A method for analyzing multi-element distribution characteristics in TA1 ingot

Abstract

The application discloses a kind of TA1 ingot element distribution characteristic analytical method, belong to titanium alloy smelting technical field.The application is to TA1 titanium ingot slice, through carbon sulfur analyzer, oxygen nitrogen hydrogen analyzer, inductively coupled plasma emission spectrometry accurately determine the concentration of C, N, O, Fe in 16 characteristic detection points, reveal the macroscopic distribution law and segregation difference of element in ingot longitudinal, transverse;Rely on ANSYS Fluent, through C language combination specific macro of Fluent and write UDF to realize the redistribution of solute and heat solute buoyancy, and construct multi-physics field coupling model by combining key parameters, simulate the segregation evolution law of element in TA1 ingot solidification process, ascertain the influence mechanism of solute redistribution coefficient on element distribution, quantitatively analyze the element migration and enrichment behavior in solidification process.The application can systematically reveal the distribution characteristics and segregation cause of key elements in TA1 ingot, provide theoretical support for electron beam cold bed furnace smelting process optimization, effectively solve the problem of TA1 ingot composition uneven.

Description

Technical Field

[0001] This invention relates to the field of titanium alloy smelting technology, specifically to an analytical method for the distribution characteristics of multiple elements in TA1 ingots. Background Technology

[0002] Titanium possesses advantages such as low density, high specific strength, and good corrosion resistance, making it valuable for applications in aerospace, chemical, biomedical, and automotive lightweighting. As industrially pure titanium, TA1's mechanical properties are extremely sensitive to the content and distribution of impurity elements such as carbon (C), nitrogen (N), oxygen (O), and iron (Fe). Microscopic segregation or uneven macroscopic distribution of these elements directly leads to problems such as increased localized hardness, decreased plasticity, and deteriorated corrosion resistance in the ingot. Currently, electron beam cold hearth furnace melting (EBCHM) is gradually becoming a key process for preparing high-quality TA1 ingots due to its advantages in removing high-density inclusions, avoiding macroscopic component segregation, and allowing for cold hearth refining.

[0003] In the electron beam cold hearth furnace smelting of TA1, the uniformity of the distribution of C, N, O, and Fe is a core indicator determining the quality of the ingot. Under high-temperature vacuum conditions (above 1600℃, 0.001–0.1 Pa), the melt undergoes complex thermophysical processes within the cold hearth and crystallizer. Precise control of process parameters such as the shape and depth of the molten pool, the morphology of the solidification interface, and the smelting power and casting speed is necessary to suppress the segregation of these elements caused by solute redistribution and hot solute convection. The purity of the raw materials, the rationality of the selection of smelting process parameters (such as electron beam power, scanning method, and cooling rate), and the rigor of process control are key factors in controlling the uniformity of C, N, O, and Fe distribution in TA1 ingots. The core scientific question lies in elucidating the migration, enrichment, and solidification distribution behavior of these elements during smelting, and revealing the coupling mechanism between heat transfer, flow, mass transfer, and the evolution of the solidification interface.

[0004] However, due to the complex environment of the electron beam cold hearth furnace, including high temperature, vacuum, metal vapor, and electron beam interference, it is extremely difficult to directly observe the distribution and evolution of elements in the melt online. Therefore, constructing a multiphysics numerical model that couples the temperature field, flow field, and concentration field has become an important means to analyze the distribution patterns of C, N, O, and Fe elements in TA1 ingots, predict segregation tendencies, and optimize the process. Summary of the Invention

[0005] To address the aforementioned problems, this invention provides an analytical method for the multi-element distribution characteristics in TA1 ingots. Based on finite element numerical simulation software, a numerical model of electron beam cold hearth furnace melting (EBCHM) is established. First, crystallizer dimensions and process parameters are collected based on the actual TA1 production process. A geometric model is then established, element types are defined, material physical property parameters are assigned, and a mesh is generated. Using k... The ε-turbulence model was used to calculate the flow field distribution in the fluid domain of the crystallizer, and the Solidification and Melting model was used to calculate the molten pool morphology during continuous casting solidification. User-defined functions (UDFs) for solute redistribution coefficients of carbon, nitrogen, oxygen, and iron were written using C language combined with Fluent-specific macros, and a UDF for hot solute buoyancy was established and added to the model as source terms. Finally, the simulation results were obtained using Fluent, and the distribution patterns of the four elements during solidification were analyzed using the post-processing software Tecplot. Simultaneously, actual sampling points were determined and samples were taken from TA1 plate slices melted in an electron beam cold hearth furnace. The samples were sent for testing: iron was analyzed using ICP, carbon and sulfur using a carbon-sulfur analyzer, and oxygen using an oxygen-nitrogen-hydrogen analyzer. The experimental results were compared with the numerical simulation results to determine the final accurate distribution characteristics. This invention can systematically reveal the microscopic and macroscopic distribution patterns and segregation causes of key impurity elements in TA1 ingots, providing theoretical support for the optimization of electron beam cold hearth furnace melting process and effectively solving the problem of uneven composition in TA1 ingots.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a method for analyzing the distribution characteristics of multiple elements in TA1 ingots, specifically including the following steps: S1. Determination of geometric model parameters: Based on the actual TA1 production process in the electron beam cold hearth furnace, collect crystallizer size parameters and process parameters.

[0007] The process parameters mentioned are common production process parameters, generally including casting speed, pouring speed, pouring temperature and heat transfer coefficient.

[0008] S2. Establish a geometric model: Based on the crystallizer size parameters and process parameters collected in S1, establish a geometric model. After performing mesh generation on the geometric model, define the unit type and set the thermophysical parameters of the TA1 matrix, as well as the solute transport parameters of carbon, nitrogen, oxygen, and iron elements contained in TA1.

