A simulation method for genetic behavior of inclusions in multistage vacuum consumable remelting

Abstract

The present application belongs to the technical field of numerical simulation of vacuum metallurgy, and specifically relates to a simulation calculation method for genetic behavior of inclusions in multi-stage vacuum consumable remelting, comprising the following steps: obtaining original three-dimensional coordinate and size data of inclusions through pre-consumable remelting simulation; removing surface inclusions through virtual turning screening according to the size of the subsequent consumable electrode processing; uniformly reconstructing the axial coordinates of the remaining inclusions to generate a genetic injection file; loading the genetic injection file into a subsequent remelting model to carry out simulation of the movement of inclusions and obtain the final distribution; and iteratively completing multi-stage genetic behavior analysis. The present application takes accurate inheritance of radial distribution as the core, avoids time sequence uncertainty through axial coordinate reconstruction, significantly reduces the calculation complexity, improves the simulation accuracy, and provides a reliable numerical tool for optimization of multi-stage consumable remelting process of high-end alloys and control of purity.

Description

Technical Field

[0001] This invention belongs to the field of vacuum metallurgical numerical simulation technology, specifically a method for simulating the genetic behavior of inclusions in multi-stage vacuum consumable remelting. Background Technology

[0002] Vacuum arc remelting (VAR) is a crucial metallurgical process for producing high-end alloys used in cutting-edge fields such as aerospace and nuclear energy. To improve solidification structure and achieve extremely high purity standards, two-stage or even multi-stage VAR processes are often employed in actual industrial production. In multi-stage VAR processes, inclusions remaining inside the preceding VAR ingot (which, after turning, becomes the subsequent VAR electrode) re-enter the molten pool as the electrode melts. Some inclusions are then recaptured within the VAR ingot during subsequent solidification, forming what is known as the "inclusion inheritance effect." The final distribution of inclusions resulting from this inheritance effect directly determines the fatigue life and service reliability of high-end metal components.

[0003] Currently, computational fluid dynamics numerical simulation is an important tool for studying the movement and removal behavior of inclusions during vacuum arc remelting (ACR). However, current research generally focuses on inclusion movement and removal during single ACR processes, with few reports on systematic studies of inclusion genetic behavior in multi-stage ACR processes. The core technical barrier restricting simulation research in this field lies in the severe computational redundancy and timing injection logic mismatch inherent in conventional cross-computational domain discrete phase transfer mechanisms. When attempting inclusion information transfer in multi-stage ACR processes, existing techniques typically require the preservation of the original three-dimensional coordinates of inclusions in previous ACR ingots and rely on a fixed time sequence for sequential injection. This data transfer method not only greatly increases the computational load of multiphase flow coupled with discrete phases and easily leads to solution divergence, but also, due to the strong nonlinearity and randomness of the melting process at the electrode tip, the liquid film convergence and disordered mixing and dripping of droplets mean that there is no accurately predictable functional relationship between the original axial position of the inclusion and its actual entry into the molten pool, rendering the accurate preservation of axial coordinates meaningless.

[0004] In contrast, the radial distribution of inclusions in the preceding consumable ingot directly determines their initial position and stress state when entering the subsequent molten pool, thus dominating their subsequent trajectory and final distribution characteristics. Therefore, radial position is the core information for revealing the genetic behavior of inclusions in a multi-stage consumable process. However, there is currently a lack of numerical methods that can effectively extract and transmit radial position data of inclusions in the preceding consumable ingot. Therefore, it is urgent to establish a novel method for simulating the genetic behavior of inclusions that focuses on the accurate inheritance of radial distribution while avoiding uncertainties in physical timing. Summary of the Invention

[0005] The purpose of this invention is to provide a method for simulating the genetic behavior of inclusions in a multi-stage vacuum arc remelting process. This method takes the accurate inheritance of the radial distribution of inclusions as its core and effectively avoids temporal uncertainties through axial coordinate reconstruction, thereby achieving efficient and high-fidelity simulation of the genetic behavior of inclusions. This provides a reliable numerical simulation tool for optimizing the multi-stage vacuum arc remelting process and controlling the purity of high-end alloys.

[0006] The technical solution adopted by this invention to achieve the above objectives is: a method for simulating and calculating the genetic behavior of inclusions in multi-stage vacuum consumable remelting, comprising the following steps:

[0007] Step 1: Obtain the original three-dimensional coordinates and size data of the inclusions inside the preceding vacuum consumable ingot through numerical simulation of the preceding vacuum consumable remelting process, and form the original data file;

[0008] Step 2: Based on the machining dimensions of the subsequent consumable electrode, perform virtual turning screening on the inclusions in the original data file to remove the inclusion data located in the turning area and obtain the genetic data;

[0009] Step 3: Reconstruct the axial coordinates of inclusions in the genetic data to generate a subsequent consumable ingot inclusion genetic injection file;

[0010] Step 4: Establish a subsequent vacuum consumable remelting model in the fluid simulation software, load the genetic injection file by file import, perform simulation calculations on the behavior of inclusions in the molten pool, and obtain the final distribution of inclusions inside the subsequent consumable ingot;

[0011] Step 5: If there is a next level of consumable remelting, then use the currently obtained subsequent consumable ingot inclusion distribution as the new preceding data and repeat steps 2 to 4; otherwise, end and compare the inclusion distribution characteristics in each level of consumable ingot to complete the simulation of inclusion genetic behavior in the multi-level consumable remelting process.

