A multi-scale simulation method for vacuum arc remelted ingots

Abstract

The application discloses a kind of multi-scale simulation methods of vacuum self-consumption electric arc smelting process ingot, it is related to metal smelting technical field, including: based on the actual working condition parameters and material thermal physical parameters of vacuum self-consumption electric arc smelting, the three-dimensional geometric model of smelting area is established and function area is divided;Multi-physics field coupling numerical model is constructed in macroscopic simulation software, and simulation calculation result is obtained;Simulation result is input to mesoscopic simulation software through standardized data interface, as the initial condition and boundary condition of mesoscopic scale simulation, based on phase field model and solute diffusion equation, the grain growth morphology, solute distribution and microstructure evolution process are simulated;Crystal growth rate, solidification rate and solute distribution result are fed back to multi-physics field coupling numerical model, and iterative calculation is carried out, to realize the closed loop coupling of macroscopic and mesoscopic simulation.The application realizes the accurate control of ingot microstructure and performance.

Description

Technical Field

[0001] This invention relates to the field of metal smelting technology, and in particular to a multi-scale simulation method for ingot casting in a vacuum consumable arc smelting process. Background Technology

[0002] Vacuum arc remelting (VAR) technology is a crucial process for preparing high-performance titanium alloys, high-temperature alloys, and mold steels, among other key structural materials. The melting process involves multi-physical field coupling behaviors, including arc discharge, metal droplet transition, molten pool flow, and solidification phase transformation. The microstructure, segregation characteristics, and defect formation mechanisms within the ingot are all jointly determined by these coupled processes. However, because the VAR melting process is significantly influenced by equipment conditions, material properties, and the dynamic behavior of the arc, its internal physical processes are difficult to observe directly through experimental means. Industrial production often relies on empirical adjustments of process parameters, resulting in high uncontrollability of the melting process and making quantitative prediction of the ingot's microstructure and properties difficult.

[0003] Existing simulation studies of the VAR process mostly focus on calculating macroscopic temperature fields, molten pool morphology, or single physical fields. While these studies can obtain basic information such as heat flux distribution and molten pool depth, they cannot accurately characterize the regional differences in key mechanisms during the smelting process, such as electrode melting, droplet transition, electromagnetic stirring, Marangoni convection, and solidification interface migration. For example, in actual smelting, the electrode end melting zone, the free surface arc-bearing zone, the molten pool natural convection zone, the paste-like solidification zone, and the crystallizer cooling zone have completely different dominant physical mechanisms. However, traditional models often treat the molten pool as a single continuum, ignoring regional functional differences, making it difficult to realistically reproduce the entire VAR process behavior.

[0004] On the other hand, most existing models remain at the macroscopic scale and cannot explain the transformation mechanism of solidification microstructure from columnar to equiaxed crystals, the formation law of interdendritic segregation, and the microscopic solute redistribution effect from the perspective of microstructure evolution. Although mesoscopic-scale simulations (such as phase-field models) can describe grain growth and dendrite morphology, their inputs usually rely on idealized temperature gradients and solidification rates, failing to effectively couple with the macroscopic temperature and flow fields of actual melting. Therefore, macroscopic simulation results cannot directly drive mesoscopic microstructure evolution, resulting in a significant gap between simulation results and actual microstructure.

[0005] Furthermore, VAR melting involves significant differences in the scales of metal droplets, molten pools, and grain growth. Existing technologies lack a unified multi-scale coupling framework and cannot simultaneously describe the entire chain of physical behavior from electrode melting to the final solidification structure of the ingot. In practical applications, due to the lack of simulation methods that can realize the mapping relationship between "equipment operating conditions—molten pool behavior—solidification structure," engineers find it difficult to directly predict the grain size, dendrite spacing, segregation degree, and shrinkage cavity distribution inside the ingot based on input process parameters. It also cannot be used to guide the optimization of melting parameters or the rapid development of new material melting processes.

[0006] Based on the above situation, there is an urgent need for a multi-scale simulation method that can combine real VAR working parameters, macroscopic multiphysics field solutions, mesoscopic grain growth models, and microstructure evolution mechanisms to achieve data transfer and bidirectional coupling between the macroscopic and mesoscopic levels. This would accurately describe the dynamic behavior of the molten pool, the evolution law of the solidification front, and the microstructure formation mechanism of the ingot, providing a scientific basis for process control and solving problems such as model fragmentation, insufficient prediction accuracy, and inability to effectively correlate with actual production parameters in existing technologies. Summary of the Invention

[0007] This invention proposes a multi-scale simulation method for ingots in the vacuum consumable arc melting process, in order to solve the technical problems in the prior art that can only simulate the flow and solidification behavior of the molten pool at the macro scale, cannot accurately predict the grain nucleation and growth process, and is difficult to establish an accurate mapping relationship between the process parameters in the melting process and the microstructure and properties of the ingot.

[0008] To achieve the above objectives, the present invention provides a multi-scale simulation method for ingot casting during the vacuum consumable arc melting process, comprising:

[0009] Based on the actual working parameters and material thermophysical parameters of vacuum self-consuming arc melting, a three-dimensional geometric model of the melting and casting area is established and functional areas are divided.