[0009] S3. Establish multi-physics field coupling control equations: Based on the geometric model established in S2 and the thermophysical parameters of the TA1 matrix, the solute transport parameters of carbon, nitrogen, oxygen and iron elements, a set of conservation equations describing mass, momentum, heat and solute transport during solidification is established by constructing multi-physics field coupling control equations. The conservation equations specifically include: the mass conservation equation, the momentum conservation equation, the turbulence model, the energy conservation equation, the solute conservation equation, and a closed set of equations for the microsegregation model.

[0010] S4. Establish the melting and solidification model: Based on the multi-physics field coupled control equations constructed in S3, the morphology of the molten pool during continuous casting solidification is obtained by activating the Solidification and Melting model and the k-ε turbulence model in ANSYS Fluent and performing steady-state iterative solution.

[0011] S5. To address the segregation behavior of carbon, nitrogen, oxygen, and iron and the buoyancy effect of hot solutes during the solidification process of TA1, a solute redistribution UDF and a hot solute buoyancy UDF were written in C language using Fluent's dedicated macros, and then compiled and loaded into the solver. The solute redistribution UDF takes the solute redistribution coefficients of the four elements as input parameters. The hot solute buoyancy UDF is embedded in the momentum conservation equation in the form of a hot solute buoyancy source term.

[0012] S6. Using the molten pool morphology obtained in S4 during continuous casting solidification, load the UDF written in S5, activate the solute conservation equation, and perform transient iterative calculations. Extract the concentration field distribution of carbon, nitrogen, oxygen, and iron at the solid-liquid front to obtain numerical simulation results. Use Tecplot post-processing software to analyze the distribution patterns of carbon, nitrogen, oxygen, and iron during the solidification process.

[0013] S7. Experimental Sampling and Testing: For TA1 titanium plates smelted in electron beam cold hearth furnace, determine the actual sampling locations and number the samples after sampling. Measure the content of carbon, nitrogen, oxygen, and iron at each sampling point. Specifically, the samples were sent for testing. Iron was detected using ICP, carbon was detected using a carbon-sulfur analyzer, and oxygen and nitrogen were detected using an oxygen-nitrogen-hydrogen analyzer. The final results were then plotted into charts.

[0014] S8. Result Comparison and Verification: Compare the detection results of S7 with the numerical simulation results of S6 to verify and determine the distribution characteristics of carbon, nitrogen, oxygen and iron elements in TA1 ingot.

[0015] Preferably, in step S3, the formation of center segregation is closely related to flow, heat, and component transport phenomena. Therefore, it is necessary to solve the conservation equations describing mass, momentum, heat, and solute transport, specifically including the following steps: S3.1 Construct the mass conservation equation based on the thermophysical parameters of the TA1 matrix; The expression for the mass equation is as follows: In the formula, For the mixed phase density, For time, For fluid The velocity component in the direction, for The coordinate components of the direction; S3.2 Based on the thermophysical parameters of the TA1 matrix, a momentum conservation equation is constructed by introducing the effective viscosity, the damping source term of the paste region, and the buoyancy source term of the hot solute. The equation for the conservation of momentum is expressed as follows: In the formula, For effective viscosity, For the damping source term in the mushy region, For the buoyancy source of hot solutes, For fluid The velocity component in the direction, For fluid The velocity component in the direction, , Represents the direction components of spatial coordinates, and , for The coordinate components of the direction, For pressure, The component of gravitational acceleration in the direction of gravity; The formula for calculating the effective viscosity is as follows: In the formula, Molecular dynamic viscosity, These are empirical constants for the turbulence model. For turbulent kinetic energy, The turbulent kinetic energy dissipation rate; The calculation expression for the damping source term in the mushy region is as follows: In the formula, It is the liquid volume fraction. The morphological constant of the pasty region, For solid phase The casting speed in the direction of the billet pulling; The calculation expression for the hot solute buoyancy source term is as follows: In the formula, The coefficient of thermal expansion is For temperature, Liquidus temperature Let be the solute swelling coefficient of the m-th element. Let m be the concentration of the m-th element in the liquid phase. Let m be the initial concentration of the m-th element, where m is the element index. ; S3.3 Based on the momentum conservation equation, the standard k-ε equation is used to describe the turbulence effect and a turbulence model is constructed. The calculation expression for the standard k-ε equation is as follows: In the formula, For the mushy region damping source term in the turbulent kinetic energy equation, For the mushy region damping source term in the dissipation rate equation, For turbulent viscosity, The turbulent Prandtl number is the turbulent kinetic energy. The Prandtl number is the turbulent kinetic energy dissipation rate. For the turbulent kinetic energy generation term, These are empirical constants for the turbulence model. These are empirical constants for the turbulence model; The calculation expression for the mushy region damping source term in the turbulent kinetic energy equation is as follows: The calculation expression for the mushy region damping source term in the dissipation rate equation is as follows: S3.4. Based on the thermophysical parameters of the TA1 matrix, construct the energy conservation equation; The calculation expression for the energy conservation equation is as follows: In the formula, For total enthalpy, For turbulent Prandtl number, Specific heat capacity at constant pressure; The expression for calculating the total enthalpy term is as follows: In the formula, For manifest enthalpy, The latent enthalpy of phase transition, The reference enthalpy at the reference temperature, For reference temperature, Latent heat of fusion; solidus temperature of the mixture With liquidus temperature The calculation is as follows: In the formula, The melting point of pure titanium TA1, Let be the slope of the liquidus line for the m-th element. Let m be the concentration of the m-th element in the mixture. Let be the solute redistribution coefficient of the m-th element; S3.5 Based on the solute transport parameters of carbon, nitrogen, oxygen and iron contained in TA1, construct the solute conservation equation; The calculation expression for the solute conservation equation is as follows: In the formula, and These are diffusion source terms and convection source terms, respectively. For transient terms, For convection terms, Let m be the diffusion coefficient of element m in the liquid phase; The calculation expression for the diffusion source term is: In the formula, The solid fraction, Let m be the diffusion coefficient of element m in the solid phase. Let m be the concentration of the m-th element in the liquid phase. Let m be the concentration of the m-th element in the solid phase. Let m be the concentration of the m-th element in the mixture; The calculation expression for the convection source term is: In the formula, For solid phase The speed of movement in the direction; S3.6 Based on the solute conservation equation and the lever law, construct a closed set of equations for the microsegregation model; The closed set of equations for the microsegregation model includes: the liquid phase fraction iterative update equation, the interface equilibrium temperature equation, the solid-liquid phase fraction normalization equation, the liquid phase concentration-mixed concentration correlation equation, and the solid phase concentration-mixed concentration correlation equation. The calculation expression for the liquid phase fraction iterative update equation is as follows: In the formula, The liquid phase fraction for the next iteration. The liquid phase fraction in the current iteration step. As a sub-relaxation factor, The heat transfer coefficient of the grid cell. To balance the temperature at the interface, For time step, For latent heat of fusion, For the volume of the grid cell; The calculation expression for the interface equilibrium temperature equation is as follows: The calculation expression for the normalized equation of the solid-liquid phase fraction is as follows: Based on classical mixture theory, the mixing concentration of the m-th element... Defined as: The calculation expression for the liquid phase concentration-mixing concentration correlation is as follows: In the formula, Let be the solute redistribution coefficient of the m-th element; The expression for the solid concentration-mixing concentration correlation is as follows: .