[0012] In step 1, the numerical simulation adopts a multiphysics coupling model, which includes: electromagnetic field calculation, flow field and solidification calculation based on the Euler solid-liquid two-phase flow method, energy conservation calculation, solute conservation calculation, and inclusion trajectory calculation.

[0013] In step 2, the virtual turning screening specifically includes:

[0014] Step 2-1: Set the radial screening threshold , It is equal to the radius of the subsequent consumable electrode;

[0015] Step 2-2: Calculate the radial distance of each inclusion. ;

[0016] Steps 2-3: If If the inclusion is located in the surface area that has been removed by turning, it is determined to be deleted; if If so, the inclusion is determined to be located within the subsequent consumable electrode matrix and is retained.

[0017] Step 3 specifically includes:

[0018] Step 3-1: Obtain the initial computational domain height for subsequent vacuum arc remelting simulation ;

[0019] Step 3-2: Set the injection height Injection height Smaller than the initial computational domain height And with the height of the initial computational domain The difference is within the preset range;

[0020] Step 3-3: Screen and retain all impurities from the original material. Coordinates changed to This allows all genetic inclusions to be released at the same horizontal plane.

[0021] Step 4 includes the following steps:

[0022] Step 4-1: Establish a subsequent vacuum self-consumption remelting model in the fluid simulation software. The subsequent vacuum self-consumption remelting model adopts the same multiphysics coupling model as in Step 1.

[0023] Step 4-2: Load the genetic injection file. At the initial moment of calculation, all inclusion particles are released simultaneously, and their radial distribution is consistent with the radial distribution of the un-turned area in the preceding consumable ingot.

[0024] Step 4-3: Perform transient calculations by solving the multiphysics coupling model to obtain the final distribution of inclusions inside the subsequent consumable ingot.

[0025] The electromagnetic field calculation is specifically as follows:

[0026] Electric potential equation: ;

[0027] Current density: ;

[0028] Magnetic vector potential equation: ;

[0029] Self-induced magnetic field strength: ;

[0030] Self-induced electromagnetic force: ;

[0031] Joule fever: ;

[0032] in For electrical conductivity, For electric potential, For current density, The magnetic vector potential, Permeability, The self-induced magnetic field strength, For self-induced electromagnetic force, It is Joule heat.

[0033] The flow field and solidification calculations employ the Eulerian solid-liquid two-phase flow method to obtain the solid-liquid phase transition rate, specifically as follows:

[0034] The solid-liquid phase transition rate for:

[0035]

[0036] in, The dendrite tip growth rate Dendrite surface concentration, For solid density, For dendrite growth surface collision;

[0037] Dendrite tip growth rate for:

[0038]

[0039] in, The solute diffusion coefficient in the liquid phase is... , These represent the solute concentrations in the liquid and solid phases at interfacial equilibrium, respectively. This refers to the solute concentration in the liquid phase. The far-field radius of the preceding dendrite trunk is denoted as . The radius of the preceding dendrite trunk is: ;

[0040] Dendrite surface concentration for:

[0041]

[0042] Dendrite growth surface collision for:

[0043]

[0044] in, This represents the spacing between preceding dendrites. , These represent the solid volume fractions.

[0045] In the subsequent vacuum self-consuming remelting model, the flow field distribution of the molten pool is calculated using the following conservation equation:

[0046] mass conservation equation:

[0047]

[0048]

[0049] Momentum conservation equation:

[0050]

[0051] in, The solid-liquid phase transition rate; The density of the liquid phase; It represents the liquid phase volume fraction; The density is the solid phase density. It represents the volume fraction of the solid phase. This is the melt velocity vector; For pressure; It is the stress-strain tensor; This is the vector of gravitational acceleration in the liquid phase; It is a self-induced electromagnetic force; This is the momentum exchange caused by the phase transition; It is the drag force between the solid and liquid phases.

[0052] In the subsequent vacuum self-consuming remelting model, the melt temperature distribution is determined by solving the energy conservation equation in enthalpy form:

[0053]

[0054]

[0055] in, , The enthalpy of the liquid phase and the enthalpy of the solid phase are respectively. , The thermal conductivity of the liquid phase and the solid phase are respectively. , These are the liquid phase and solid phase temperatures, respectively. It is Joule heat. This refers to the energy source term caused by the liquid phase transition; This refers to the energy source term caused by solid-state phase transition; This is for energy exchange between solid and liquid phases.