[0010] Based on the three-dimensional geometric model of the casting area and the divided functional areas, a multi-physics coupled numerical model is constructed in macroscopic simulation software to simulate and calculate the temperature field of the molten pool, the position of the solidification front, the cooling curve and the local temperature gradient.

[0011] The simulation results of the macroscopic simulation software are input into the mesoscopic simulation software through a standardized data interface as the initial and boundary conditions for the mesoscopic scale simulation. Based on the phase field model and solute diffusion equation, the grain growth morphology, solute distribution and microstructure evolution process are simulated.

[0012] The crystal growth rate, solidification rate, and solute distribution results obtained from the mesoscopic-scale simulation are fed back into the multiphysics coupled numerical model to correct the heat source term, latent heat of phase transition, and / or solute diffusion coefficient in the macroscopic model, and iterative calculations are performed to achieve closed-loop coupling between macroscopic and mesoscopic simulations.

[0013] Preferably, the actual operating parameters include current, voltage, smelting rate, cooling water flow rate and vacuum degree that vary with time; the material thermal properties parameters include the density, thermal conductivity, specific heat capacity, thermal conductivity, viscosity, surface tension and latent heat of phase change of the material to be smelted.

[0014] Preferably, the functional area division includes:

[0015] The arc action area is used to equate the arc heat input to a surface heat source acting on the free surface of the molten pool. The heat flux density within the arc action area is radially non-uniformly distributed along the free surface of the molten pool.

[0016] The heat exchange area includes the convective heat exchange area between the outer layer of the crystallizer and the cooling water, and the radiative heat exchange area between the surface of the molten pool and the vacuum environment.

[0017] The melt flow and solidification region is used to describe the melt flow and solidification process by coupling the Navier-Stokes equations, the energy equations, and the latent heat of phase change.

[0018] The vacuum smelting range is used to define the vacuum environment within the computational domain.

[0019] Preferably, the surface heat source input power of the arc action area is determined based on the working voltage and working current during the vacuum self-consuming arc melting process; the heat flux density is described using a decay function related to the radial distance from the arc center axis.

[0020] Preferably, the standardized data interface is used to export the temperature field, solidification front position, cooling curve and local temperature gradient data output by the macroscopic simulation software in a standardized format, and convert them into initial conditions and boundary conditions that the mesoscopic simulation software can recognize.

[0021] Preferably, the phase-field model uses the Allen-Cahn equation and free energy density function to describe the solid-liquid interface evolution, wherein the crystal growth rate is related to the local undercooling and solute concentration.

[0022] Preferably, the solute diffusion equation is based on Fick's law and coupled with the melt flow velocity field to simulate the diffusion and redistribution of the solute during the solidification process.

[0023] Preferably, the macroscopic simulation software is ProCAST; the mesoscopic simulation software is ComsolMultiphysics.

[0024] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of a multi-scale simulation method for ingot casting in a vacuum consumable arc melting process.

[0025] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of a multi-scale simulation method for ingot casting in a vacuum consumable arc melting process.

[0026] Compared with the prior art, the present invention has the following advantages and technical effects:

[0027] The multi-scale simulation method for ingots in the vacuum consumable arc melting process provided by this invention can achieve seamless coupling of macroscopic and mesoscopic simulations and make accurate predictions based on actual working condition data. By constructing a macroscopic multiphysics model based on working condition data, key parameters such as the molten pool temperature field, solidification front position, and cooling rate are extracted and used as inputs to the mesoscopic phase field model, thereby accurately simulating the entire process of electrode melting, droplet transition, molten pool flow, solidification interface migration, and grain structure evolution. Through the feedback mechanism of multiphysics coupling and mesoscopic simulation, this method can not only visualize and predict the grain morphology, solute distribution, and potential defect formation mechanism of the ingot, but also optimize the melting process parameters based on the simulation results, achieving precise control of the ingot's microstructure and properties. This technical solution can significantly improve ingot quality, reduce quality problems caused by process parameter mismatch during production, and provide a reliable optimization basis for actual production. Attached Figure Description

[0028] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0029] Figure 1 This is a schematic diagram of the vacuum self-consuming arc melting process parameters (as of time) according to an embodiment of the present invention;

[0030] Figure 2 This is a schematic diagram of the material thermophysical parameters (Young's modulus, Poisson's ratio, and Newtonian viscosity) in an embodiment of the present invention.

[0031] Figure 3 This is a schematic diagram of the material thermophysical parameters (density, thermal conductivity, and enthalpy) in an embodiment of the present invention;

[0032] Figure 4 This is a schematic diagram of the macroscopic simulation computational domain according to an embodiment of the present invention;

[0033] Figure 5 This is a schematic diagram of the macroscopic simulation of the ingot temperature field and solidification in an embodiment of the present invention;

[0034] Figure 6 This is a schematic diagram of the solidification structure distribution in vacuum consumable melting according to an embodiment of the present invention;

[0035] Figure 7 This is a schematic diagram of the mesoscopic simulated dendrite growth distribution in an embodiment of the present invention. Detailed Implementation

[0036] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0037] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0038] This embodiment proposes a multi-scale simulation method for ingot casting during the vacuum consumable arc melting process, including:

[0039] Based on the actual working parameters and material thermophysical parameters of vacuum self-consuming arc melting, a three-dimensional geometric model of the melting and casting area is established and functional areas are divided.