[0016] Compared with the prior art, the present invention provides an analytical method for the distribution characteristics of multiple elements in TA1 ingots, which has the following beneficial effects: This invention establishes a 16-point element concentration detection system covering the longitudinal and transverse directions of the ingot, systematically revealing the macroscopic distribution patterns of C, N, O, and Fe in EB furnace-smelted T1 titanium ingots: Fe concentration fluctuates significantly in the longitudinal direction (0.025-0.05wt%), with a "high concentration in the middle and low concentration on both sides" on the outer side of the slab; C concentration is "high concentration in the middle and low concentration on both sides" in both the longitudinal and transverse directions, with greater fluctuations on the outer side of the slab due to its distance from the overflow outlet; O concentration is higher in the front and middle of the longitudinal direction, with a "low concentration in the middle and high concentration on both sides" negative segregation on the outer side of the slab; N concentration is dispersed at high values ​​in the longitudinal direction, uniform on the outer side of the slab and exhibits negative segregation, indicating that the uniformity of sidewall cooling has a significant effect on suppressing segregation. Further relying on ANSYS FLUENT and combining authoritative solute redistribution coefficients (Fe 0.270342, N 35.9667, O 1.39329, C 0.50431) and physical parameters, a coupled temperature-fluid-concentration field model was constructed. This model clarified the mechanism by which elements are enriched at the solid-liquid front when the solute redistribution coefficient is <1 (Fe, C), and preferentially precipitated in the condensation shell when the coefficient is >1 (N, O). Through "steady-state first, then transient" simulation (step size 0.005s), the simulation results highly matched the elemental segregation patterns, and the 1.7 million fine mesh (minimum 0.1mm³) ensured the accuracy of the calculations. This invention achieves mutual verification between experimental detection and numerical simulation, accurately predicting the distribution characteristics and segregation causes of C, N, O, and Fe in TA1 ingots, providing a reliable theoretical basis and technical support for optimizing the electron beam cold hearth furnace melting process and suppressing compositional inhomogeneity. Attached Figure Description

[0017] Figure 1 This is a flowchart of an analytical method for the distribution characteristics of multiple elements in TA1 ingots according to the present invention; Figure 2 This is a diagram of the molten pool morphology in the numerical model established in this invention. Figure 3 The distribution diagram of the four elements carbon, nitrogen, oxygen, and iron in the model established in this invention, wherein, Figure 3 In the middle (a), carbon is represented. Figure 3 (b) represents nitrogen. Figure 3 (c) represents oxygen. Figure 3 (d) represents iron. Figure 4 The distribution diagram of carbon, nitrogen, oxygen, and iron in the solid-liquid front section of the model established in this invention, wherein... Figure 4 (a) represents carbon. Figure 4 (b) represents nitrogen. Figure 4 (c) represents oxygen. Figure 4 (d) represents iron. Figure 5 Schematic diagram of the sampling scheme for TA1 slices melted in an electron beam cold hearth furnace; Figure 6 This is a display of 16 samples taken from the slides; Figure 7 This is a graph showing the carbon element detection results for a sample. Figure 7 (a) shows the concentration distribution of element C at 8 points along the vertical axis; Figure 7 (b) shows the concentration distribution of element C at 5 points horizontally below; Figure 7 (c) shows the concentration distribution of element C at 5 points horizontally; Figure 8 This is a graph showing the results of nitrogen element analysis in a sample. Figure 8 (a) shows the concentration distribution of N element at 8 points along the vertical axis; Figure 8 (b) shows the concentration distribution of N element at 5 points in the horizontal direction; Figure 8 (c) shows the concentration distribution of N element at 5 points horizontally; Figure 9 This is a graph showing the results of oxygen element analysis in a sample. Figure 9 (a) shows the concentration distribution of element O at 8 points along the vertical axis; Figure 9 (b) shows the concentration distribution of O element at 5 points in the horizontal direction; Figure 9 (c) shows the concentration distribution of O element at 5 points on the horizontal axis; Figure 10 The results of the iron element test are as follows: Figure 10 (a) shows the concentration distribution of Fe at 8 points along the vertical axis; Figure 10 (b) shows the concentration distribution of Fe at 5 points in the horizontal direction; Figure 10 (c) shows the concentration distribution of Fe at 5 points on the horizontal axis. Detailed Implementation

[0018] Various exemplary embodiments of the present invention will now be described in detail. This detailed description should not be considered as a limitation of the present invention, but rather as a more detailed description of certain aspects, features, and embodiments of the present invention. It should be understood that the terminology used in this invention is merely for describing particular embodiments and is not intended to limit the present invention.