[0056] In the subsequent vacuum self-consuming remelting model, the solute distribution is obtained by solving the following solute conservation equation:

[0057]

[0058]

[0059] in, The density of the liquid phase; It represents the liquid phase volume fraction; The density is the solid phase density. It represents the volume fraction of the solid phase. , These represent the solute concentrations in the liquid and solid phases, respectively. The diffusion coefficient of the solute in the liquid phase; The solid-phase solute diffusion coefficient; For solute exchange between solid and liquid phases;

[0060] The volume average concentration c of the solid-liquid two-phase mixture mix Characterizing local solute concentration:

[0061]

[0062] The motion of the inclusion is governed by Newton's second law, and its trajectory prediction equation is as follows:

[0063]

[0064] in, This represents the volume-average concentration of the solid-liquid two-phase mixture. The density of the liquid phase; It represents the liquid phase volume fraction; The density is the solid phase density. It represents the volume fraction of the solid phase. , These represent the solute concentrations in the liquid and solid phases, respectively. The mass of the inclusion particles; Particle velocity; , , , , , These are the resultant force of gravity and buoyancy acting on the particle, the interphase drag force, the lift force, the virtual mass force, the pressure gradient force, and the electromagnetic pressure, respectively.

[0065] The present invention has the following beneficial effects and advantages:

[0066] 1. This invention clarifies that the radial position of inclusions is the core information for revealing their genetic behavior. By accurately extracting and transmitting the radial position data of inclusions, the true initial position and stress state of inclusions when entering the subsequent molten pool are restored, thereby significantly improving the numerical prediction accuracy of the final distribution characteristics of inclusions in the multi-stage self-consumption process.

[0067] 2. This invention transforms the complex three-dimensional timing injection into a timing-independent equivalent mapping by reconstructing the axial coordinates, thus completely avoiding the timing uncertainty of inclusion injection caused by nonlinear melting of electrodes and significantly reducing the complexity of the simulation.

[0068] 3. This invention develops a practical numerical calculation framework for systematically revealing the genetic behavior of inclusions in multi-stage vacuum arc remelting (ACR) processes. Based on this framework, the improvement effect of multi-stage ACR processes on inclusion size levels and distribution characteristics can be intuitively and quantitatively evaluated, thus providing reliable digital tools and theoretical support for the targeted optimization and purity control of high-end alloy ACR processes. Attached Figure Description

[0069] Figure 1 This is a schematic diagram of the overall process of the method of the present invention.

[0070] Figure 2 This is a schematic diagram of virtual turning and screening of inclusion data.

[0071] Figure 3 A schematic diagram for reconstructing the axial coordinates of inclusions and injecting the equivalent surface.

[0072] Figure 4 This is a comparison of inclusion distribution in two-stage consumable ingots of 316L stainless steel simulated using the method of this invention; wherein, Figure 4 (a) shows the original distribution of Al2O3 inclusions in a primary consumable ingot. Figure 4 (b) shows the distribution of Al2O3 inclusions in consumable ingots obtained by secondary remelting based on inclusion genetic data. Detailed Implementation

[0073] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0074] This invention proposes a method for simulating the genetic behavior of inclusions during multi-stage vacuum arc remelting (ARR). The complex genetic behavior of inclusions in this multi-stage ARR process is decomposed into two relatively independent sub-problems: "precise inheritance of radial distribution" and "data reconstruction to avoid temporal uncertainties." By extracting the radial coordinates of the inclusions and performing data reconstruction with a unified height on the axial coordinates, the complex three-dimensional temporal injection is transformed into a temporally independent equivalent mapping. This invention, based on the practicality of engineering calculations, ensures the complete inheritance of key information (radial distribution) of inclusion genetic behavior while significantly reducing the complexity of the simulation and the computational resource requirements.

[0075] like Figure 1 The diagram shown is a schematic representation of the overall process of the method of the present invention. The specific method of the method for simulating and calculating the genetic behavior of inclusions in a multi-stage vacuum consumable remelting process of the present invention is as follows:

[0076] Step 1: Obtain the original three-dimensional coordinates and size data of the inclusions inside the preceding vacuum consumable ingot through numerical simulation of the preceding vacuum consumable remelting process, and form the original data file;

[0077] Step 2: Based on the machining dimensions of the subsequent consumable electrode, perform virtual turning screening on the inclusions in the original data file to remove the inclusion data located in the turning area and obtain the genetic data;

[0078] Step 3: Reconstruct the axial coordinates of inclusions in the genetic data to generate a subsequent consumable ingot inclusion genetic injection file;

[0079] Step 4: Establish a subsequent vacuum consumable remelting model in the fluid simulation software, load the genetic injection file by file import, perform simulation calculations on the behavior of inclusions in the molten pool, and obtain the final distribution of inclusions inside the subsequent consumable ingot;

[0080] Step 5: If there is a next level of consumable remelting, then use the currently obtained subsequent consumable ingot inclusion distribution as the new preceding data and repeat steps 2 to 4; otherwise, end and compare the inclusion distribution characteristics in each level of consumable ingot to complete the simulation of inclusion genetic behavior in the multi-level consumable remelting process.