[0040] Based on the three-dimensional geometric model of the casting area and the divided functional areas, a multi-physics coupled numerical model is constructed in macroscopic simulation software to simulate and calculate the temperature field of the molten pool, the position of the solidification front, the cooling curve and the local temperature gradient.

[0041] The simulation results of the macroscopic simulation software are input into the mesoscopic simulation software through a standardized data interface as the initial and boundary conditions for the mesoscopic scale simulation. Based on the phase field model and solute diffusion equation, the grain growth morphology, solute distribution and microstructure evolution process are simulated.

[0042] The crystal growth rate, solidification rate, and solute distribution results obtained from the mesoscopic-scale simulation are fed back into the multiphysics coupled numerical model to correct the heat source term, latent heat of phase transition, and / or solute diffusion coefficient in the macroscopic model, and iterative calculations are performed to achieve closed-loop coupling between macroscopic and mesoscopic simulations.

[0043] Specifically, this embodiment constructs a macroscopic multiphysics model based on actual working condition data, extracts key data such as the molten pool temperature field, solidification front position, and cooling rate, and uses these as inputs for the mesoscopic phase field model and microstructure simulation, ensuring seamless coupling between the macroscopic and mesoscopic models. This method can achieve accurate simulation of the entire process, including electrode melting, droplet transition, molten pool flow, solidification interface migration, and grain structure evolution. Furthermore, it allows for visualized prediction of the grain morphology, solute distribution, segregation characteristics, and potential defect formation mechanisms of the ingot, thus providing a scientific and quantitative basis for optimizing the smelting process and improving ingot quality.

[0044] Furthermore, the actual operating parameters include current, voltage, smelting rate, cooling water flow rate, and vacuum degree that vary with time; the material thermal properties parameters include the density, thermal conductivity, specific heat capacity, thermal conductivity, viscosity, surface tension, and latent heat of phase change of the material to be smelted.

[0045] Specifically, based on the operating data of vacuum consumable arc furnaces in actual production enterprises, a numerical model of the macroscopic physical field of ingot casting is established, and multiphysics coupling calculations are performed on ProCAST software. The process includes:

[0046] Operating Parameter Acquisition: Based on the actual operating conditions of the vacuum self-consuming arc melting equipment, key process parameters of the melting process are collected, including data such as the size of the vacuum self-consuming arc melting furnace casting unit, current and voltage, cooling water flow rate, smelting rate, and vacuum degree.

[0047] Determination of material thermophysical parameters: Combining material composition and melting temperature range, using thermophysical database, ProCAST's built-in calculation module, and experimental results, parameters such as density, thermal conductivity, specific heat capacity, viscosity, surface tension, solute diffusion coefficient, and latent heat of phase change of the material to be melted are obtained.

[0048] Furthermore, based on the obtained structural parameters of the vacuum consumable arc furnace, a geometric model of the casting area was established in 3D modeling software. The established model represents the internal space of the crystallizer, and is cylindrical in shape. The specific dimensions can be adjusted accordingly based on different specifications of ingots.

[0049] After the geometric model is output in igs format and imported into the ProCAST numerical simulation software, the mesh generation of the geometric model is completed in the mesh generation module of the ProCAST software.

[0050] Furthermore, the functional area division includes:

[0051] The arc action area is used to equate the arc heat input to a surface heat source acting on the free surface of the molten pool. The heat flux density within the arc action area is radially non-uniformly distributed along the free surface of the molten pool.

[0052] The heat exchange area includes the convective heat exchange area between the outer layer of the crystallizer and the cooling water, and the radiative heat exchange area between the surface of the molten pool and the vacuum environment.

[0053] The melt flow and solidification region is used to describe the melt flow and solidification process by coupling the Navier-Stokes equations, the energy equations, and the latent heat of phase change.

[0054] The vacuum smelting range is used to define the vacuum environment within the computational domain. This range includes the arc action zone, the heat exchange zone, and the melt flow and solidification zone.

[0055] Specifically, the arc action region: Located at the top of the three-dimensional geometric model, the arc action region corresponds to the space between the self-consuming arc electrode end face and the free liquid surface of the molten pool, as well as the local molten pool region below it. It is used to describe the heat input behavior of the arc discharge on the molten pool during vacuum self-consuming arc melting. In macroscopic numerical simulations, the arc action is equivalent to a surface heat source acting on the free liquid surface of the molten pool, and its input power is determined by the working voltage and working current during the vacuum self-consuming arc melting process.

[0056] Arc input heat power Calculate using the following formula:

[0057] ;

[0058] In the formula, This indicates the working voltage during the vacuum consumable arc melting process; This represents the working current during the vacuum consumable arc melting process; This represents the arc thermal efficiency coefficient, used to characterize the efficiency of converting electrical energy into molten pool heat energy.

