CN113987892B

CN113987892B - Vacuum arc remelting 3D model for controlling segregation of high-temperature alloy and control method

Info

Publication number: CN113987892B
Application number: CN202111614333.XA
Authority: CN
Inventors: 曲敬龙; 陈正阳; 谷雨; 杜金辉; 杨树峰; 毕中南; 杨玉军; 田沛玉; 赵斌; 安腾; 孔豪豪; 王迪; 段方震; 史玉亭; 孟令胜
Original assignee: FUSHUN SPECIAL STEEL SHARES CO LTD; Central Iron and Steel Research Institute; University of Science and Technology Beijing USTB; Pangang Group Jiangyou Changcheng Special Steel Co Ltd; Gaona Aero Material Co Ltd; Baowu Special Metallurgy Co Ltd
Current assignee: FUSHUN SPECIAL STEEL SHARES CO LTD; Central Iron and Steel Research Institute; University of Science and Technology Beijing USTB; Pangang Group Jiangyou Changcheng Special Steel Co Ltd; Gaona Aero Material Co Ltd; Baowu Special Metallurgy Co Ltd
Priority date: 2021-12-28
Filing date: 2021-12-28
Publication date: 2022-04-29
Anticipated expiration: 2041-12-28
Also published as: CN113987892A

Abstract

The application relates to the field of vacuum arc remelting and discloses a vacuum arc remelting 3D model for controlling segregation of high-temperature alloy and a control method, wherein the vacuum arc remelting 3D model comprises a solidification heat transfer macro model, a solidification ingot casting micro model and a smelting process parameter model of the vacuum arc remelting high-temperature alloy; the control method comprises the following steps: step A, establishing a vacuum arc remelting 3D model; b, simulating process parameters; step C, simulating a smelting process; and D, smelting the high-temperature alloy. The method is based on the vacuum arc remelting 3D model, can convert the vacuum closed vacuum arc remelting smelting process into visual operation, can visually represent macro-microstructure of a solidified ingot, and can formulate more suitable smelting process parameters of the vacuum arc remelting high-temperature alloy, so that alloy segregation is reduced, the metallurgical quality is improved, and theoretical basis and engineering guidance are provided for adjustment and matching of the smelting process parameters and control of the solidified ingot structure and the smelting quality.

Description

Vacuum arc remelting 3D model for controlling segregation of high-temperature alloy and control method

Technical Field

The application relates to the field of vacuum arc remelting, in particular to a vacuum arc remelting 3D model for controlling segregation of high-temperature alloy and a control method.

Background

At present, the high-temperature alloy plays a very important role in national defense construction and national economic development, and is an indispensable key material for advanced ground combustion engines, aerospace engines and other high-end manufacturing industries. The high-temperature alloy gradually develops towards large size, high alloying and the like, more than ten strengthening elements such as Al, Ti, Nb, Co, Mo, Cr, W, Re and the like are required to be added to ensure that the alloy has proper high-temperature strength, excellent high-temperature oxidation or corrosion resistance and good structural stability, but the adopted strengthening elements also easily cause the alloy to form segregation due to low homogenization degree, so that the uniformity and the hot working plasticity of the alloy are reduced, and the service life and the working performance of the alloy are further seriously influenced.

For controlling the homogenization degree of the alloy, a source prevention mode is generally adopted at present, and mainly smelting equipment, technology, process and other methods are controlled to reduce the generation of segregation. However, in the triple smelting system of the high-temperature alloy, vacuum arc remelting is used as a final smelting process of the high-temperature alloy, and has important influence on ingot homogenization and metallurgical quality stability control.

For the control of the vacuum arc remelting process, the related technology at home and abroad adopts a computer simulation technology to predict and judge the smelting process and the ingot quality of the vacuum arc remelting high-temperature alloy, and then the internal segregation and the metallurgical quality of the alloy are controlled by adjusting and optimizing process parameters. In contrast, foreign researchers have already set up vacuum arc remelting 3D models, but the vacuum arc remelting simulation process involves multidimensional, multiphase, multiscale and multi-physical fields, and the solving process is complicated, so that at present, only a certain part (electrode, arc, solidified ingot and the like) of vacuum arc remelting is studied, but the simulation process of multidimensional, multiphase, multiscale and multi-physical fields cannot be realized.