[0081] Example: Simulation of the genetic behavior of inclusions during two-stage vacuum arc remelting of 316L stainless steel

[0082] This embodiment uses 316L austenitic stainless steel produced by a special steel company as the object (chemical composition shown in Table 1 below). The inclusions mainly consist of Al2O3 and rare earth oxide sulfides Ce-OS. The physical properties of 316L stainless steel are shown in Table 2 below, and the main process parameters of the two-stage consumable remelting process are shown in Table 3 below. The method of this invention is used to simulate the inclusion inheritance behavior during the two-stage consumable remelting process, fully demonstrating the entire process from primary consumable ingot data extraction to secondary remelting simulation, such as... Figure 1 As shown.

[0083] Table 1 Chemical composition (wt.%) of the steel in the examples

[0084] 18.22 14.98 2.82 1.34 0.27 0.03 margin

[0085] Table 2 Physical property parameters of the steel in the examples

[0086] <![CDATA[Density (kg·m -3 )]]> 7200 Primary dendrite spacing (m) <![CDATA[3.0×10 -4 ]]> <![CDATA[Specific heat capacity (J·kg -1 ·K -1 )]]> 780 Secondary dendrite arm spacing (m) <![CDATA[1.2×10 -4 ]]> <![CDATA[Thermal conductivity (W·m -1 ·K -1 )]]> 30 Reference temperature (K) 1722 <![CDATA[Viscosity (kg·m -1 ·s -1 )]]> <![CDATA[7.8×10 -3 ]]> Melting temperature of pure solvent (K) 1811 <![CDATA[Latent heat of phase change (J·kg -1 )]]> <![CDATA[1.88×10 5 ]]> <![CDATA[Electrical Conductivity (Ω -1 ·m -1 )]]> <![CDATA[6.0×10 5 ]]> <![CDATA[Coefficient of Thermal Expansion (K -1 )]]> <![CDATA[7.8×10 -5 ]]> <![CDATA[permeability (H·m -1 )]]> <![CDATA[1.26×10 -6 ]]>

[0087] Table 3. Main process parameters of the two-stage consumable remelting process

[0088] Radius of a single consumable ingot (mm) 205 <![CDATA[Melting rate during a self-consumption stable period (kg·min -1 )]]> 4.4 Radius of a single consumable electrode (mm) 170 <![CDATA[melting rate during a self-consuming heat topping period (kg·min -1 )]]> 4.4 (12840 s), 1.5 (17640 s) Radius of secondary consumable ingot (mm) 230 Secondary self-consumption steady-state current (A) 7800 Secondary consumable electrode radius (mm) 190 Secondary self-consuming heat capping period current (A) 7800 (10400 s), 4200 (15200 s) Effective radius of electric arc (mm) 250 <![CDATA[Melting rate in the secondary consumable stabilization period (kg·min -1 )]]> 4.5 Primary self-consumption steady-state current (A) 6600 <![CDATA[Melting rate in the secondary consumable heat topping period (kg·min -1 )]]> 4.5 (10400 s), 1.5 (15200 s) Current during the capping period of a single self-consuming heat treatment cycle (A) 6600 (12840 s), 4000 (17640 s) Main arc current percentage 0.9

[0089] Step 1: Establish a vacuum consumable remelting process model. The diameter of the primary consumable ingot is set to Φ410 mm. A consumable remelting process model is established using the fluid simulation software ANSYS Fluent. This model includes a coupled thermomagnetic flow-solidification-solidification redistribution model based on the Euler solid-liquid two-phase flow method, an inclusion trajectory prediction method based on a discrete phase model, and a dynamic computational domain based on dynamic mesh technology. Details are as follows:

[0090] The electromagnetic field distribution during vacuum arc remelting is calculated using the following formula:

[0091] Electric potential equation: ;

[0092] Current density: ;

[0093] Magnetic vector potential equation: ;

[0094] Self-induced magnetic field strength: ;

[0095] Self-induced electromagnetic force: ;

[0096] Joule fever: ;

[0097] in, The conductivity is expressed in S / m. J is the electric potential (V), and J is the current density (A / m). 2 ), denoted as magnetic vector potential (Wb / m). ρ is the magnetic permeability (H / m). The value is the self-induced magnetic field strength (T). Self-induced electromagnetic force (N / m) 3 ), Joule heating (W / m 3 ).