[0059] The heat flux density within the arc region exhibits a radially non-uniform distribution along the free surface of the molten pool, and its distribution relationship is determined by the following formula:

[0060] ;

[0061] In the formula, This indicates the radial distance from the center axis of the electric arc. Heat flux density per unit area at that location; It represents the radial distance from any position on the free surface of the molten pool to the central axis of the electric arc; Indicates the radius of the electric arc, used to characterize the range of the electric arc heat flow on the surface of the molten pool; This represents the attenuation function of the arc heat flow along the radial direction.

[0062] In the ProCAST numerical simulation software, the arc effect area is set as follows:

[0063] In the ProCAST software, go to the heat source / heat flux boundary condition setting module, select the surface heat source function, and input the calculated arc input heat power. Input current in boundary condition settings. and voltage The value, and set the thermal efficiency coefficient. ;

[0064] In ProCAST, use the radial heat flux density function as input, selecting the boundary heat source distribution option. Input the functional form of the heat flux density distribution and specify the arc radius. and the location of the heat source.

[0065] The heat transfer region of the computational domain mainly includes two parts: (1) the heat transfer generated by the contact between the outer layer of the crystallizer and the high-temperature melt, and (2) the radiative heat transfer between the surface of the molten pool and the vacuum environment.

[0066] (1) Heat transfer between the outer layer of the crystallizer and the high-temperature melt: The high-temperature melt in the molten pool and the outer wall of the crystallizer are transferred through convective heat transfer between the crystallizer wall and the cooling water.

[0067] The heat transfer is described using a combined model of heat conduction and convection, and taking into account the temperature changes of the cooling water, the following convection heat transfer formula is adopted:

[0068] ;

[0069] In the formula, This refers to the heat flow between the crystallizer and the cooling water. The convective heat transfer coefficient of the cooling water; The surface area of ​​the melt in contact with the crystallizer wall; The thermal diffusivity of the cooling water; The thickness of the crystallizer wall; The temperature of the melt; This refers to the temperature of the cooling water.

[0070] In ProCAST, follow these steps:

[0071] In the heat source / heat flux boundary condition setting module, select the "thermal convection" boundary condition. Enter the convective heat transfer coefficient of the cooling water. Cooling water temperature And set the thermal diffusivity of the cooling water. and the thickness of the crystallizer wall .

[0072] (2) Radiative heat transfer between the molten pool and the vacuum: The surface of the molten pool radiates heat energy to the surroundings in a vacuum environment. The calculation of the radiative heat flux density follows the Stefan-Boltzmann law. Considering the relationship between surface emissivity and ambient temperature, the expression is as follows:

[0073] ;

[0074] In the formula, σ is the heat flux radiated from the surface of the molten pool; σ is the Stefan-Boltzmann constant, with a value of ; The emissivity of the molten pool surface; The total surface area radiated from the molten pool surface; The temperature of the melt; The temperature of the surrounding environment.

[0075] In ProCAST, the settings for radiative heat transfer are as follows:

[0076] In the ProCAST software's heat source / heat flux boundary condition setting module, select "Radiative Heat Transfer". Set the radiation emissivity of the molten pool surface. Temperature of the melt and the temperature of the surrounding environment Define the total surface area of ​​radiation on the molten pool surface. And input the Stefan-Boltzmann constant. .

[0077] Melt flow and solidification zone: In the vacuum consumable arc melting process, the flow and solidification of the melt are a complex process involving the interaction of multiple physical mechanisms.

[0078] Melt flow is dominated by natural convection caused by temperature gradients, while the solidification process is closely related to heat conduction, latent heat of phase change, and changes in the temperature field. Melt flow: Navier-Stokes equations and temperature-driven natural convection. The main driving force of melt flow comes from natural convection caused by temperature gradients. The flow equations are described by the Navier-Stokes equations, which include the conservation of fluid momentum, temperature convection terms, viscous terms, and gravitational effects.

[0079] Heat transfer and solidification of melts: The energy equation and the latent heat of phase change in solidification processes are controlled by the evolution of the temperature field and the diffusion of heat within the molten pool. In this process, changes in the temperature field within the molten pool not only affect flow but also determine the occurrence of solidification.

[0080] Combining the complex processes of flow, heat transfer, and latent heat of phase change, the following coupled equations describe the flow and solidification processes of the melt:

[0081] ;

[0082] In the formula, The density of the melt; The specific heat capacity of the melt; The temperature of the melt; This represents the velocity field of the melt flow. For temperature gradient; The thermal conductivity of the melt; Heat input to an electric arc or other external heat source; Latent heat of phase transition; The degree of solidification indicates the extent to which a liquid transforms into a solid state; This refers to the solidification rate; It is the acceleration due to gravity; This represents the melt flow driving term caused by temperature gradient and gravity; Operators that describe how physical quantities change in space are used in the above equations to characterize temperature gradients, heat conduction, and convective heat transfer.

[0083] In ProCAST, follow these steps:

[0084] Flow model settings: In ProCAST, select the flow module and input the melt density. Specific heat capacity of melt Thermal conductivity of the melt Melt flow velocity field And set the gravitational acceleration. and internal heat source.