For the vacuum Arc remelting simulation process for realizing multidimensional, multiphase, multiscale and multi-physical fields, foreign researchers couple the related single-sided models developed before together in a data sharing manner to form a bar (basic axial symmetry remetering) of a 2D model, a MeltFlow-VAR of the 2D model and a solar (solid reduction Arc remetering) of a 3D model, and realize the multidimensional, multiscale and multi-physical field simulation of the vacuum Arc remelting process through the software. For example, Patel et al uses BAR software to predict the temperature and flow field changes at different positions in the mushy zone in the vacuum arc remelting process in real time, but the software replaces the corresponding flow model with a method of multiplying the viscosity coefficient by a constant, which results in that the software cannot accurately represent the turbulent flow in the vacuum arc remelting process. The Meltflow-VAR software adopts a CFD (computational Fluid dynamics) flow model, makes up the defects of BAR software, and effectively predicts and analyzes evolution and heat transfer of a metal molten pool, heat transfer loss and current conduction between an ingot and a crystallizer, concentration distribution of alloy elements in the ingot, local solidification time and the like by combining corresponding modules of convection heat transfer, solidification, element distribution and the like, but both the Meltflow-VAR software and the BAR software are 2D models, and only linear stage change is considered in material physical parameter setting, so that the Meltflow-VAR software is not comprehensive and specific enough, and cannot represent microstructure morphology (grain size and orientation distribution) of the alloy ingot, and the segregation and metallurgical quality of the alloy ingot cannot be accurately predicted and controlled. While the SOlAR software has a similar CFD flow model as the Meltflow-VAR software, and combines modules such as a solidification micro model, PHYSICA software, an Euler-Euler model and the like, and by means of the control ideas of a genetic algorithm and an iterative algorithm, the electrodes with 2 or 3 successive VAR processes are continuously predicted, and 3D simulation of the microstructure of the cast ingot is realized, for example, Beaman et al simulates the influence of multiple vacuum arc remelting on the segregation of oxygen elements in a solidified ingot based on SOLAR software, and the simulation result shows that the situation of the segregation of the oxygen elements at the top end of the ingot can be effectively improved by multiple smelting, although the software is based on a 3D model, the software is mainly used for simulating a plurality of VAR smelting processes, and because the simulation process of the vacuum arc remelting process has the technical barrier problem at home and abroad, the vacuum arc remelting process is difficult to import to domestic application in China, and the detailed process of building a vacuum arc remelting 3D model at home and abroad is difficult to understand at home.

Therefore, China needs to independently research and develop the simulation process of the vacuum arc remelting process. However, compared with foreign countries, domestic basic research on temperature field, solidification field, heat transfer conditions and the like of a metal molten pool in a vacuum arc remelting process is still in an exploration stage, so that the domestic theoretical basis and conditions of a related metal molten pool model are lacked, a vacuum arc remelting 3D model cannot be established comprehensively and systematically, and the obtained research result is difficult to guide actual production, namely the problems of difficult control of internal segregation, metallurgical quality and the like of the alloy are solved.

Disclosure of Invention

In order to solve the problem that a vacuum arc remelting 3D model built in China is difficult to control alloy segregation in actual production, the application provides a vacuum arc remelting 3D model for controlling high-temperature alloy segregation and a control method.

In a first aspect, the application provides a vacuum arc remelting 3D model for controlling segregation of a high-temperature alloy, which adopts the following technical scheme:

a vacuum arc remelting 3D model for controlling the segregation of high-temperature alloy comprises a solidification heat transfer macro model, a solidification ingot casting micro model and a smelting process parameter model of the vacuum arc remelting high-temperature alloy;

the solidification heat transfer macro model comprises a convection heat transfer model between molten alloy and a solidification ingot, a conduction heat transfer model inside the solidification ingot, a heat transfer model between the solidification ingot and the inner wall of the crystallizer, a conduction heat transfer model between the inner wall and the outer wall of the crystallizer, and a convection heat transfer model between the outer wall of the crystallizer and cooling circulating water;

the solidification ingot casting micro model comprises a heat transfer model, a mass transfer model, a crystal face curvature model, a crystal grain nucleation model, a secondary dendrite spacing model and a dendrite growth dynamics model.

