclusions;

[0043] m The mass of the inclusions;

[0044] k Thermal conductivity represents a substance's ability to transfer heat.

[0045] The temperature gradient represents the spatial rate of temperature change.

[0046] μ The dynamic viscosity of a melt represents the resistance to melt flow.

[0047] r The radius of the inclusion;

[0048] To represent the effect of Reynolds number on flow state;

[0049] The turbulence influence factor represents the intensity of the influence of turbulence on inclusions;

[0050] is the turbulence intensity, and represents the standard deviation of the turbulence velocity;

[0051] The turbulence effect factor represents the intensity of the effect of turbulence on inclusions;

[0052] ρ The density of the melt;

[0053] The effect of the melt on the acceleration of inclusions;

[0054] d is the differential operator;

[0055] t represents time;

[0056] V The flow rate of the melt;

[0057] The pressure gradient represents the rate of change of pressure in space.

[0058] (2) The interaction between inclusions is as follows:

[0059] ;

[0060] Where: N is the inclusion number concentration;

[0061] Maximum inclusion concentration represents the maximum concentration of inclusions that can be achieved in the system;

[0062] σ ( v ) is the function relating the collision cross section of the inclusion to its velocity;

[0063] P ( v ) is the velocity distribution function, representing the probability distribution of the velocity of the inclusions;

[0064] Δ HThis represents the enthalpy change corresponding to the temperature change;

[0065] Boltzmann constant, which describes the relationship between energy and temperature in a physical system;

[0066] The effective velocity of the inclusions;

[0067] This is the maximum velocity that the inclusion can reach in the system;

[0068] D The diffusion coefficient is denoted as .

[0069] The gradient operator represents the differentiation operation on the change of the spatial variable;

[0070] (3) The interaction between inclusions and the semi-solid phase;

[0071] ;

[0072] Where: u is the liquid phase velocity;

[0073] It represents the volume fraction of the solid phase.

[0074] The normal growth rate at the solid-liquid interface;

[0075] The baseline capture rate;

[0076] and These are the constants that adjust the volume fraction of the solid phase and the critical velocity for solid-liquid interface movement, respectively.

[0077] This is a region indicator function.

[0078] To better implement the present invention, step S1 further includes the following steps:

[0079] Step S11: Collect actual operating data and obtain the attribute parameters and operating parameters of the cooling bed unit:

[0080] Step S12: Perform 3D modeling of the cooling bed unit to obtain the cooling bed unit model; based on numerical simulation, divide the cooling bed unit model into functional areas and perform mesh generation.

[0081] To better realize the present invention, further, in step S11, according to the actual working conditions of the electron beam cold hearth furnace, the following data are collected: the specifications and dimensions of the cold hearth unit, the cooling water flow rate data arranged on the cold hearth unit, the current and voltage data, the electron beam energy input data, the action path of the electron beam in the cold hearth unit, the melt flow rate entering the cold hearth unit, the melt overflow flow rate at the cold hearth outlet, the vacuum degree data, and the composition and concentration data of the residual gas.

[0082] To better realize the present invention, the melt flow rate entering the cooling bed unit is further calculated based on the feed rate;

[0083] ;

[0084] in: This refers to the melt flow rate;

[0085] and These represent the mass flow rates of the left and right feeds, respectively.

[0086] and These are the effective melting coefficients for left and right feeding, respectively;

[0087] ρ is the density of the liquid phase.

[0088] To better realize the present invention, in step S12, numerical simulation is performed using any one of ProCAST, FLOW-3D Cast, COMSOL Multiphysics, or OpenFOAM.

[0089] To better realize the present invention, further, in step A3, the heat exchange per unit time is:

[0090] ;

[0091] in: The heat exchange between the cooling bed and the cooling water per unit time;

[0092] h The convective heat transfer coefficient between the cooling bed and the cooling water;

[0093] A cool This refers to the heat exchange area where the cooling bed contacts the cooling water.

[0094] The surface temperature of the cooling bed;

[0095] T water This refers to the cooling water temperature.

[0096] To better realize the present invention, it is further applied to electron beam cold hearth furnace melting of titanium alloys, zirconium alloys, niobium alloys, tantalum alloys, molybdenum alloys, tungsten alloys, and nickel-based and cobalt-based high-temperature alloys.

[0097] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described method for analyzing the migration and distribution of inclusions in electron beam cold hearth furnace melting.

[0098] An electronic device includes a memory and a processor; the memory stores a computer program; the processor is used to execute the computer program in the memory to implement the above-described method for analyzing the migration and distribution of inclusions in electron beam cold hearth furnace melting.

[0099] The beneficial effects of this invention are as follows:

[0100] (1) This invention accurately simulates the migration behavior of different types of inclusions inside the cooling bed unit through numerical simulation, and can extract the removal rate of inclusions with different densities, sizes and compositions to optimize the cooling bed process parameters. It also controls and screens inclusions at the raw material stage to ensure that as few inclusions as possible flow into the crystallizer, thereby improving the overall efficiency of the smelting process and the quality of the final product.