[0019] Furthermore, regarding the numerical ranges in this invention, it should be understood that each intermediate value between the upper and lower limits of the range is also specifically disclosed. Every smaller range between any stated value or intermediate value within a stated range, and any other stated value or intermediate value within said range, is also included within this invention. The upper and lower limits of these smaller ranges may be independently included or excluded from the range.

[0020] Unless otherwise stated, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art. While only preferred methods and materials have been described herein, any methods and materials similar or equivalent to those described herein may be used in the implementation or testing of this invention. All references to this specification are incorporated by way of citation to disclose and describe methods and / or materials associated with those references. In the event of any conflict with any incorporated reference, the content of this specification shall prevail.

[0021] Various modifications and variations can be made to the specific embodiments described in this specification without departing from the scope or spirit of the invention, as will be apparent to those skilled in the art. Other embodiments derived from this specification will also be apparent to those skilled in the art. This specification and embodiments are merely exemplary.

[0022] The terms “include,” “including,” “have,” “contain,” etc., used in this article are all open-ended terms, meaning that they include but are not limited to.

[0023] Example 1 This implementation method provides an analytical approach to the distribution characteristics of carbon, nitrogen, oxygen, and iron elements in TA1 ingots based on experiments and numerical simulations. Figure 1 As shown, the specific steps include: S1. Determination of geometric model parameters: Based on the actual TA1 production process in the electron beam cold hearth furnace, collect crystallizer size parameters and process parameters.

[0024] The process parameters mentioned are common production process parameters, generally including casting speed, pouring speed, pouring temperature and heat transfer coefficient.

[0025] S2. Establish a geometric model: Based on the crystallizer size parameters and process parameters collected in S1, establish a geometric model. After performing mesh generation on the geometric model, define the unit type and set the thermophysical parameters of the TA1 matrix, as well as the solute transport parameters of carbon, nitrogen, oxygen, and iron elements contained in TA1.

[0026] S3. Establish multi-physics field coupling control equations: Based on the geometric model established in S2 and the thermophysical parameters of the TA1 matrix, the solute transport parameters of carbon, nitrogen, oxygen and iron elements, a set of conservation equations describing mass, momentum, heat and solute transport during solidification is established by constructing multi-physics field coupling control equations. The conservation equations specifically include: the mass conservation equation, the momentum conservation equation, the turbulence model, the energy conservation equation, the solute conservation equation, and a closed set of equations for the microsegregation model.

[0027] The expression for the mass equation is as follows: In the formula, For the mixed phase density, For time, For fluid The velocity component in the direction, for The coordinate components of the direction; The equation for the conservation of momentum is expressed as follows: In the formula, For effective viscosity, For the damping source term in the mushy region, For the buoyancy source of hot solutes, For fluid The velocity component in the direction, For fluid The velocity component in the direction, , Represents the direction components of spatial coordinates, and , for The coordinate components of the direction, For pressure, The component of gravitational acceleration in the direction of gravity; The formula for calculating the effective viscosity is as follows: In the formula, Molecular dynamic viscosity, These are empirical constants for the turbulence model. For turbulent kinetic energy, The turbulent kinetic energy dissipation rate; The calculation expression for the damping source term in the mushy region is as follows: In the formula, It is the liquid volume fraction. The morphological constant of the pasty region, For solid phase The casting speed in the direction of the billet pulling; The calculation expression for the hot solute buoyancy source term is as follows: In the formula, The coefficient of thermal expansion is For temperature, Liquidus temperature Let be the solute swelling coefficient of the m-th element. Let m be the concentration of the m-th element in the liquid phase. Let m be the initial concentration of the m-th element, where m is the element index. ; The calculation expression for the standard k-ε equation is as follows: In the formula, For the mushy region damping source term in the turbulent kinetic energy equation, For the mushy region damping source term in the dissipation rate equation, For turbulent viscosity, The turbulent Prandtl number is the turbulent kinetic energy. The Prandtl number is the turbulent kinetic energy dissipation rate. For the turbulent kinetic energy generation term, These are empirical constants for the turbulence model. These are empirical constants for the turbulence model; The calculation expression for the mushy region damping source term in the turbulent kinetic energy equation is as follows: The calculation expression for the mushy region damping source term in the dissipation rate equation is as follows: The recommended standard parameter values ​​in this embodiment are: =1.0、 =1.3、 =1.44、 =1.92、 =0.09.