[0098] The Euler solid-liquid two-phase flow method establishes separate mass, momentum, energy, and solute conservation equations for the solid and liquid phases, and utilizes the solid-liquid phase transition rate. Connect the two sets of equations. It can be obtained from the following formula:

[0099]

[0100] in, The dendrite tip growth rate Dendrite surface concentration, For solid density, For dendrite growth surface collision;

[0101] Among them, the dendrite tip growth rate:

[0102]

[0103] Radius of the preceding dendrite trunk: ;

[0104] Far-field radius of the preceding dendrite trunk: ;

[0105] Dendrite surface concentration: ;

[0106] Dendrite growth surface collision:

[0107] in, Solid-liquid phase transition rate (kg / (m)) 3 ·s)); S is the dendrite tip growth rate (m / s); A Dendrite surface concentration (m -1 ); Solid density (kg / m³) 3 ); This represents the volume fraction of solute that occurs during surface collisions during dendrite growth. The radius of the preceding dendrite trunk (m); The far-field radius (m) of the preceding dendrite trunk; The diffusion coefficient of the solute in the liquid phase (m) 2 / s); and The concentrations of solute in the liquid and solid phases at the interface equilibrium are (wt.%), respectively. The concentration of solute in the liquid phase (wt.%) The preceding dendrite spacing (m); , These represent the volume fractions of the liquid and solid phases, respectively.

[0108] The flow field distribution in a molten metal pool is calculated using the following formula:

[0109] mass conservation equation:

[0110]

[0111]

[0112] Momentum conservation equation:

[0113]

[0114] Among them, the momentum exchange caused by phase transition: ;

[0115] Solid-liquid phase drag: ;

[0116] in, Solid-liquid phase transition rate (kg / (m)) 3 ·s)); Liquid phase density (kg / m³) 3 ); It represents the liquid phase volume fraction; Solid density (kg / m³) 3 ); It represents the volume fraction of the solid phase. is the melt velocity (m / s); p is the pressure (Pa); The stress-strain tensor (kg / (m·s)) 2 )); The liquid phase gravitational acceleration vector (m / s²) 2 ); Self-induced electromagnetic force (N / m) 3 ); The momentum exchange caused by phase transition (kg / (m) 2 ·s 2 )); The interphase drag force (kg / (m)) 2 ·s 2 )); Solid phase velocity (m / s); K is the viscosity of the liquid phase (Pa·s); K is the permeability of the paste region (m³). 2 ).

[0117] The temperature distribution of the melt is determined by solving the energy conservation equation in enthalpy form:

[0118]

[0119]

[0120] Among them, the energy source term caused by the phase transition: ;

[0121]

[0122] Solid-liquid phase energy exchange: ;

[0123] in, Liquid phase density (kg / m³) 3 ); It represents the liquid phase volume fraction; Solid density (kg / m³) 3 ); It represents the volume fraction of the solid phase. The melt velocity is (m / s). , These are the liquid phase enthalpy and the solid phase enthalpy (J / kg), respectively. , These are the liquid phase and solid phase temperatures (K), respectively. , The values ​​are the thermal conductivity of the liquid phase and the solid phase, respectively (W / (m·K)). Energy source term caused by liquid phase transition (W / m) 3 ); Energy source term caused by solid-state phase transition (W / m) 3 ); For solid-liquid phase energy exchange (W / m 3 ); Joule heating (W / m 3 ); Latent heat of phase transition (J / kg); Solid-liquid phase transition rate (kg / (m)) 3 ·s)); The volumetric heat transfer coefficient (W / (m)) 3 ·K)).

[0124] The solute distribution in a melt can be obtained by solving the solute conservation equation:

[0125]

[0126]

[0127] Among them, solute exchange between solid and liquid phases: ;

[0128] in, Liquid phase density (kg / m³) 3 ); It represents the liquid phase volume fraction; Solid density (kg / m³) 3 ); It represents the volume fraction of the solid phase. , The concentrations of solute in the liquid and solid phases are respectively (wt.%); D l The diffusion coefficient of the solute in the liquid phase (m) 2 / s); The solid solute diffusion coefficient (m) 2 / s); For solid-liquid phase solute exchange (kg / (m 3 ·s)); k is the equilibrium distribution coefficient; The concentration of solute in the liquid phase at interface equilibrium (wt.%) Solid-liquid phase transition rate (kg / (m)) 3·s). The volume-average concentration of the solid-liquid two-phase mixture. Characterizing local solute concentration:

[0129] The volume average concentration c of the solid-liquid two-phase mixture mix Characterizing local solute concentration:

[0130]

[0131] The motion of the inclusion is governed by Newton's second law, and its trajectory prediction equation is as follows:

[0132]

[0133] in, The volume average concentration (wt.%) of the solid-liquid two-phase mixture. Mass of the inclusion particles (kg); Particle velocity (m / s); , , , , , These are the resultant force of gravity and buoyancy acting on the particle, the interphase drag force, the lift force, the virtual mass force, the pressure gradient force, and the electromagnetic pressure (N).