[0101] (2) Based on the traditional enthalpy-porous medium solidification / melting model, this invention introduces the coupling relationship between liquid phase fraction, porosity, and enthalpy, making the model more suitable for simulating the melting process in a cold bed unit. This improvement can more accurately describe the heat transfer characteristics of the phase transition region during the solidification and melting process of metals, and improves the analytical accuracy of the model for complex heat exchange and phase transition behaviors. This invention can realistically reflect the three material states of solid, semi-solid, and liquid existing simultaneously in a cold bed unit, and the simulation results are highly consistent with the actual melting process, significantly improving the reliability and computational efficiency of numerical simulation.

[0102] (3) This invention can effectively improve the efficiency of inclusion removal in the cooling bed unit by accurately simulating the migration, collision, aggregation, and capture processes of inclusions in the melt. Specifically, by introducing corresponding control equations and combining the interactions between inclusions and the melt, the behavior of inclusions in the semi-solid region, this invention can achieve accurate prediction of inclusion behavior and optimize the material distribution and temperature field in the cooling bed unit. This process not only helps to improve the purity of the metal material, but also effectively controls the morphology of the solidified shell and prevents damage to the cooling bed unit by the high-temperature melt, thereby improving the efficiency and quality of the entire smelting process. This invention ensures high accuracy of the simulation through the precise setting of the jet source module and control module of ANSYS, providing strong theoretical support and technical guarantee for the intelligent removal of inclusions and process optimization in industrial production.

[0103] (4) Regarding the setting of electron beam energy input, compared with the traditional numerical model that uses constant heat flux or simplified uniform surface heat source, the present invention sets the electron beam parameters... , , By incorporating the same heat flux control equation along with the spot radius σ and scanning frequency ω, the organic coupling of the total electron beam power, spatial energy distribution, and temporal scanning characteristics is achieved.

[0104] 1) Through Accurately reflects the effective power that the electron beam can actually absorb on the surface of the cold bed;

[0105] 2) Through the Gaussian distribution term A detailed description of the energy decrease relationship between the center and edge of the electron beam;

[0106] 3) By correlating the scanning frequency with the heat flux change through cos(ωt), the heating process at any point on the cooling bed has a clear periodicity and pulsation characteristics;

[0107] The aforementioned parameters work synergistically in the heat flux equation, enabling the numerical simulation to simultaneously consider total energy, spatial focusing characteristics, and scanning motion effects. Simulation results show that the temperature field distribution obtained by this invention is in better agreement with actual measurements, and can more accurately predict the temperature gradient and cooling rate in the cooling bed region, thus providing a reliable basis for subsequent microstructure regulation and defect control.

[0108] (3) Regarding the control of metal solidification and melting, traditional enthalpy-porous medium models typically calculate enthalpy based solely on temperature changes, neglecting the influence of solid-liquid ratio, porosity changes, and local heat flux decay on the phase transition process. This leads to significant deviations in the calculation of the solid-liquid interface advancement position, solidification rate, and temperature gradient. This invention introduces the liquid phase volume fraction into the enthalpy change expression. Porosity and local heat flow correction term This approach allows phase transformation calculations to be constrained simultaneously by the solid-liquid structure, local thermal resistance, and material temperature field, enabling the liquid phase fraction to be dynamically updated at each time step and accurately reflecting the heat transfer behavior in the solid-liquid mixing zone. Through simulation and experimental comparisons, the model of this invention significantly improves upon traditional methods in predicting solidification location, fitting liquid phase fraction curves, and calculating cooling rates, thereby significantly enhancing the accuracy and reliability of simulating the solidification / melting process of metals in a cold bed. Attached Figure Description

[0109] Figure 1 A schematic diagram of the cooling bed unit of an electron beam cold hearth melting furnace for both practical and modeling purposes;

[0110] Figure 2Temperature variation curves of thermophysical properties of TC4 titanium alloy;

[0111] Figure 3 This is a coupled diagram of the temperature field, density field, phase field, and flow field of the electron beam cold hearth furnace melting cold hearth unit;

[0112] Figure 4 This describes the migration behavior of single-particle inclusions within the cooling bed unit.

[0113] Figure 5 A schematic diagram showing the migration trajectories of inclusions of different densities and sizes in a cooling bed unit;

[0114] Figure 6 This is a flowchart of the method for tracking the migration of inclusions in electron beam cold hearth furnace melting according to the present invention. Detailed Implementation

[0115] Example 1:

[0116] A method for analyzing the migration and distribution of inclusions in electron beam cold hearth furnace melting, such as Figure 6 As shown, it includes the following steps:

[0117] 1.1 Obtain actual operating data of the electron beam cold hearth furnace;

[0118] Based on the actual operating conditions of the electron beam cold hearth furnace in production, data are collected on the specifications and dimensions of the cold hearth unit, the flow rate of the cooling water arranged on the cold hearth unit, current and voltage data, electron beam energy input data, the action path of the electron beam in the cold hearth unit, the melt flow rate entering the cold hearth unit, the melt overflow flow rate at the cold hearth outlet, vacuum level data, and the composition and concentration data of residual gases. Preferably, the melt flow rate entering the cold hearth unit is calculated based on the feed rate. The melt flow rate is calculated by using the feed rates at the feed ports on both sides of the electron beam cold hearth furnace.