For establishing a systematic vacuum arc remelting 3D model, a few researchers in China carry out research on the vacuum arc remelting 3D model on the basis of Procast or Ansys commercial software, a geometric model of the model is established by using a finite element method, and then the establishment of the metal model is completed by setting simple boundary conditions such as the surface temperature of a metal molten pool, thermophysical parameters of alloy materials, the heat exchange coefficient of a crystallizer and the like, and the problems that the actual production is difficult to be guided by the obtained research result, the internal segregation and the metallurgical quality of the alloy are difficult to control and the like due to the lack of the setting of important boundary conditions such as the heat transfer process of the metal molten pool-helium-crystallizer, the motion state of alloy liquid in the metal molten pool, different heat exchange coefficients of the bottom and the side wall of an ingot and the like are caused. If a certain steel mill reduces the internal segregation of the alloy by improving the cooling strength of the cast ingot in the vacuum arc remelting process, the unilateral thinking that the larger the flow rate of the cooling circulating water is, the better the cooling performance of the cast ingot is, even the cooling circulating water pump in the original equipment is replaced by a water pump with higher power, but the steel mill neglects the key problem that the faster the flow rate of the cooling circulating water is, the shorter the contact time with the wall of a crystallizer is, so that the temperature difference of a water inlet and a water outlet is reduced, and the theoretical calculation and the arrangement and analysis of actual smelting data discover that the pursuit of the larger flow rate of the cooling circulating water is not beneficial to the improvement of the cooling strength of the cast ingot, but can play a role in inhibition, and the optimal flow rate of the cooling circulating water exists under different smelting conditions.

In contrast, the method is based on the smelting characteristics, the control flow and the computer simulation technology of the actual industrial vacuum arc remelting process, theoretically calculates the corresponding relation between multiple process parameters such as smelting voltage and current, melting rate, cooling circulating water flow, helium pressure and the like and control conditions such as arc temperature, heat introduction of a metal molten pool, heat brought away by cooling circulating water and the like, and establishes a multi-dimensional, multi-scale and multi-phase field coupling vacuum arc remelting 3D model by means of simulation software such as Solidworks, Thermal-Calc, Visual Studio, Procast and the like and simultaneously combining models such as a heat transfer model, a nucleation model, CAFE and the like and an external control equation independently and autonomously developed. Wherein, simulation software such as Solidworks, Thermal-Calc, Visual Studio, Procast and the like are all known software.

The vacuum arc remelting 3D model comprises a multi-dimensional model consisting of a solidification heat transfer macro model of a vacuum arc remelting high-temperature alloy, a solidification ingot casting micro model and a smelting process parameter model, the solidification heat transfer macro model of the high-temperature alloy, the solidification ingot casting micro model, the smelting process parameter model and other models can be used for visualizing the vacuum closed arc remelting high-temperature alloy process, representing phenomena which are difficult to find in experimental observation, solving the problems of time and labor waste and the like caused by the traditional trial and error method, comprehensively designing and optimizing more suitable smelting process parameters of the vacuum arc remelting high-temperature alloy based on the information such as the appearance and depth of a metal molten pool, the dendritic spacing and the structural appearance of the solidification ingot and the like, and further controlling and reducing the problem of element segregation of the high-temperature alloy.

Because different high-temperature alloys have different theoretical process parameters, the process parameters are regulated and controlled and input into an external control equation independently developed, calculation factors required by a 3D model are calculated in an iterative mode, the calculation factors are combined into a vacuum arc remelting high-temperature alloy 3D model, a plurality of groups of smelting condition parameters are obtained through simulation, information of the alloy metal molten pool morphology and the average depth of a prepared solidified ingot, the ingot dendrite spacing, the solidified structure and the like corresponding to each group of smelting condition parameters is analyzed, and the appropriate smelting condition parameters are determined. Through the model and the simulated solidification ingot casting information, the vacuum arc remelting process is visualized, appropriate smelting condition parameters are analyzed through the model and the simulation result, the problems of time consumption, material consumption, manpower consumption and the like caused by the trial-and-error method of carrying out actual production verification on multiple groups of smelting condition parameters are avoided, and the practicability is high.