[0028] The calculation expression for the energy conservation equation is as follows: In the formula, For total enthalpy, For turbulent Prandtl number, Specific heat capacity at constant pressure; The expression for calculating the total enthalpy term is as follows: In the formula, For manifest enthalpy, The latent enthalpy of phase transition, The reference enthalpy at the reference temperature, For reference temperature, Latent heat of fusion; solidus temperature of the mixture With liquidus temperature The calculation is as follows: In the formula, The melting point of pure titanium TA1, Let be the slope of the liquidus line for the m-th element. Let m be the concentration of the m-th element in the mixture. Let be the solute redistribution coefficient of the m-th element; The calculation expression for the solute conservation equation is as follows: In the formula, and These are diffusion source terms and convection source terms, respectively. For transient terms, For convection terms, Let m be the diffusion coefficient of element m in the liquid phase; The calculation expression for the diffusion source term is: In the formula, The solid fraction, Let m be the diffusion coefficient of element m in the solid phase. Let m be the concentration of the m-th element in the liquid phase. Let m be the concentration of the m-th element in the solid phase. Let m be the concentration of the m-th element in the mixture; The calculation expression for the convection source term is: In the formula, For solid phase The speed of movement in the direction; The closed set of equations for the microsegregation model includes: the liquid phase fraction iterative update equation, the interface equilibrium temperature equation, the solid-liquid phase fraction normalization equation, the liquid phase concentration-mixed concentration correlation equation, and the solid phase concentration-mixed concentration correlation equation. The calculation expression for the liquid phase fraction iterative update equation is as follows: In the formula, The liquid phase fraction for the next iteration. The liquid phase fraction in the current iteration step. As a sub-relaxation factor, The heat transfer coefficient of the grid cell. To balance the temperature at the interface, For time step, For latent heat of fusion, For the volume of the grid cell; The calculation expression for the interface equilibrium temperature equation is as follows: The calculation expression for the normalized equation of the solid-liquid phase fraction is as follows: Based on classical mixture theory, the mixing concentration of the m-th element... Defined as: The calculation expression for the liquid phase concentration-mixing concentration correlation is as follows: In the formula, Let be the solute redistribution coefficient of the m-th element; The expression for the solid concentration-mixing concentration correlation is as follows: .

[0029] S4. Establishing a melting and solidification model: Based on the multiphysics coupled control equations constructed in S3, the morphology of the molten pool during continuous casting solidification is obtained by activating the Solidification and Melting model and the k-ε turbulence model in ANSYS Fluent and performing steady-state iterative solutions. Figure 2 The figure shown is a morphology diagram of the molten pool in the numerical model established in this invention.

[0030] S5. To address the segregation behavior of carbon, nitrogen, oxygen, and iron and the buoyancy effect of hot solutes during the solidification process of TA1, a solute redistribution UDF and a hot solute buoyancy UDF were written in C language using Fluent's dedicated macros, and then compiled and loaded into the solver. The solute redistribution UDF takes the solute redistribution coefficients of the four elements as input parameters. The hot solute buoyancy UDF is embedded in the momentum conservation equation in the form of a hot solute buoyancy source term.

[0031] S6. Using the molten pool morphology obtained in S4 during continuous casting solidification, the UDF written in S5 is loaded, the solute conservation equation is activated, and transient iterative calculations are performed. The concentration field distribution of carbon, nitrogen, oxygen, and iron at the solid-liquid front is extracted to obtain numerical simulation results. The distribution patterns of carbon, nitrogen, oxygen, and iron during solidification are analyzed using Tecplot post-processing software, such as... Figure 3 and Figure 4 As shown, Figure 3 To solve for the elemental concentration distribution after transient iteration, Figure 4 This represents the elemental concentration distribution extracted along the solidification front.

[0032] S7. Experimental Sampling and Testing: For TA1 titanium plates melted in an electron beam cold hearth furnace, determine the actual sampling locations, number the samples taken, and determine the content of carbon, nitrogen, oxygen, and iron at each sampling point. Figure 5 and Figure 6 As shown; Figure 5 The image shows 16 samples taken from the slice, specifically 16 points, divided into 8 points vertically (points 1, 2, 5, 8, 9, 12, 15, 16), 5 points horizontally at the bottom (points 3, 4, 5, 6, 7), and 5 points horizontally at the top (points 10, 11, 12, 13, 14).

[0033] Specifically, the samples were sent for testing. Iron was detected using ICP, carbon was detected using a carbon-sulfur analyzer, and oxygen and nitrogen were detected using an oxygen-nitrogen-hydrogen analyzer. The final results were then plotted into charts.

[0034] S8. Result Comparison and Verification: Compare the detection results of S7 with the numerical simulation results of S6 to verify and determine the distribution characteristics of carbon, nitrogen, oxygen and iron elements in TA1 ingot.

[0035] Example 2 The concentration distribution characteristics of element C at 8 points (points 1, 2, 5, 8, 9, 12, 15, 16) in the vertical direction, as follows: Figure 7As shown in (a), the detection points are distributed along the central axis of the TA1 titanium slab, reflecting the distribution pattern of C element in the longitudinal central region. The data shows that the overall C element concentration is in the range of 0.012wt%-0.035wt%, with significant fluctuations: point 12 has the highest concentration at 0.035wt%, point 1 has a concentration of 0.03wt%, and points 5 and 11 both have a concentration of 0.026wt%. Low concentration points also exist, such as point 9 (0.013wt%) and point 10 (0.012wt%), with a concentration difference of approximately 0.023wt%. This discontinuous concentration variation along the central axis indicates macroscopic segregation of C element in the longitudinal central region of the titanium slab. The concentration distribution at the five points (points 3, 4, 5, 6, and 7) in the lower transverse direction is shown below. Figure 7 As shown in (b), the overall C element concentration in this area is concentrated, with a stable range of 0.017wt%-0.026wt% and small fluctuations. Point 5 has the highest concentration at 0.026wt%, while points 3 and 4 have the lowest concentrations at 0.017wt%. Points 6 and 7 have the same concentration at 0.019wt%, exhibiting a central segregation characteristic of "high in the middle and low on both sides." The maximum concentration difference between the detection points is only 0.009wt%, a distribution pattern consistent with segregation when the solute redistribution coefficient is less than 1. The C element concentration distribution at the five horizontal points (points 10, 11, 12, 13, and 14) is shown below. Figure 7 As shown in (c), compared to the lower horizontal region, the upper horizontal region, being farther from the overflow outlet, exhibits significantly increased C element concentration fluctuations, with the concentration range extending to 0.012%-0.035%. Point 12 shows the highest concentration at 0.035 wt%, representing the peak concentration in this horizontal group; point 10 shows the lowest concentration at only 0.012 wt%, the lowest among all 16 detection points; the concentrations at the remaining points (points 11, 13, and 14) are 0.026 wt%, 0.022 wt%, and 0.021 wt%, respectively. The concentration difference between high and low C elements in this region reaches 0.023 wt%, and the concentration distribution still exhibits a "high in the middle, low on both sides" pattern, consistent with the typical characteristics of central segregation.