[0119] ;

[0120] in This is the melt volumetric flow rate. and The left and right feed mass flow rates are respectively. and These are the effective melting coefficients for left and right feeds, respectively. ρ is the density of the liquid phase.

[0121] 1.2 Modeling of the cooling bed unit;

[0122] Based on the geometric dimensions of the cooling bed unit obtained in section 1.1, the cooling bed unit was modeled using 3D modeling software; the functional areas of the cooling bed unit were then divided using ANSYS numerical simulation software.

[0123] 1) Electron gun action area: This area is where the high-energy electron beam output by the electron gun acts, providing a continuous heat source to heat the melt in the cold bed unit.

[0124] 2) Heat exchange zone of the cooling bed unit: The temperature of the cooling bed unit is controlled by the heat exchange between the cooling bed and the cooling water to prevent high-temperature melt from damaging the cooling bed unit and to adjust the heat exchange to affect the morphology of the solidified shell.

[0125] 3) The melt flow, solidification and melting zone, which is the main area of ​​the cooling bed unit;

[0126] 4) Melt and inclusion input port: The raw material is converted into a melt under the action of the electron beam. The melt enters the cooling bed unit through the input port, and the inclusions in the raw material enter along with the melt.

[0127] 5) Melt outlet area: The melt in the cooling bed unit enters the crystallizer through the outlet;

[0128] 6) Vacuum Smelting Region: The functional areas of the cooling bed unit are subjected to vacuum treatment, using vacuum level data from the smelting process. Different mesh sizes are used for different functional areas to ensure the accuracy and economy of the numerical simulation. Meshing can be performed in the ANSYS software meshing module or in software with meshing capabilities, such as Hypermesh.

[0129] Obtaining the thermal properties of materials and the specifications, types, and sizes of inclusions: Thermal properties of materials are obtained through software calculations and experiments; data on the specifications, types, and sizes of raw material inclusions are established through the company's raw material inclusion classification archives or through testing. Preferably, the thermal properties of materials include, but are not limited to, thermal conductivity, specific heat capacity, density, coefficient of thermal expansion, latent heat of phase change, thermal diffusivity, Young's modulus, Poisson's ratio, and Newtonian viscosity. Specifically, methods for obtaining the thermal properties of materials include software calculation methods and experimental methods. Software calculation methods include JmatPro, ANSYS, COMSOL, ProCAST, FactSage, and Thermo-Calc; experimental methods include: laser flash method (used to determine the thermal conductivity of materials), differential scanning calorimetry (DSC, used to determine the latent heat of phase change), dynamic mechanical analysis (DMA, used to measure Young's modulus and Poisson's ratio), dilatometer method (used to determine the coefficient of thermal expansion), and calorimeter (used to determine specific heat capacity), etc.

[0130] Enter the above parameters in the ANSYS material definition module. For parameters whose corresponding attribute items are not provided in the interface, they can be supplemented by defining them through UDFs (User-Defined Functions). To ensure that the data can be correctly integrated into the simulation system, the UDF program must be written based on the C language interface provided by ANSYS. During the writing process, the ANSYS specifications for input and output formats should be strictly followed, and functional verification should be performed before importing to ensure that the program can run correctly and seamlessly integrate with the numerical simulation system.

[0131] 1.3 Based on ANSYS numerical simulation software, the parameters of the cooling bed unit model are set;

[0132] A1: Electron Beam Energy Input Module Settings; After acceleration and focusing, the electron beam from the electron gun concentrates its energy onto the surface of the molten pool, generating localized high temperatures and providing continuous heat to the melt. In the ANSYS numerical simulation software, the electron beam energy is used to heat the molten pool surface through the heat module. The heat flux control equation for the electron beam energy is input into this module, which describes the heat distribution of the electron beam at different locations on the molten pool surface. Details are as follows:

[0133] (1) Determination of the total input power of the electron beam;

[0134] The theoretical power of the electron beam emitted by the electron gun at the workpiece surface after acceleration is:

[0135] ;

[0136] in, For electron beam current, The accelerating voltage for the electron beam is given. The absorption rate of the electron beam at the workpiece surface is considered. The actual effective power absorbed by the molten pool is:

[0137] ;

[0138] (2) Spatial energy distribution hypothesis (Gaussian distribution);

[0139] In electron beam welding and selective area melting, the energy distribution on the workpiece surface after electron beam focusing can usually be approximated as a two-dimensional Gaussian distribution. Assuming the origin of the molten pool surface is the center of electron beam action, and its coordinates are (x, y), the steady-state heat flux distribution per unit area can be written as:

[0140] ;

[0141] Where σ represents the effective radius of the electron beam spot, and C is a normalization coefficient to be determined.