[0085] Phase change model settings: Select the phase change module and input the latent heat of phase change. And define the solidification temperature and melting temperature.

[0086] Coupled Flow and Solidification: ProCAST automatically handles the coupling between melt flow and solidification processes, ensuring consistency in the temperature field, flow field, and phase transformation process. Through solidification-flow coupling in ProCAST, the melt flow and solidification processes are simulated.

[0087] Vacuum smelting range: The entire calculation area is set to a vacuum state, and the vacuum degree is the collected parameter.

[0088] Based on the three-dimensional geometric model and functional area division, macroscopic multiphysics coupling calculations were performed on the vacuum consumable arc melting process. This process was implemented using ProCAST numerical simulation software, aiming to calculate and obtain the temperature field, flow field, and solute field distribution in the melting and casting region.

[0089] Furthermore, the standardized data interface is used to export the temperature field, solidification front position, cooling curve and local temperature gradient data output by the macroscopic simulation software in a standardized format, and convert them into initial conditions and boundary conditions that the mesoscopic simulation software can recognize.

[0090] Specifically, after completing the macroscopic-scale multiphysics coupling calculations, the calculated temperature field, solidification front location, cooling curve, local temperature gradient, and other results are exported and used for subsequent mesoscopic-scale simulations. For this purpose, the macroscopic simulation results need to be output in a standardized data format (such as CSV or HDF5) for use in mesoscopic simulations. This includes the following steps:

[0091] Output results: Data such as temperature field, solidification front, and cooling curves were exported as standardized files using ProCAST software for easier subsequent processing. The exported data includes temperature-time curves, solidification rates, and local temperature gradients at different locations (such as the central axis and near the wall).

[0092] Data interface construction: Representative regions within the molten pool, such as the central axis and near-wall edge regions, are selected, and their temperature-time curves and solidification rate parameters are extracted. These data are then input as thermal boundary conditions into the mesoscale simulation model.

[0093] Furthermore, mesoscale simulations are performed based on the results of macroscale simulations, relying entirely on data such as temperature fields, solidification fronts, cooling curves, and solute distributions obtained from the macroscale simulations. These data provide initial and boundary conditions for the mesoscale simulations, ensuring seamless coupling between the macroscale and mesoscale scales. Mesoscale simulations primarily involve accurate modeling of crystal growth, solute diffusion, heat conduction, and phase transition processes. All initial and boundary conditions are passed to the Comsol Multiphysics model through the results of the macroscale simulations.

[0094] When implementing mesoscale simulations in Comsol Multiphysics, multiple physics modules are used: HeatTransfer, Phase Change, Transport of Diluted Species, and Navier-Stokes, among others. All input data comes from macroscale simulations; the following are the setup details for each physics field.

[0095] Temperature field and cooling rate:

[0096] The evolution of the temperature field has a direct impact on crystal growth and solidification processes. In Comsol Multiphysics, the temperature field is modeled using the Heat Transfer in Solids module. Changes in the temperature field are not only caused by heat conduction but are also closely related to the flow (natural convection) within the molten pool and the cooling rate.

[0097] Operating steps:

[0098] a) Open Comsol Multiphysics, select the Heat Transfer module and then select the Heat Transfer in Solids submodule;

[0099] b) Input the thermal properties of the melt;

[0100] c) Using the extracted macroscopic temperature field data as initial conditions, input the temperature field into the Initial Values ​​module. ;

[0101] d) Set convection boundary conditions in Boundary Settings to account for heat transfer between the molten pool and the cooling water.

[0102] The heat transfer formula is:

[0103] ;

[0104] In the formula, The thermal conductivity of the melt. For temperature gradient, The convective heat transfer coefficient of the cooling water. The temperature of the melt. The temperature of the cooling water. This refers to the heat exchanged.

[0105] The Probes module defines temperature variations at key locations such as the center, edges, and walls of the molten pool, providing more accurate local temperature field data.

[0106] Solidification rate and crystal growth:

[0107] Crystal growth rate is affected by changes in the temperature field. Crystal growth rate is related to undercooling. It is related to the solute concentration.

[0108] The crystal growth rate φ during solidification is described by the following formula:

[0109] ;

[0110] In the formula, The crystal growth factor; The temperature of the melt; Local temperature; These are nonlinear coefficients; This refers to the local solute concentration. This represents the equilibrium concentration of the solute.

[0111] Operating steps:

[0112] In Comsol, select the Phase Change module and use the Phase Field equation to describe the crystal growth process.

[0113] The free energy density function φ of the phase-field model can be expressed as:

[0114] ;

[0115] In the formula, For interfacial tension; For phase field variables, representing the solid-liquid interface; The free energy terms related to phase transitions are usually described using quadratic functions or higher-order polynomials; Phase field variables The spatial gradient reflects the direction and intensity of change of the solid-liquid interface.

[0116] Furthermore, the solute diffusion equation is based on Fick's law and coupled with the melt flow velocity field to simulate the diffusion and redistribution of the solute during the solidification process.