[0036] Example 3 The distribution characteristics of element N at 8 points (points 1, 2, 5, 8, 9, 12, 15, 16) in the vertical direction, such as... Figure 8As shown in (a), this group of measuring points is set along the central axis of the TA1 titanium slab and is the key observation object for revealing the distribution law of N element in the longitudinal central region. From the detection data, the N element concentration is generally controlled in the range of 0.002wt%-0.016wt%, and shows a differentiated fluctuation characteristic of "dispersed high values ​​and low values ​​at the front end": the high concentration measuring points have no obvious clustering, among which point 15 has the highest concentration of 0.015wt%, followed by point 11 (0.014wt%), point 8 and point 9 (both 0.011wt%); the low concentration measuring points are concentrated at the longitudinal front end, with point 1 having the lowest concentration (0.003wt%), and points 2 and 4 (both 0.005wt%) also at a low level, with the difference between high and low concentrations reaching 0.012wt%. The discontinuous concentration fluctuations along the central axis directly confirm the macroscopic segregation of nitrogen (N) in the longitudinal central region of the titanium slab. Its distribution exhibits a similar "discontinuity" to the segregation characteristics of oxygen (O) in the longitudinal direction, while also demonstrating elemental specificity in the spatial distribution of high / low concentration measurement points. For example... Figure 8 As shown in (b), the concentration distribution at the five points (points 3, 4, 5, 6, and 7) in the lower transverse direction is shown. This group of measuring points is arranged along the lower transverse section of the TA1 titanium slab and is the core observation group for capturing the differences in the distribution of N element in the transverse region. The data shows that the nitrogen concentration in this region exhibits an "extremely polarized" characteristic: the overall range extends beyond the vertical range, reaching 0.005wt%-0.045wt%, with fluctuations far exceeding those in the vertical range—point 6 becomes the abnormal enrichment point in the entire detection system, with a concentration as high as 0.042wt%, not only the peak value in this horizontal group but also the highest value among the 16 detection points, its concentration being 4-4.7 times that of adjacent points in the same region (point 5 at 0.01wt%, point 7 at 0.009wt%); the concentrations at the other four detection points are relatively flat, with points 3 (0.009wt%), 5 (0.01wt%), and 7 (0.009wt%) having similar concentrations, while point 4 has the lowest concentration in this group at 0.005wt%, and the maximum concentration difference between the detection points reaches 0.037wt%. Figure 8 As shown in (c), the concentration distribution characteristics of the five points (points 10, 11, 12, 13, and 14) in the upper horizontal direction are as follows. Compared with the lower horizontal region, the overall N element concentration distribution in this region is more concentrated, with the range narrowing to 0.009wt%-0.014wt%, and the fluctuation range is significantly reduced: point 11 has the highest concentration (0.014wt%), points 10, 12, and 14 have the same concentration (all 0.011wt%), and point 13 has the lowest concentration (0.009wt%). The maximum concentration difference between the detection points is only 0.005wt%. The overall distribution shows a negative segregation trend of "low in the middle and high on both sides". Only the concentration at point 10 deviates slightly from the theoretical trend, which is presumably due to testing error.

[0037] Example 4 The distribution characteristics of element O at 8 points (points 1, 2, 5, 8, 9, 12, 15, 16) in the vertical direction, as follows: Figure 9 As shown in (a), this group of measuring points is arranged along the central axis of the TA1 titanium slab and is the core observation object characterizing the distribution pattern of O element in the longitudinal central region. From the concentration data, the overall O element concentration is in the range of 0.06wt%-0.13wt%, exhibiting non-smooth fluctuations: the concentrations at the front and middle measuring points are generally higher, with point 5 reaching 0.122wt% and point 3 at 0.115wt%, forming a high-concentration cluster within the region; low-concentration measuring points show no obvious aggregation, with point 12 having the lowest concentration at 0.062wt%, and points 7 (0.066wt%), 8 (0.068wt%), and 16 (0.067wt%) also at low levels, with a high-to-low concentration difference of 0.06wt%. The discontinuous concentration fluctuations along the axis confirm that there is significant macroscopic segregation of O element in the longitudinal central region of the titanium slab, the cause of which is directly related to the stress during the rolling stage of the material, or the element migration and aggregation effects in the central region during solidification. Figure 9 The concentration distribution at five points (points 3, 4, 5, 6, and 7) in the lower horizontal direction (b) is shown in Figure 2. Compared to the vertical region, the concentration fluctuation of O element in this horizontal region is significantly increased, with the overall range expanding to 0.06wt%-0.24wt%, and showing a markedly high value: the concentration at point 6 reaches as high as 0.235wt%, which is not only the peak value of this horizontal group but also the highest value among all 16 detection points, with a significant difference in concentration compared to other points in the same region; the concentration changes at the other detection points are relatively gradual, with points 5 (0.122wt%) and 3 (0.115wt%) at relatively high levels, while points 4 (0.084wt%) and 7 (0.066wt%) are at low levels, and the maximum concentration difference between the detection points reaches 0.169wt%. From a theoretical perspective, because the solute redistribution coefficient of O element is greater than 1, the solute is easily precipitated in the solidified shell during the solidification process, and theoretically, it should exhibit a negative segregation characteristic of "low in the middle and high on both sides". However, due to testing errors, the results of this horizontal group did not reflect this regular distribution. Therefore, five additional horizontal detection points were added to further verify the horizontal distribution pattern of element O. Figure 9The concentration distribution characteristics at the five points (points 10, 11, 12, 13, and 14) in the upper horizontal direction (c) are shown. Compared with the lower horizontal region, the overall O element concentration distribution in this region is more concentrated, narrowing to 0.06wt%-0.09wt%, with significantly reduced fluctuations. Point 10 has the highest concentration (0.088wt%), while point 12 has the lowest (0.062wt%). The concentrations at the other points (points 11, 13, and 14) are 0.078wt%, 0.079wt%, and 0.087wt%, respectively. The maximum concentration difference between the detection points is only 0.026wt%, exhibiting a typical negative segregation distribution characteristic of "low in the middle and high on both sides." The weak O element segregation in this region is presumably related to the location characteristics of the measurement points near the sidewalls—the sidewall region cools more uniformly during solidification, resulting in less element replenishment and limited element migration, thus reducing concentration differences.