[0142] Will Integrating over the electron beam's active region A, the result should equal the total power P:

[0143] ;

[0144] Substituting into the above formula, we get:

[0145] ;

[0146] To facilitate engineering implementation, this invention equates the integral of a two-dimensional Gaussian distribution over region A to the coefficient πσ. 2 A, and thus the constant C can be approximated as:

[0147] ;

[0148] Therefore, the spatial heat flux distribution of the electron beam on the surface of the molten pool can be written as:

[0149] ;

[0150] Will Substituting into the above equation, we get:

[0151] ;

[0152] (3) The introduction of time-periodic scanning effect;

[0153] In the operating conditions of this invention, the electron beam periodically scans the surface of the cooling bed or molten pool at a frequency ω. For any point (x, y) on the surface of the molten pool, this point is not continuously at the center of the electron beam, but rather receives a large instantaneous heat flux when the electron beam scans to the vicinity of this point, and the heat flux decreases after the scan leaves, thus the heat flux changes periodically with time.

[0154] To describe this periodic heating behavior, this invention uses a cosine function to modulate the heat flux, introducing a time term:

[0155] ;

[0156] Right now:

[0157] ;

[0158] in Let be the instantaneous heat flux of the electron beam at position (x, y) on the surface of the molten pool. The absorption rate of the electron beam. The current of the electron beam, σ is the accelerating voltage of the electron beam, σ is the radius of the electron beam spot (related to the scanning mode), and A is the area of ​​the region affected by the electron beam. (x, y) are the position coordinates of the molten pool surface; the heat flux density varies with its position. ω is the scanning frequency of the electron beam, and t is time, taking into account the periodicity of the scan. During setup, ensure that the above parameters are consistent with the operating parameters obtained in section 1.1.

[0159] A2: Metal Solidification and Melting Module Settings; Based on the traditional enthalpy-porous medium model, this module incorporates the relationship between liquid phase fraction, porosity, and enthalpy to make it more suitable for metal solidification and melting processes in a cold bed unit. By calculating a new liquid phase fraction in each iteration, accurate simulation of the metal solidification and melting process is ensured within each time step. This is configured in the solidification / melting module of ANSYS, where the governing equations are input. The specific details are as follows:

[0160] (1) Establish the expression for the liquid phase fraction from the enthalpy equation;

[0161] The enthalpy of a metal during solidification / melting can be expressed as:

[0162] ;

[0163] in For sensible heat, This is a latent heat term.

[0164] From this, we can obtain the differential change in enthalpy:

[0165] ;

[0166] In discrete calculations, the enthalpy change corresponding to a temperature change is:

[0167] .

[0168] (2) Introducing the permeation and volume fraction effects based on the porous media model;

[0169] In the enthalpy–porosity model, solid metals are treated as porous media with extremely low permeability. The flow resistance term is expressed as the liquid volume fraction. .

[0170] Porosity Describes the actual flowable volume of the porous region, as a percentage:

[0171] ;

[0172] Therefore, the effective enthalpy change that actually participates in heat absorption / excitation should be written as:

[0173] ;

[0174] (3) Construct the iterative relationship of liquid phase fraction;

[0175] Depend on:

[0176] ;

[0177] To correct the heat flow term and compensate for the enthalpy distribution deviation caused by the thermal resistance of the porous medium.

[0178] After sorting, we get:

[0179] ;

[0180] Therefore, the iterative update of the liquid phase fraction in the discrete time step is:

[0181] ;

[0182] in, and These represent the liquid phase fractions at the (n+1)th and nth iterations, respectively. This is the change in enthalpy;

[0183] For specific heat capacity, The initial temperature, This is the final temperature. Given the initial enthalpy, Porosity is the porosity of the porous medium. and These represent the volume of the liquid portion and the total volume at the current temperature, respectively. α This is the temperature dependence coefficient. Δ is the enthalpy during the phase transition process, and β is the heat flux gain factor, used to describe the distribution and change of heat flux in the porous medium. This represents the current local temperature.