[0134] The dynamic computational domain based on the dynamic mesh technology is specifically the molten metal melted by the electrode continuously entering the computational domain through the top boundary. In each time step, an equivalent mass corresponding to the melting rate is added to the surface of the melt, and the top boundary moves upward in real time accordingly, thus equivalent to the continuous growth process of the ingot.

[0135] Step Two: Simulation Calculation of Inclusion Movement and Removal Behavior in a Single Consumable Remelting Process. Multiphysics coupling simulation calculations are performed using the process model from Step One. The physical fields include the electromagnetic field, flow field, temperature, and solute distribution of the continuous phase melt, and the motion trajectory of inclusion particles in the discrete phase. A calculation baseline is established through parameter initialization. The phase-coupled SIMPLE algorithm is used to discretize and solve the continuous phase equations (electromagnetic field-flow field-temperature-solute distribution equations) and the discrete phase equations (inclusion movement). An axisymmetric mesh is used for discretization, where the main mesh stores scalar parameters, and staggered meshes record current density and velocity vectors. The time step is dynamically adjusted during the calculation, with a maximum of 60 iterations per time step to reduce normalization residuals. Inclusion positions and velocities are updated in real-time based on the Lagrange method, and calculation results are output for each iteration. Simulation parameters are set according to the actual production process curve. Melting current and melting rate varying with time are imported through user-defined functions. After solidification, the original data of inclusion distribution inside the single consumable ingot is obtained, such as... Figure 4 As shown in (a).

[0136] Step 3: Extraction of raw data from inclusions in a single consumable ingot. Using CFD-POST post-processing software, export relevant information for typical inclusions Al2O3 and Ce-OS, generating a raw data file in CSV format. This file contains information on 7155 inclusions, with each inclusion record including: density (ρ), three-dimensional coordinates (X, Y, Z), and diameter (D). Figure 4 As shown in (a), the inclusions in the primary consumable ingot exhibit obvious radial non-uniform distribution characteristics, with the number density of inclusions in the edge region being higher than that in the core.

[0137] Step 4: Virtual turning screening based on the secondary consumable electrode dimensions. The secondary consumable electrode is machined from a primary consumable ingot by turning, with a turning amount of 15 mm, meaning the diameter of the secondary consumable electrode is Φ380 mm, corresponding to a radius R. max = 190 mm (with the spindle center as the origin). Virtual turning screening is implemented through computer programming: the radial distance of each inclusion is calculated. If R > R max If R ≤ R, then the inclusion is determined to be located in the surface area that was removed by turning and is deleted; max If so, then it will be retained.

[0138] After screening, 7155 original inclusions were identified, of which 6951 remained, and 204 inclusions located in the surface turning area were removed. Figure 2 As shown, the virtual turning screening replicates the physical removal of surface inclusions during actual electrode processing—the left side shows the original inclusion distribution, and the right side shows the inclusion distribution retained after screening. The inclusions in the outer annular region have been effectively removed.

[0139] Step 5: Inclusion Data Reconstruction and Genetic Injection File Generation. Set the initial computational domain height H = 240 mm for the secondary consumable remelting simulation (corresponding to the starting point of the stable melting stage). To ensure inclusions enter the computational domain from the top of the molten pool, set the injection height. ,Right now Slightly smaller than H and close to the initial liquid level at the top of the molten pool. Reconstruct the axial coordinates of all inclusions retained after screening: uniformly modify the original axial coordinate Z to... The original radial coordinates (X, Y) and diameter D of all inclusions are preserved. The reconstructed data is written to a genetic injection file (TXT format), which contains the radial position coordinates, reconstructed axial position coordinates, and diameter of each inclusion. The generated file contains 6951 lines of particle data. Figure 3 As shown, all genetic inclusions were uniformly reconstructed to the same height plane at the top of the molten pool. The radial distribution of the area is completely consistent with the radial distribution of the unmachined area in a primary consumable ingot.

[0140] Step Six: Simulation Calculation of the Secondary Vacuum Consumable Remelting Process. The diameter of the secondary consumable ingot is set to Φ460 mm. The process model and solution method used for the secondary consumable remelting simulation are the same as in Steps One and Two, respectively. The relevant simulation parameters and boundary conditions are set according to the actual process parameters of the secondary consumable remelting. In the discrete phase model settings of the software, select the "injection from file" method and load the genetic injection file generated in Step Five. After loading, all inclusion particles are released simultaneously at the next moment. The radial distribution of the release location is completely consistent with the radial distribution of the un-machined area in the primary consumable ingot, and the axial position is uniformly located near the top of the molten pool. (Location). Subsequently, transient calculations of the secondary consumable remelting process were performed using a process model. The final distribution of inclusions in the secondary consumable ingot was compared with the original distribution of inclusions in the primary consumable ingot, revealing the genetic behavior and distribution evolution of inclusions in the multi-stage consumable remelting process.