[0038] Example 5 The concentration distribution of Fe element at 8 points along the vertical axis, as follows: Figure 10 As shown in (a), the eight detection points are distributed along the central axis of the titanium slab, serving as key measurement points reflecting the elemental distribution characteristics in the longitudinal central region of the material. In the longitudinal dimension, the Fe element concentration at the eight detection points distributed along this central axis exhibits significant fluctuations within the range of 0.025 wt%–0.05 wt%, with particularly pronounced concentration differences between adjacent detection points. Some detection points have concentrations close to 0.05 wt%, while adjacent points drop sharply to below 0.03 wt%. This discontinuous variation along the central axis clearly reflects a significant macroscopic segregation of Fe element in the longitudinal central region, further confirming that this segregation phenomenon is closely related to the migration and accumulation of elements in the central region during the rolling or solidification process of the titanium slab. Figure 10 As shown in (b), the concentration distribution at the five points in the lower horizontal direction shows that the iron concentration in this region is relatively concentrated in the range of 0.032wt%-0.042wt%. The concentration at different numbered detection points shows only slight fluctuations with small amplitude, indicating relatively weak segregation. The elemental distribution in the lower horizontal region does not exhibit the expected "high in the middle, low at both ends" pattern. To minimize the potential errors of a single test group, two sets of horizontal distribution tests were specifically set up (lower horizontal and upper horizontal) to improve the reliability of the results through comparative analysis of multiple sets of data. Figure 10 As shown in (c), the concentration distribution at the five points in the upper horizontal direction: the iron concentration in this region ranges from 0.034 wt% to 0.048 wt%, exhibiting a typical "high in the middle, low on both sides" central segregation characteristic. Further comparison reveals that the concentration at the detection points in the upper horizontal direction is significantly higher than the corresponding positions in the lower horizontal direction, and a concentration peak of 0.00048 wt% appears at a specific point, indicating that the local segregation phenomenon is more prominent in the upper horizontal region.

Claims

1. An analytical method for the distribution characteristics of multiple elements in TA1 ingots, characterized in that, Includes the following steps: S1. Determination of geometric model parameters: Based on the actual TA1 production process of electron beam cold hearth furnace melting, collect crystallizer size parameters and process parameters; S2. Establish a geometric model: Based on the crystallizer size parameters and process parameters collected in S1, establish a geometric model. After performing mesh generation on the geometric model, define the element type and set the thermophysical parameters of the TA1 matrix, as well as the solute transport parameters of carbon, nitrogen, oxygen, and iron elements contained in TA1. S3. Establish multi-physics field coupling control equations: Based on the geometric model established in S2 and the thermophysical parameters of the TA1 matrix, the solute transport parameters of carbon, nitrogen, oxygen and iron elements, a set of conservation equations describing mass, momentum, heat and solute transport during solidification is established by constructing multi-physics field coupling control equations. The conservation equations specifically include: the mass conservation equation, the momentum conservation equation, the turbulence model, the energy conservation equation, the solute conservation equation, and the closed set of equations for the microsegregation model; S4. Establish the melting and solidification model: Based on the multi-physics field coupled control equations constructed in S3, the morphology of the molten pool during continuous casting solidification is obtained by activating the Solidification and Melting model and the k-ε turbulence model in ANSYS Fluent and performing steady-state iterative solution. S5. To address the segregation behavior of carbon, nitrogen, oxygen, and iron and the buoyancy effect of hot solutes during the solidification process of TA1, a solute redistribution UDF and a hot solute buoyancy UDF were written in C language using Fluent's dedicated macros, and then compiled and loaded into the solver. S6. Using the molten pool morphology obtained in S4 during continuous casting solidification, load the UDF written in S5, activate the solute conservation equation, and perform transient iterative calculations to obtain the numerical simulation results of the concentration field distribution of carbon, nitrogen, oxygen, and iron during the solidification process of TA1 ingot; use Tecplot post-processing software to analyze the distribution law of carbon, nitrogen, oxygen, and iron during the solidification process. S7. Experimental Sampling and Testing: For the TA1 plate slices melted by the electron beam cold hearth furnace, the actual sampling points are determined and samples are taken. The contents of carbon, nitrogen, oxygen and iron at each sampling point are measured and the test results are obtained. S8. Result Comparison and Verification: Compare the detection results of S7 with the numerical simulation results of S6 to verify and determine the distribution characteristics of carbon, nitrogen, oxygen and iron elements in TA1 ingot.