[0184] A3: Cooling Bed Unit Heat Exchange Module Settings; In the heat exchange area of ​​the cooling bed unit, heat is transferred between the cooling water and the cooling bed surface through convection, thereby removing heat from the cooling bed surface and reducing the temperature of the cooling bed unit. The heat exchange between the cooling bed and the cooling water effectively controls the temperature of the cooling bed unit, preventing damage to the cooling bed from the high-temperature melt, and precisely controlling the morphology of the solidified shell by adjusting the heat exchange. In the simulation, the heat exchange process between the cooling bed and the cooling water is described by the convection heat exchange control equation. The control equation is entered into the heat exchange module in ANSYS, as follows:

[0185] To achieve effective temperature control of the cooling bed unit, this invention employs a convective heat transfer model to describe the heat exchange process between the cooling bed surface and the cooling water. Convective heat transfer is based on the principle of energy conservation, and its basic form is that the heat transfer is equal to the linear superposition of the convective heat transfer coefficient and the temperature difference over the heat transfer area. Its derivation is derived from Newton's law of cooling:

[0186] ;

[0187] Integrating this over the cooling bed-cooling water contact region, we can obtain the expression for the heat transfer per unit time:

[0188] ;

[0189] Where Q is the heat exchange between the cooling bed and the cooling water per unit time, h is the convective heat transfer coefficient between the cooling bed and the cooling water, and A is the heat transfer area in contact with the cooling bed and the cooling water. This refers to the surface temperature of the cooling bed. This refers to the cooling water temperature.

[0190] 1.4 Inclusion migration motion control settings;

[0191] In ANSYS, the movement of inclusions in the melt is simulated using the "Discrete Random Trajectory Model" in the jet source settings. First, the input location for inclusions is selected in the "Melte and Inclusion Input Port" function area. The characteristics of the inclusions are set based on the information collected in 1.2, and the relevant parameters are input into the jet source module.

[0192] This invention details the motion of inclusions in a melt, including their interactions with the melt and the inclusions themselves, as well as their behavior in the semi-solid region. By introducing corresponding governing equations, the model can accurately simulate the migration, collision, coalescence, and capture processes of inclusions in a cooling bed unit. In ANSYS, the governing equations are set using the jet source module and the corresponding control module.

[0193] Specifically, the role of inclusions in the cooling bed unit is analyzed based on the interactions between inclusions, between inclusions and the melt, and between inclusions and the semi-solid phase (intermediate between the melt and the solid phase). The details are as follows:

[0194] 1) Interaction between inclusions and melt: To accurately describe the interaction between inclusions and melt, a unified equation of motion for inclusions was optimized, taking into account key factors such as thermophoretic force and viscous drag. This equation significantly improves the accuracy of inclusion motion prediction in the melt.

[0195] ;

[0196] in The acceleration of the inclusion is m; the mass of the inclusion is m; the thermophoretic force is m. The effect of temperature gradient on inclusions; viscous resistance ( ) represents the viscous resistance to melt flow, including turbulent effects; virtual mass force ( The effect of the melt on the acceleration of inclusions; Saffman lift force ( The vertical force caused by the velocity gradient; the pressure gradient force ( The effect of pressure gradient in the melt on inclusions. Turbulent forces ( () represents the disturbance force of turbulence on inclusions.

[0197] 2) Inclusion-inclusion interactions (collisions / coalescing / agglomeration / dispersion): Considering the complexity of collisions and interactions between inclusions in the melt, and taking into account factors such as viscous effects, turbulent flow, particle shape, and surface properties, a particle diffusion model, long-term interactions, and nonlinear effects are introduced to further improve the accuracy of the governing equations.

[0198] ;

[0199] in This indicates the net effect of inclusion fragmentation producing more small particles or exogenous generation / injection, and is modulated by concentration crowding and velocity statistics. This indicates the cohesion loss of inclusions. To "smooth out" local concentration inhomogeneities in spatial mixing / turbulent diffusion, boundary conditions directly affect the shape of the solution.

[0200] 3) The interaction of inclusions with the semi-solid region (this region is between liquid and solid; inclusions falling into this region will be captured):

[0201] ;

[0202] Where N is the inclusion number concentration, u is the liquid phase velocity, and D is the diffusion coefficient. This represents the volume fraction of the solid phase. The normal growth rate at the solid-liquid interface. As the baseline capture rate, and To adjust the constant of solid volume fraction and the critical velocity of solid-liquid interface migration, This is a region indicator function, which is 1 in the semi-solid region and 0 elsewhere.

[0203] 1.5 Steady-state simulation of the cooling bed unit, and acquisition of inclusion migration trajectory;

[0204] Based on the settings in sections 1.1 to 1.3, a steady-state simulation of the cooling bed unit is first performed. This process ensures that the melt inside the cooling bed unit reaches a steady state, thereby obtaining various physical fields within the cooling bed unit, including the temperature field, density field, phase state field, and flow field. When these fields reach a steady state in the simulation, the inclusion migration settings in section 1.4 are activated. At this stage, by simulating the movement trajectory of inclusions under different operating conditions, and combining the temperature, flow velocity, and initial position of inclusions in the cooling bed unit, the migration process of inclusions is accurately tracked, and the inclusion migration trajectory is obtained.