The vacuum arc remelting process comprises remelting of a smelting electrode, filling of metal and solidification of an ingot, and is a complex physical and chemical metallurgical process. In order to calculate and simulate the vacuum arc remelting process, the method is properly simplified and assumed before establishing a vacuum arc remelting 3D model, and the contents are as follows:

(1) the physical parameters of the selected alloy grade and the steel grade of the material used by the crystallizer are assumed to be functions changing along with the temperature.

(2) The smelting process parameters such as melting rate, cooling circulating water flow, helium pressure, voltage current, cooling circulating water temperature and the like are assumed to be constant constants.

(3) In the vacuum arc remelting process, the alloy liquid in the metal melting pool is assumed to transfer heat in a heat conduction mode, and chemical reactions in the metal melting pool are ignored.

(4) In the cooling process of the solidified ingot, the solidified shell of the solidified ingot is supposed to be mainly in a heat conduction mode with the side wall and the bottom surface of the crystallizer.

(5) The crystallizer is positioned in the cooling circulating water jacket, heat conduction and radiation heat transfer between the outer wall of the crystallizer and the external environment are neglected, and only the heat convection effect between the cooling circulating water and the crystallizer is considered.

(6) When the simulation temperature of all the alloy liquid is lower than the solidus temperature, the steel ingot is considered to be completely solidified, and the solidification structure form is not changed any more.

And then establishing a finite element model of the ingot in the vacuum arc remelting superalloy process by utilizing SolidWorks and Procast software according to the actual size (such as 508mm, 660mm, 460mm and the like) of the crystallizer in the vacuum arc remelting superalloy process, and intuitively integrating the change process of the ingot in the metal molten pool through the finite element model.

In the vacuum arc remelting process, the solidification heat transfer of the solidified ingot is relatively complex and belongs to an unsteady heat transfer mode, so that in the establishment of a solidification heat transfer macro model of the vacuum arc remelting high-temperature alloy, a Fourier heat conduction differential equation is used for representing the whole heat transfer process of the solidified ingot, and the mathematical expression of the Fourier heat conduction differential equation is shown as the formula (1-1):

（1-1）；

in the formula (1-1), ρ represents the density of the alloy in kg.m^-3(ii) a Cp represents the constant pressure heat capacity of the alloy and has the unit of kJ/(kg.K); t represents the heat transfer temperature of a heat transfer link in the vacuum arc remelting process, and the unit is K; t represents time in units of s; λ represents the thermal conductivity, in units of W/(m.k); q represents a heat source term in W.m^-3(ii) a And x, y and z represent three-dimensional coordinates of the heat transfer direction in the heat transfer link. The ingot has a three-dimensional structure, so that the heat conduction direction of the ingot is also three-dimensional, x, y and z are set to represent the three-dimensional heat transfer direction of the ingot, and the internal node temperature is solved by using the temperature combination formula (1-1) of the boundary node.

The heat source term Q represents the heat released by the latent heat of solidification in the simulated ingot solidification process, and the solid phase ratio in unit volume and unit time is assumed to be

Then the ingot is solidifiedHeat released in the course of solidificationQComprises the following steps:

（1-2）；

in the formula (1-2), H represents the latent heat of solidification in W.m^-3；

Represents the solid phase ratio;

the formula (1-3) can be obtained by substituting the formula (1-2) into the formula (1-1):

（1-3）。

through the above formula (1-3), the heat transfer process of the ingot casting solidification process can be simulated from the three-dimensional direction, and multi-dimensional simulation is realized.