[0117] Specifically, solute diffusion is a crucial phenomenon in the solidification process, and the distribution and diffusion of the solute affect the uniformity of the final ingot. Solute diffusion follows Fick's Law and can be implemented in Comsol using the Transport of DilutedSpecies module.

[0118] Operating steps:

[0119] a) In Comsol, select the Transport of Diluted Species module and enter the diffusion coefficient of the solute. ;

[0120] b) Set the initial concentration C0 to the concentration data extracted from the macroscopic simulation results;

[0121] c) In Boundary Settings, use the Convection-Diffusion equation to describe the diffusion of the solute:

[0122] ;

[0123] in, For the melt flow velocity field, For concentration gradient, is the mass diffusion coefficient of the solute in the melt.

[0124] The mesoscopic simulation employs multiple modules from Comsol Multiphysics, such as Phase Field and Transport of Diluted Species, to simulate phenomena such as crystal growth and solute diffusion during solidification. All input conditions are derived from macroscopic simulation results to ensure simulation accuracy.

[0125] The specific steps are as follows:

[0126] 1. Phase-field model and crystal growth:

[0127] In Comsol, the Phase Field module is used to describe the evolution of the solid-liquid interface by solving the Allen-Cahn equation and the free energy density function.

[0128] Operating steps:

[0129] a) Define the free energy density function in the Phase Field module. and phase field variables;

[0130] b) Set up the Allen-Cahn equations to describe the evolution of phase field variables:

[0131] ;

[0132] In the formula, M is the phase-field mobility, which represents the ability of the phase field variable to respond to the free energy driving force and is used to control the migration speed of the solid-liquid interface and the dynamic characteristics of the phase transition process.

[0133] 2. Solute diffusion and repulsion effects:

[0134] Solute diffusion is affected by the crystal growth process, and the distribution of solute changes with crystal growth.

[0135] The diffusion and repulsion effects of solutes are achieved through the Convection-Diffusion equation.

[0136] Operating steps:

[0137] a) In the Transport of Diluted Species module, input the solute diffusion coefficient and concentration obtained from the macroscopic simulation;

[0138] b) Set up the solute diffusion equation and define the initial and boundary conditions for concentration.

[0139] The simulation yielded the following results:

[0140] Crystal growth process and morphological evolution: Simulates the growth rate, direction, and morphological changes of crystals. The dynamic process of crystal growth, grain morphology, and grain size are output through Comsol's Result module.

[0141] Solute distribution and concentration gradient: Simulate the distribution of solutes during solid-liquid phase transitions to assess solute homogeneity and whether separation occurs;

[0142] Microstructure evolution: Predict the microstructure of ingots by simulating crystal growth, solute diffusion and interface evolution.

[0143] Furthermore, after completing the mesoscale simulation, the key parameters such as crystal growth rate, solidification rate, and solute distribution obtained from the mesoscale simulation are fed back to the macroscopic model to update the physical parameters such as heat conduction, latent heat of solidification, and solute diffusion in the macroscopic model, ensuring seamless coupling between the two.

[0144] Specifically, the mesoscopic simulation results are used to correct parameters such as heat flux distribution, latent heat of phase change, and solute diffusion coefficient in the macroscopic model, optimizing the temperature field, solidification process, and solute distribution of the molten pool. Subsequently, based on the updated macroscopic model, multiphysics coupling calculations at the macroscopic and mesoscopic scales are performed again to verify and optimize the temperature field, flow field, and solute field distribution, ensuring compliance with production process requirements.

[0145] This embodiment also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of a multi-scale simulation method for casting ingots in a vacuum self-consuming arc melting process.

[0146] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of a multi-scale simulation method for ingot casting in a vacuum consumable arc melting process.

[0147] To more clearly illustrate the technical solution of the present invention, the following specific embodiments demonstrate how to perform macroscopic-mesoscopic multiphysics coupling simulation based on operating condition data and optimize the process.

[0148] A multi-scale simulation method for ingot casting during vacuum consumable arc melting process, specifically including:

[0149] Step 1: Obtaining operating parameters:

[0150] First, the operating conditions of the vacuum self-consuming arc melting equipment in actual production are obtained, including but not limited to key process parameters such as the size of the melting furnace casting unit, current, voltage, cooling water flow rate, smelting rate, and vacuum degree. This data is collected through a real-time monitoring system or sensors and transmitted to the computer system via a data acquisition system. Specific parameters are detailed in [link to relevant documentation]. Figure 1 .

[0151] Step 2: Determination of material thermophysical parameters:

[0152] Thermophysical properties of TC4 titanium alloy are shown in [reference needed]. Figure 2 , Figure 3 These temperature-dependent thermophysical parameters will be used as input data and fed into the ProCAST and Comsol Multiphysics models, where they will be dynamically updated during the simulation.