[0205] This invention can accurately reflect the three material states that exist simultaneously in the cooling bed unit during the smelting process: 1) Solid phase: At the beginning of the smelting process, the melt enters the cooling bed unit, first comes into contact with the cooling bed wall, and after heat exchange with the cooling water, it begins to solidify, forming a solidified shell, which is located at the bottom of the cooling bed unit; 2) Liquid phase: Located above the cooling bed unit, the melt enters the cooling bed and maintains the liquid phase state under the continuous action of the high-energy electron beam; 3) Semi-solid phase: Between the solid phase and the liquid phase.

[0206] Preferably, the numerical simulation includes, but is not limited to, ANSYS software, and may also include numerical simulation tools such as ProCAST, FLOW-3D Cast, COMSOL Multiphysics, and OpenFOAM.

[0207] Example 2:

[0208] A method for analyzing the migration and distribution of inclusions in electron beam cold hearth furnace melting includes the following steps:

[0209] 1. Based on the actual operating conditions of the electron beam cooled hearth furnace in production at the enterprise, relevant cooling hearth unit data and operating parameters were collected to provide a basis for subsequent numerical simulations. Specifically, the collected data included:

[0210] (1) Cooling bed unit specifications and dimensions: Obtain the geometric dimensions of the cooling bed unit through on-site measurements and technical documents provided by the company, including key parameters such as the length, width, and height of the cooling bed unit, the thickness of the cooling bed, and the positions of the inlet and outlet. Figure 1 As shown in (a), the internal dimensions of the actual electron beam cold hearth melting furnace cold hearth unit are 1400 mm × 405 mm × 80 mm, and the inlet and outlet are complex structures.

[0211] (2) Cooling water flow rate data: The cooling water flow rate was monitored in real time by installing a flow meter, and the instantaneous flow rate and velocity of the cooling water in the cooling bed unit were recorded. The monitoring results showed that the cooling water flow rate fluctuated during the smelting process, ranging from 230 to 960 L / min; when the smelting process tended to stabilize, the cooling water flow rate stabilized at about 640 L / min, and the cooling water temperature remained at 20℃.

[0212] (3) Current and voltage data: The current and voltage data of the electron beam are collected through the electrical control system of the electron beam cold hearth furnace. According to the actual working conditions, the current is 57~65 A and the voltage is maintained at a stable 30 kV. The current range of each electron beam gun is as follows: Gun 1~4# current 8~10 A; Gun 5# current 4±0.5 A; Gun 6~7# current 6.6~7.0 A;

[0213] (4) Vacuum degree data: The vacuum degree of the cooling bed unit is monitored in real time using a vacuum degree sensor, and the refining vacuum degree is controlled at (5~8)×10. -3 Torr.

[0214] (5) Residual gas composition and concentration data: The composition and concentration of residual gas in the cooling bed unit were detected by a gas analyzer. The test results showed that the gas composition mainly included oxygen (O2) and nitrogen (N2), with an oxygen concentration of 0.03%.

[0215] 2. Based on the acquired geometric dimensions and operating condition data, such as Figure 1 As shown in (b), a three-dimensional model of the cooling bed unit of the electron beam cold hearth melting furnace is performed. In this embodiment, the geometric model of the cooling bed unit is built using SolidWorks, and the model is imported into the numerical simulation software ANSYS Workbench for further processing.

[0216] After dividing the functional areas of the cooling bed unit, differentiated meshing was performed for each area, with different mesh densities set according to the complexity of the area and the required computational accuracy. The electron gun action area has a cell size of 2–5 mm and approximately 27,483 cells. Due to the complex internal cooling channels, the cooling bed heat exchange area uses an unstructured tetrahedral mesh with a cell size of approximately 3–4 mm and approximately 41,276 cells. The melt flow and solidification area is the core computational region, locally densified to 2–3 mm with approximately 62,384 cells. The melt inlet and outlet areas, due to their relatively regular geometry, use coarser meshes with approximately 8,237 and 10,135 cells respectively. The vacuum smelting area has a relatively small temperature field variation and uses a sparse mesh with approximately 4,592 cells.

[0217] The material selected is TC4 titanium alloy. Its thermophysical parameters were obtained through a combination of numerical calculations and experimental testing, mainly including key thermophysical properties such as density, thermal conductivity, enthalpy, elastic modulus, Poisson's ratio, and Newtonian viscosity. Figure 2As shown, (a) represents the temperature variation curves of density, thermal conductivity, and enthalpy of TC4 titanium alloy, and (b) represents the temperature variation curves of Young's modulus, Poisson's ratio, and Newtonian viscosity of TC4 titanium alloy. For inclusions present in the melt, the specifications, types, and size distribution characteristics of the inclusions are determined based on the raw material inclusion classification archives established by the enterprise and actual test data. Based on their physical characteristics, the inclusions are classified and managed according to two key indicators: density and size. The particle diameter range of the inclusions is 30~300μm, and the density range is 3500~5000 kg / m³.

[0218] 3. The functional modules of the cooling bed unit are configured using ANSYS numerical simulation software. First, the electron beam energy input module is configured to set the energy input of the electron beam. This module describes the heat distribution of the electron beam at different locations on the surface of the molten pool; the relevant parameters are obtained from step 1. Then, the metal solidification and melting module and the cooling bed unit heat exchange module are configured.