2. The analytical method for the distribution characteristics of multiple elements in a TA1 ingot according to claim 1, characterized in that, S3 specifically includes the following steps: S3.1 Construct the mass conservation equation based on the thermophysical parameters of the TA1 matrix; The expression for the mass conservation equation is as follows: ； In the formula, For the mixed phase density, For time, For fluid The velocity component in the direction, for The coordinate components of the direction; S3.2 Based on the thermophysical parameters of the TA1 matrix, a momentum conservation equation is constructed by introducing the effective viscosity, the damping source term of the paste region, and the buoyancy source term of the hot solute. The equation for the conservation of momentum is expressed as follows: ； In the formula, For effective viscosity, For the damping source term in the mushy region, For the buoyancy source of hot solutes, For fluid The velocity component in the direction, For fluid The velocity component in the direction, , Represents the direction components of spatial coordinates, and , for The coordinate components of the direction, For pressure, The component of gravitational acceleration in the direction of gravity; S3.3 Based on the momentum conservation equation, the standard k-ε equation is used to describe the turbulence effect and a turbulence model is constructed. The calculation expression for the standard k-ε equation is as follows: ； ； In the formula, For the mushy region damping source term in the turbulent kinetic energy equation, For the mushy region damping source term in the dissipation rate equation, For turbulent viscosity, The turbulent Prandtl number is the turbulent kinetic energy. The Prandtl number is the turbulent kinetic energy dissipation rate. For the turbulent kinetic energy generation term, and These are empirical constants for the turbulence model, and ; The calculation expression for the mushy region damping source term in the turbulent kinetic energy equation is as follows: ； The calculation expression for the mushy region damping source term in the dissipation rate equation is as follows: ； S3.

4. Based on the thermophysical parameters of the TA1 matrix, construct the energy conservation equation; The calculation expression for the energy conservation equation is as follows: ； In the formula, For total enthalpy, For turbulent Prandtl number, Specific heat capacity at constant pressure; The expression for calculating the total enthalpy term is as follows: ； In the formula, For manifest enthalpy, The latent enthalpy of phase transition, The reference enthalpy at the reference temperature, For reference temperature, Latent heat of fusion; solidus temperature of the mixture With liquidus temperature The calculation is as follows: In the formula, The melting point of pure titanium TA1, Let be the slope of the liquidus line for the m-th element. Let m be the concentration of the m-th element in the mixture. Let be the solute redistribution coefficient of the m-th element; S3.5 Based on the solute transport parameters of carbon, nitrogen, oxygen and iron contained in TA1, construct the solute conservation equation; The calculation expression for the solute conservation equation is as follows: ； In the formula, and These are diffusion source terms and convection source terms, respectively. For transient terms, For convection terms, Let m be the diffusion coefficient of element m in the liquid phase; S3.6 Based on the solute conservation equation and the lever law, construct a closed set of equations for the microsegregation model; The closed set of equations for the microsegregation model includes: the liquid phase fraction iterative update equation, the interface equilibrium temperature equation, the solid-liquid phase fraction normalization equation, the liquid phase concentration-mixed concentration correlation equation, and the solid phase concentration-mixed concentration correlation equation. The calculation expression for the liquid phase fraction iterative update equation is as follows: ； In the formula, The liquid phase fraction for the next iteration. The liquid phase fraction in the current iteration step. As a sub-relaxation factor, The heat transfer coefficient of the grid cell. To balance the temperature at the interface, For time step, For latent heat of fusion, For the volume of the grid cell; The calculation expression for the interface equilibrium temperature equation is as follows: ； The calculation expression for the normalized equation of the solid-liquid phase fraction is as follows: ； Based on mixture theory, the mixture concentration of the m-th element... Defined as: ； The calculation expression for the liquid phase concentration-mixing concentration correlation is as follows: ； In the formula, Let be the solute redistribution coefficient of the m-th element; The expression for the solid concentration-mixing concentration correlation is as follows: 。 3. The analytical method for the distribution characteristics of multiple elements in a TA1 ingot according to claim 2, characterized in that, In S3.2, the calculation expression for the effective viscosity is as follows: ； In the formula, Molecular dynamic viscosity, These are empirical constants for the turbulence model. For turbulent kinetic energy, The turbulent kinetic energy dissipation rate; The calculation expression for the damping source term in the mushy region is as follows: ； In the formula, It is the liquid volume fraction. The morphological constant of the pasty region, For solid phase The casting speed in the direction of the billet pulling; The calculation expression for the hot solute buoyancy source term is as follows: ； In the formula, The coefficient of thermal expansion is For temperature, Liquidus temperature Let be the solute swelling coefficient of the m-th element. Let m be the concentration of the m-th element in the liquid phase. Let m be the initial concentration of the m-th element, where m is the element index. .

4. The analytical method for the distribution characteristics of multiple elements in a TA1 ingot according to claim 3, characterized in that, In S3.4, the expression for calculating the total enthalpy term is as follows: ； In the formula, For manifest enthalpy, The latent enthalpy of phase transition, The reference enthalpy at the reference temperature, For reference temperature, This is the latent heat of fusion.

5. The analytical method for the distribution characteristics of multiple elements in a TA1 ingot according to claim 3, characterized in that, In S3.5, the calculation expression for the diffusion source term is: ； In the formula, The solid fraction, Let m be the diffusion coefficient of element m in the solid phase. Let m be the concentration of the m-th element in the liquid phase. Let m be the concentration of the m-th element in the solid phase. Let m be the concentration of the m-th element in the mixture; The calculation expression for the convection source term is: In the formula, For solid phase The speed of movement in a certain direction.

6. The analytical method for the distribution characteristics of multiple elements in a TA1 ingot according to claim 1, characterized in that, In S5, the solute redistribution UDF uses the solute redistribution coefficients of the four elements as input parameters; the hot solute buoyancy UDF embeds the momentum conservation equation in the form of a hot solute buoyancy source term.

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