[0153] Step 3: Establishment of macroscopic-scale numerical models and functional region division:

[0154] Based on the working condition data obtained in step 1 and the thermophysical parameters determined in step 2, a geometric model of the casting zone of TC4 titanium alloy was established in 3D modeling software. Assuming the diameter of the casting unit is 860 mm and the height of the cylindrical crystallizer is 2402 mm, the model dimensions were adjusted according to the ingot specifications. The geometric model was output in IGS format and imported into ProCAST numerical simulation software. Figure 4 The functional areas of this model are divided as follows:

[0155] 1. Arc Action Zone: This zone is located at the upper end of the molten pool, and the input power is determined by the working voltage during the vacuum consumable arc melting process. Working current in vacuum consumable arc melting process calculate:

[0156] ;

[0157] In the formula, To input heat power into the electric arc, This represents the arc thermal efficiency coefficient, used to characterize the efficiency of converting electrical energy into molten pool heat energy.

[0158] 2. Heat exchange zone: This zone includes convective heat exchange between the crystallizer and the cooling water, and radiative heat exchange between the molten pool and the vacuum. The specific formulas are as follows:

[0159] Heat transfer between the crystallizer and cooling water:

[0160] ;

[0161] In the formula, This refers to the heat flow between the crystallizer and the cooling water. The convective heat transfer coefficient of the cooling water; The surface area of ​​the melt in contact with the crystallizer wall; The thermal diffusivity of the cooling water; The thickness of the crystallizer wall; The temperature of the melt; This refers to the temperature of the cooling water.

[0162] Radiative heat transfer between the molten pool and the vacuum:

[0163] ;

[0164] In the formula, The heat flow radiated from the surface of the molten pool; The value is the Stefan-Boltzmann constant. ; The emissivity of the molten pool surface; The total surface area radiated from the molten pool surface; The temperature of the melt; The temperature of the surrounding environment.

[0165] 3. Melt Flow and Solidification Region: Melt flow is described by the Navier-Stokes equations, and the solidification process is described by the energy equations.

[0166] 4. Vacuum smelting range: This is used to set the vacuum environment within the calculation domain. This range includes the arc action zone, the heat exchange zone, and the melt flow and solidification zone.

[0167] The entire computational domain was set to a vacuum state, with the vacuum level determined by collected parameters. Based on the three-dimensional geometric model and functional region division, macroscopic multiphysics coupling calculations were performed on the vacuum self-consuming arc melting process. This process was implemented using ProCAST numerical simulation software, aiming to calculate and obtain the temperature field, flow field, and solute field distribution in the melting and casting region.

[0168] Step 4, Macroeconomic Data Output:

[0169] After performing multiphysics coupling calculations in ProCAST, key macroscopic data are output as input conditions for mesoscopic simulations.

[0170] Key macroeconomic data include:

[0171] Temperature field: The temperature data of different locations in the molten pool (such as the center, edge, and crystallizer wall) as a function of time are calculated; this temperature data will be used as the initial temperature field input in the mesoscopic simulation.

[0172] Solidification front location: The location of the solidification interface is obtained through simulation calculation, and a solidification front curve is generated as a function of time; this data will provide the solidification boundary conditions for the mesoscopic model.

[0173] Cooling curves: Extract temperature curves of different locations (such as the central axis and the edge of the molten pool) over time for subsequent mesoscopic simulations.

[0174] Local temperature gradient: Extracting local temperature gradient data from the temperature field helps mesoscopic simulations determine the rate of temperature change.

[0175] Output Format: This data will be exported in CSV or HDF5 format for direct use in mesoscopic simulations within Comsol Multiphysics. Specifically, these macroscopic data outputs form the basis of the mesoscopic simulation inputs, providing the necessary initial and boundary conditions for the mesoscopic model. Using this data, the mesoscopic model can simulate more refined crystal growth, solute diffusion, and solidification processes. See [link to relevant documentation]. Figure 5 .

[0176] Step 5: Input and boundary conditions for mesoscale simulation:

[0177] Using the macroscopic simulation results output by ProCAST as input for the Comsol Multiphysics mesioscopic simulation, the following simulations were performed:

[0178] Temperature field and cooling rate: In Comsol, the Heat Transfer in Solids module is used, with the temperature field data output from ProCAST as the initial input. This simulates the temperature change of the molten pool during crystal growth.

[0179] Crystal growth and solidification rate: In the Phase Change module, the phase field equation is used to describe the crystal growth process, and the solidification rate is corrected based on the temperature field and solute concentration obtained from the macroscopic simulation.

[0180] Solute diffusion equation: The diffusion process of solute is simulated by inputting the solute diffusion coefficient and solute concentration data obtained from ProCAST simulation through the Transport of Diluted Species module.

[0181] Step 6, Multi-scale Coupling and Feedback:

[0182] The mesoscopic simulation results are fed back to the macroscopic model to correct parameters such as heat source terms, latent heat of solidification, and solute diffusion coefficient. This feedback mechanism ensures seamless coupling between the macroscopic and mesoscopic simulations. The updated macroscopic model will then undergo further multiphysics coupling calculations to verify and optimize the temperature, flow, and solute field distributions, ultimately achieving precise optimization of process parameters. Figure 6 This is a schematic diagram of the solidification structure distribution in vacuum arc remelting. Figure 7This is a schematic diagram of the mesoscopic simulated dendrite growth distribution.