[0219] After completing the above module settings, set the time step to 1e. -3 The simulation process was optimized to ensure accuracy and stability. Convergence criteria were set as the residuals of the temperature field, flow field, and liquid phase fraction. The convergence criteria for the temperature field were 10^-6, for the flow field 10^-4, and for the liquid phase fraction 10^-5, ensuring numerical stability and approximation of the real-world conditions. Initial conditions were set with the melt temperature of the cooling bed unit at the required melting point, the cooling bed surface temperature at 20°C, and the cooling water flow rate at 20 L / min. Boundary conditions included the cooling bed surface temperature, cooling water flow state, and electron beam energy input. A steady-state solver was selected, employing the SIMPLE pressure basis method, with a maximum iteration count of 200 to ensure convergence and stability. Figure 3 As shown, (a), (b), (c), and (d) are coupled diagrams of the temperature field, density field, phase field, and flow field of the electron beam cold hearth furnace melting unit, respectively. These settings ensure simulation accuracy and stability, and obtain results such as the temperature field, density field, phase state field, and flow field of the cold hearth unit.

[0220] 4. When the temperature field, density field, phase state field, and flow field of the cooling bed unit reach a steady state, the inclusion setting stage begins. In ANSYS, the movement of inclusions in the melt is simulated using the "Discrete Random Trajectory Model" in the jet source module.

[0221] This case study employed two types of settings during the simulation:

[0222] First, we studied the trajectory of single-particle inclusions. We selected two inclusions with different densities, 3500 kg / m³ and 5000 kg / m³, and simulated their migration behavior in the melt.

[0223] Second, a multi-particle inclusion simulation was used. 100 inclusion particles were added at the inlet and divided into three groups. The inclusion properties of each group were 5000 kg / m³-300 μm in diameter, 4500 kg / m³-300 μm in diameter, and 4500 kg / m³-30 μm in diameter, respectively. This simulated the interaction, collision, aggregation, and capture process of multiple inclusions in the melt.

[0224] 5. For example Figure 4 As shown in (a), low-density (3500 kg / m³) inclusions are driven upwards by the flow field and migrate to the outlet, where they remain for approximately 36.2 s; Figure 4 As shown in (b), the high-density (5000 kg / m³) inclusions sink under the influence of gravity and are deposited in the mushy area after about 11.4 s. The density difference leads to significant differentiation in migration behavior.

[0225] like Figure 5 As shown, (a) is the migration trajectory of an inclusion with a density of 4500 kg / m³ and a diameter of 30 μm in the cooling bed unit; (b) is the migration trajectory of an inclusion with a density of 4500 kg / m³ and a diameter of 300 μm in the cooling bed unit; and (c) is the migration trajectory of an inclusion with a density of 5000 kg / m³ and a diameter of 300 μm in the cooling bed unit. In the simulation of multi-particle inclusions in the cooling bed molten pool, the inclusion with a density of 5000 kg / m³ and a diameter of 300 μm was rapidly captured near the inlet and achieved the highest removal rate (98.2%).

[0226] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Any simple modifications or equivalent changes made to the above embodiments based on the technical essence of the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for analyzing the migration and distribution of inclusions in electron beam cold hearth furnace melting, characterized in that, Includes the following steps: Step S1: Obtain actual operating data of the electron beam cold hearth furnace and construct a cold hearth unit model based on numerical simulation; then, set the parameters of the cold hearth unit model. A1: Set the electron beam energy input, where the heat flux control equation for the electron beam energy is: ； in: Let t be the instantaneous heat flux of the electron beam at position (x,y) on the surface of the molten pool at time t; The absorption rate of the electron beam; The current of the electron beam; The accelerating voltage of the electron beam; σ is the radius of the electron beam spot; A is the area of ​​the region affected by the electron beam; ω is the scanning frequency of the electron beam; (x, y) are the position coordinates of the molten pool surface; t represents time; A2: Set up the metal solidification and melting process, and the control equation is: ； in, The liquid phase fraction at the (n+1)th iteration; The liquid phase fraction at the nth iteration; Specific heat capacity; The initial temperature; T represents temperature; The final temperature; Given the initial enthalpy; Porosity is the porosity of the porous medium. The volume of the liquid portion at the current temperature The total volume at the current temperature; α This is the temperature dependence coefficient; This refers to the enthalpy value during the phase transition process. β This is the heat flux gain factor; This represents the current local temperature. A3: Heat transfer settings for the cold bed unit based on a convection heat transfer model; Step S2: Based on the cold bed unit model, perform steady-state simulation on the cold bed unit to bring the melt inside the cold bed unit to a steady state, and then obtain the various physical fields inside the cold bed unit; Step S3: When the field of the physical field reaches a steady state, based on numerical simulation, a discrete random trajectory model is used to simulate the motion of inclusions in the melt; the motion trajectory of inclusions under different operating conditions is simulated, the migration process of inclusions is tracked, and the migration distribution of inclusions is obtained.