[0141] like Figure 4 As shown, the distribution of inclusions in two-stage consumable ingots of the embodiment simulated using the method of the present invention is compared: (a) the original distribution of Al2O3 inclusions in the primary consumable ingot; (b) the distribution of Al2O3 inclusions in the consumable ingot obtained by secondary remelting based on inclusion genetic data. It can be observed that the aggregation degree of inclusions near the central axis of the secondary consumable ingot is significantly weaker than that of the primary ingot, the edge enrichment effect is more significant, and the overall distribution of inclusions shows a more "wall-adhering" trend. Based on the radial distribution characteristics of inclusions in the primary consumable ingot, the secondary consumable process can more effectively push inclusions to the edge region, creating favorable conditions for improving the cleanliness of the ingot during subsequent turning processing.

[0142] The results show that the present invention effectively avoids the problem of uncertainty in the injection timing caused by nonlinear melting of electrodes by innovative design of precise inheritance of radial distribution of inclusions and reconstruction of axial coordinates. It also significantly reduces the computational cost of multi-stage consumable remelting simulation and provides an efficient and reliable digital tool for systematically revealing the genetic behavior of inclusions and optimizing the purity control process of high-end alloys.

[0143] In summary, the proposed method for simulating the genetic behavior of inclusions in multi-stage vacuum arc remelting effectively solves the problem of uncertainty in inclusion injection timing caused by nonlinear melting of electrodes during multi-stage arc remelting through precise radial distribution inheritance and axial coordinate reconstruction. This significantly reduces the computational complexity of discrete phase transfer across computational domains and improves the engineering feasibility and numerical accuracy of simulating inclusion genetic behavior during multi-stage remelting. This method can systematically reveal the distribution and evolution of inclusions during multi-stage arc remelting, quantitatively evaluate the impact of different remelting stages on inclusion removal and aggregation behavior, and provide advanced digital simulation tools and theoretical support for the directional optimization of high-end alloy arc remelting processes, ingot purity control, and service reliability assessment. This invention is applicable to the simulation of multi-stage vacuum arc remelting processes in various alloy systems and has good versatility, scalability, and industrial application prospects.

[0144] It should be noted that the specific embodiments described above are only for helping to understand the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be considered to fall within the scope of protection of the present invention.

Claims

1. A method for simulating the genetic behavior of inclusions in multi-stage vacuum consumable remelting, characterized in that, Includes the following steps: Step 1: Obtain the original three-dimensional coordinates and size data of the inclusions inside the preceding vacuum consumable ingot through numerical simulation of the preceding vacuum consumable remelting process, and form the original data file; Step 2: Based on the machining dimensions of the subsequent consumable electrode, perform virtual turning screening on the inclusions in the original data file to remove the inclusion data located in the turning area and obtain the genetic data; Step 3: Reconstruct the axial coordinates of inclusions in the genetic data to generate a subsequent consumable ingot inclusion genetic injection file; Step 4: Establish a subsequent vacuum consumable remelting model in the fluid simulation software, load the genetic injection file by file import, perform simulation calculations on the behavior of inclusions in the molten pool, and obtain the final distribution of inclusions inside the subsequent consumable ingot; Step 5: If there is a next level of consumable remelting, then use the currently obtained subsequent consumable ingot inclusion distribution as the new preceding data and repeat steps 2 to 4; otherwise, end and compare the inclusion distribution characteristics in each level of consumable ingot to complete the simulation of inclusion genetic behavior in the multi-level consumable remelting process.

2. The method for simulating the genetic behavior of inclusions in multi-stage vacuum consumable remelting according to claim 1, characterized in that, In step 1, the numerical simulation adopts a multiphysics coupling model, which includes: electromagnetic field calculation, flow field and solidification calculation based on the Euler solid-liquid two-phase flow method, energy conservation calculation, solute conservation calculation, and inclusion trajectory calculation.

3. The method for simulating the genetic behavior of inclusions in multi-stage vacuum consumable remelting according to claim 1, characterized in that, In step 2, the virtual turning screening specifically includes: Step 2-1: Set the radial screening threshold , It is equal to the radius of the subsequent consumable electrode; Step 2-2: Calculate the radial distance of each inclusion. ; Steps 2-3: If If the inclusion is located in the surface area that has been removed by turning, it is determined to be deleted; if If so, the inclusion is determined to be located within the subsequent consumable electrode matrix and is retained.

4. The method for simulating the genetic behavior of inclusions in multi-stage vacuum consumable remelting according to claim 1, characterized in that, Step 3 specifically includes: Step 3-1: Obtain the initial computational domain height for subsequent vacuum arc remelting simulation ; Step 3-2: Set the injection height Injection height Smaller than the initial computational domain height And with the height of the initial computational domain The difference is within the preset range; Step 3-3: Screen and retain all impurities from the original material. Coordinates changed to This allows all genetic inclusions to be released at the same horizontal plane.