[0183] This embodiment combines macroscopic and mesoscopic simulations to accurately predict physical phenomena such as molten pool flow, solidification process, grain growth, and solute distribution, overcoming the limitation of existing methods that can only perform single-scale simulations.

[0184] By precisely coupling time-varying process parameters (such as current, voltage, smelting rate, etc.) with temperature-dependent physical properties (such as specific heat capacity, density, thermal conductivity, etc.), this embodiment provides highly accurate simulation conditions for processes such as molten pool flow, heat conduction, and solidification in macroscopic simulations, providing reliable data support for subsequent mesoscopic simulations.

[0185] This embodiment proposes to accurately describe the crystal growth process using a phase transition model and the Phase Field equation, and combines the solute diffusion coefficient and latent heat of phase transition to simulate grain morphology, solute distribution, and interface evolution at the mesoscale, providing a quantitative basis for ingot quality optimization.

[0186] This embodiment proposes an innovative data standardization interface method that transforms macroscopic data output by ProCAST (such as temperature fields and solidification fronts) into initial and boundary conditions that can be directly input into Comsol Multiphysics mesoscopic simulations. This interface technology provides strong technical support for accurate transfer between macroscopic and mesoscopic simulations, ensuring coupling and collaborative operation between different physical fields.

[0187] This embodiment innovatively proposes a closed-loop feedback mechanism for multi-scale simulation results. By feeding back the mesoscopic simulation results to the macroscopic model, the physical parameters such as heat source terms, latent heat of solidification, and solute diffusion coefficient in the macroscopic model are corrected, thereby optimizing the temperature field, solidification process, and solute distribution of the molten pool and providing a reliable quantitative basis for smelting process optimization.

[0188] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A multi-scale simulation method for ingot casting during vacuum consumable arc melting process, characterized in that, include: Based on the actual operating parameters and material thermophysical properties of vacuum consumable arc melting, a three-dimensional geometric model of the melting and casting zone is established and functional areas are divided; wherein, the functional area division includes: The arc action area is used to equate the arc heat input to a surface heat source acting on the free surface of the molten pool. The heat flux density within the arc action area is radially non-uniformly distributed along the free surface of the molten pool. The heat exchange area includes the convective heat exchange area between the outer layer of the crystallizer and the cooling water, and the radiative heat exchange area between the surface of the molten pool and the vacuum environment. The melt flow and solidification region is used to describe the melt flow and solidification process by coupling the Navier-Stokes equations, the energy equations, and the latent heat of phase change. Vacuum smelting range area, used to define the vacuum environment within the computational domain; Based on the three-dimensional geometric model of the casting area and the divided functional areas, a multi-physics coupled numerical model is constructed in macroscopic simulation software to simulate and calculate the temperature field of the molten pool, the position of the solidification front, the cooling curve and the local temperature gradient. The simulation results of the macroscopic simulation software are input into the mesoscopic simulation software through a standardized data interface as the initial and boundary conditions for the mesoscopic scale simulation. Based on the phase field model and solute diffusion equation, the grain growth morphology, solute distribution and microstructure evolution process are simulated. The crystal growth rate, solidification rate and solute distribution results obtained from the mesoscopic simulation are fed back into the multiphysics coupled numerical model to correct the heat source term, latent heat of phase change and / or solute diffusion coefficient in the macroscopic model, and iterative calculations are performed to achieve closed-loop coupling between macroscopic and mesoscopic simulations. The macroscopic simulation software is ProCAST; the mesoscopic simulation software is Comsol Multiphysics.

2. The multi-scale simulation method for ingot casting in the vacuum consumable arc melting process according to claim 1, characterized in that, The actual operating parameters include current, voltage, smelting rate, cooling water flow rate and vacuum degree that vary with time; the material thermal properties parameters include the density, thermal conductivity, specific heat capacity, thermal conductivity, viscosity, surface tension and latent heat of phase change of the material to be smelted.

3. The multi-scale simulation method for ingot casting in the vacuum consumable arc melting process according to claim 1, characterized in that, The surface heat source input power of the arc action area is determined based on the working voltage and working current during the vacuum self-consuming arc melting process; the heat flux density is described using a decay function related to the radial distance from the arc center axis.

4. The multi-scale simulation method for ingot casting in the vacuum consumable arc melting process according to claim 1, characterized in that, The standardized data interface is used to export the temperature field, solidification front position, cooling curve and local temperature gradient data output by the macroscopic simulation software in a standardized format, and convert them into initial conditions and boundary conditions that the mesoscopic simulation software can recognize.

5. The multi-scale simulation method for ingot casting in the vacuum consumable arc melting process according to claim 1, characterized in that, The phase-field model uses the Allen-Cahn equation and free energy density function to describe the solid-liquid interface evolution, where the crystal growth rate is related to local undercooling and solute concentration.

6. The multi-scale simulation method for ingot casting in the vacuum consumable arc melting process according to claim 5, characterized in that, The solute diffusion equation is based on Fick's law and coupled with the melt flow velocity field to simulate the diffusion and redistribution of solute during solidification.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method as described in any one of claims 1 to 6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1 to 6.

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