2. The method for analyzing the migration and distribution of inclusions in electron beam cold hearth furnace melting according to claim 1, characterized in that, In step S3, when simulating the movement of inclusions in the melt, the role of inclusions in the cooling bed unit is analyzed based on the interactions between inclusions, between inclusions and the melt, and between inclusions and the semi-solid phase. (1) The interaction between inclusions and melt is as follows: ； in: The acceleration of the inclusions; v The velocity of the inclusions; m The mass of the inclusions; k Thermal conductivity; For temperature gradient; μ The dynamic viscosity of the melt; r The radius of the inclusion; To represent the effect of Reynolds number on flow state; Turbulence influencing factors; Turbulence intensity; It is the turbulence effect factor; ρ The density of the melt; The effect of the melt on the acceleration of inclusions; d is the differential operator; t represents time; V The flow rate of the melt; For pressure gradient; (2) The interaction between inclusions is as follows: ； Where: N is the inclusion number concentration; Maximum inclusion concentration represents the maximum concentration of inclusions that can be achieved in the system; σ ( v ) is the function relating the collision cross section of the inclusion to its velocity; P ( v ) is the velocity distribution function, representing the probability distribution of the velocity of the inclusions; Δ H This represents the enthalpy change corresponding to the temperature change; Boltzmann constant, which describes the relationship between energy and temperature in a physical system; The effective velocity of the inclusions; This is the maximum velocity that the inclusion can reach in the system; D The diffusion coefficient is denoted as . For gradient operators; (3) The interaction between inclusions and the semi-solid phase; ； Where: u is the liquid phase velocity; It represents the volume fraction of the solid phase. The normal growth rate at the solid-liquid interface; The baseline capture rate; and These are the constants that adjust the volume fraction of the solid phase and the critical velocity for solid-liquid interface movement, respectively. This is a region indicator function.

3. The method for analyzing the migration and distribution of inclusions in electron beam cold hearth furnace melting according to claim 1, characterized in that, Step S1 includes the following steps: Step S11: Collect actual operating data and obtain the attribute parameters and operating parameters of the cooling bed unit: Step S12: Perform 3D modeling of the cooling bed unit to obtain the cooling bed unit model; based on numerical simulation, divide the cooling bed unit model into functional areas and perform mesh generation.

4. The method for analyzing the migration and distribution of inclusions in electron beam cold hearth furnace melting according to claim 3, characterized in that, In step S11, based on the actual operating conditions of the electron beam cold hearth furnace, the following data are collected: the specifications and dimensions of the cold hearth unit, the cooling water flow rate data arranged on the cold hearth unit, the current and voltage data, the electron beam energy input data, the action path of the electron beam in the cold hearth unit, the melt flow rate entering the cold hearth unit, the melt overflow flow rate at the cold hearth outlet, the vacuum degree data, and the composition and concentration data of the residual gas.

5. The method for analyzing the migration and distribution of inclusions in electron beam cold hearth furnace melting according to claim 4, characterized in that, The melt flow rate entering the cooling bed unit is calculated based on the feed rate; ； in: This refers to the melt flow rate; and These represent the mass flow rates of the left and right feeds, respectively. and These are the effective melting coefficients for left and right feeds, respectively; ρ is the density of the liquid phase.

6. The method for analyzing the migration and distribution of inclusions in electron beam cold hearth furnace melting according to claim 3, characterized in that, In step S12, numerical simulation is performed using any one of ProCAST, FLOW-3D Cast, COMSOL Multiphysics, or OpenFOAM.

7. The method for analyzing the migration and distribution of inclusions in electron beam cold hearth furnace melting according to claim 1, characterized in that, In step A3, the heat exchange per unit time is: ； in: The heat exchange between the cooling bed and the cooling water per unit time; h The convective heat transfer coefficient between the cooling bed and the cooling water; A cool This refers to the heat exchange area where the cooling bed contacts the cooling water. The surface temperature of the cooling bed; T water This refers to the cooling water temperature.

8. The method for analyzing the migration and distribution of inclusions in electron beam cold hearth furnace melting according to claim 1, characterized in that, Electron beam cold hearth furnace melting is applied to titanium alloys, zirconium alloys, niobium alloys, tantalum alloys, molybdenum alloys, tungsten alloys, as well as nickel-based and cobalt-based high-temperature alloys.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the migration and distribution analysis method for inclusions in electron beam cold hearth furnace smelting as described in any one of claims 1-8.

10. An electronic device, characterized in that, It includes a memory and a processor; the memory stores a computer program; the processor is used to execute the computer program in the memory to implement the method for analyzing the migration and distribution of inclusions in electron beam cold hearth furnace smelting according to any one of claims 1-8.

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