5. The method for simulating the genetic behavior of inclusions in multi-stage vacuum consumable remelting according to claim 1, characterized in that, Step 4 includes the following steps: Step 4-1: Establish a subsequent vacuum self-consumption remelting model in the fluid simulation software. The subsequent vacuum self-consumption remelting model adopts the same multiphysics coupling model as in Step 1. Step 4-2: Load the genetic injection file. At the initial moment of calculation, all inclusion particles are released simultaneously, and their radial distribution is consistent with the radial distribution of the un-turned area in the preceding consumable ingot. Step 4-3: Perform transient calculations by solving the multiphysics coupling model to obtain the final distribution of inclusions inside the subsequent consumable ingot.

6. The method for simulating the genetic behavior of inclusions in multi-stage vacuum consumable remelting according to claim 1, characterized in that, The electromagnetic field calculation is specifically as follows: Electric potential equation: ; Current density: ; Magnetic vector potential equation: ; Self-induced magnetic field strength: ; Self-induced electromagnetic force: ; Joule fever: ; in For electrical conductivity, For electric potential, For current density, The magnetic vector potential, Permeability, The self-induced magnetic field strength, For self-induced electromagnetic force, It is Joule heat.

7. The method for simulating the genetic behavior of inclusions in multi-stage vacuum consumable remelting according to claim 6, characterized in that, The flow field and solidification calculations employ the Eulerian solid-liquid two-phase flow method to obtain the solid-liquid phase transition rate, specifically as follows: The solid-liquid phase transition rate for: ; in, The dendrite tip growth rate Dendrite surface concentration, For solid density, For dendrite growth surface collision; Dendrite tip growth rate for: ; in, The solute diffusion coefficient in the liquid phase is... , These represent the solute concentrations in the liquid and solid phases at interfacial equilibrium, respectively. This refers to the solute concentration in the liquid phase. The far-field radius of the preceding dendrite trunk is denoted as . The radius of the preceding dendrite trunk is: ; Dendrite surface concentration for: Dendrite growth surface collision for: in, This represents the spacing between preceding dendrites. , These represent the solid volume fractions.

8. The method for simulating the genetic behavior of inclusions in multi-stage vacuum consumable remelting according to claim 7, characterized in that, In the subsequent vacuum self-consuming remelting model, the flow field distribution of the molten pool is calculated using the following conservation equation: mass conservation equation: Momentum conservation equation: in, The solid-liquid phase transition rate; The density of the liquid phase; It represents the liquid phase volume fraction; The density is the solid phase density. It represents the volume fraction of the solid phase. This is the melt velocity vector; For pressure; It is the stress-strain tensor; This is the vector of gravitational acceleration in the liquid phase; It is a self-induced electromagnetic force; This is the momentum exchange caused by the phase transition; It is the drag force between the solid and liquid phases.

9. The method for simulating the genetic behavior of inclusions in multi-stage vacuum consumable remelting according to claim 8, characterized in that, In the subsequent vacuum self-consuming remelting model, the melt temperature distribution is determined by solving the energy conservation equation in enthalpy form: in, , The enthalpy of the liquid phase and the enthalpy of the solid phase are respectively. , The thermal conductivity of the liquid phase and the solid phase are respectively. , These are the liquid phase and solid phase temperatures, respectively. It is Joule heat. This refers to the energy source term caused by the liquid phase transition; This refers to the energy source term caused by solid-state phase transition; This is for energy exchange between solid and liquid phases.

10. The method for simulating the genetic behavior of inclusions in multi-stage vacuum consumable remelting according to claim 9, characterized in that, In the subsequent vacuum self-consuming remelting model, the solute distribution is obtained by solving the following solute conservation equation: in, The density of the liquid phase; It represents the liquid phase volume fraction; The density is the solid phase density. It represents the volume fraction of the solid phase. , These represent the solute concentrations in the liquid and solid phases, respectively. The diffusion coefficient of the solute in the liquid phase; The solid-phase solute diffusion coefficient; For solute exchange between solid and liquid phases; The volume average concentration c of the solid-liquid two-phase mixture mix Characterizing local solute concentration: The motion of the inclusion is governed by Newton's second law, and its trajectory prediction equation is as follows: in, This represents the volume-average concentration of the solid-liquid two-phase mixture. The density of the liquid phase; It represents the liquid phase volume fraction; The density is the solid phase density. It represents the volume fraction of the solid phase. , These represent the solute concentrations in the liquid and solid phases, respectively. The mass of the inclusion particles; Particle velocity; , , , , , These are the resultant force of gravity and buoyancy acting on the particle, the interphase drag force, the lift force, the virtual mass force, the pressure gradient force, and the electromagnetic pressure, respectively.

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