The heat transfer schematic diagram of the ingot casting solidification heat transfer link is shown as the attached figure 1, wherein the reference numeral 1 represents a metal melting bath, the reference numeral 2 represents a solidification ingot, the reference numeral 3 represents a gap between the solidification ingot and the inner wall of the crystallizer, the gap is formed due to solidification shrinkage of the ingot, the reference numeral 4 represents the crystallizer, the reference numeral 5 represents cooling circulating water, and T in the attached figure 1 represents T heat transfer between molten alloy liquid and the solidification ingot, conduction heat transfer in the solidification ingot, conduction heat transfer between the solidification ingot and the inner wall of the crystallizer, conduction heat transfer between the inner wall and the outer wall of the crystallizer, and convection heat transfer between the outer wall of the crystallizer and the cooling circulating water₁Indicating the temperature of the molten alloy, T, melted in the molten metal bath₂Indicating the temperature, T, of the solidified ingot on the side close to the molten alloy₃Indicating the temperature, T, of the solidified ingot on the side close to the inner wall of the crystallizer₄Indicating the temperature, T, of the inner wall of the crystallizer₅Indicating the temperature, T, of the outer wall of the crystallizer₆Indicating the temperature, T, of the cooling circulation water₁And T₂The heat convection exists between the alloy liquid and the solidified cast ingot, and is characterized by a heat convection model between the melted alloy liquid and the solidified cast ingot,T₂and T₃There is conduction heat transfer between, characterized by a model of conduction heat transfer inside the solidified ingot, T₃And T₄There is conductive heat transfer between them, characterized by a heat transfer model between the solidified ingot and the inner wall of the crystallizer, T₄And T₅There is a conduction heat transfer between them, characterized by a model of conduction heat transfer between the inner and outer walls of the crystallizer, T₅And T₆The mold simulates the solidification heat transfer process of the cast ingot more finely and accurately by the representation of a convection heat transfer model between the outer wall of the crystallizer and the cooling circulating water so as to comprehensively and accurately control the vacuum arc remelting process and further accurately regulate and control the segregation condition of the high-temperature alloy.

Preferably, the convective heat transfer model between the molten alloy and the solidified ingot is shown in the following formula (1-4):

（1-4）；

in the formula (1-4), T₁-T₂Represents the temperature gradient of the alloy liquid and the solidified cast ingot, and has the unit of K, wherein T₁Expressed as the temperature of the alloy liquid in units of K, T₂The temperature of the solidified cast ingot close to one side of the alloy liquid is expressed in K; h is₁The heat convection coefficient between the molten alloy and the solidified cast ingot is expressed in W.m^-2•K^-1。

According to the method, the temperature gradient and the convection heat transfer coefficient are used as the convection heat transfer boundary between the molten alloy and the solidified ingot, the convection heat transfer condition between the molten alloy and the solidified ingot can be accurately calculated, and the heat transfer condition is combined with other heat transfer conditions, so that the more suitable vacuum arc remelting process condition parameters can be accurately determined.

Preferably, the conduction heat transfer model inside the solidified ingot is represented by the following formula (1-5):

（1-5）；

in the formula (1-5), the metal oxide,λ _{alloy (I)}The thermal conductivity of the solidified ingot is expressed in W.m^-1•K^-1；T ₂-T ₃Denotes the temperature gradient of the solidified ingot in K, where T₂The temperature of the solidified ingot close to the molten metal is expressed in units of K and T₃The temperature of the solidified ingot close to one side of the crystallizer is expressed in K; Δ d represents the thickness of the solidified ingot in m.

The temperature gradient, the heat conductivity coefficient and the thickness of the solidified ingot are used as the solution conditions of the conduction heat transfer model inside the solidified ingot, the conduction heat transfer condition inside the solidified ingot can be calculated more accurately, and the conduction heat transfer condition is combined with other heat transfer conditions, so that the more suitable vacuum arc remelting process condition parameters can be determined accurately.

Preferably, the heat transfer model between the solidified ingot and the inner wall of the crystallizer is as shown in the following formula (1-6):

（1-6）；

in the formula (1-6),λ _{air conditioner}Denotes the thermal conductivity of helium in W.m^-1•K^-1；d_{Air conditioner}The gap distance between the solidified ingot and the inner wall of the crystallizer is expressed in m, and the solidified ingot and the inner wall of the crystallizer have a clearance distance because the metal is contracted due to solidification and is not attached to the inner wall of the crystallizer any more. h is_radRepresents the radiant heat transfer coefficient of the air gap and has the unit of W.m^-1•K^-1；h₃The heat convection coefficient between the solidified ingot and the inner wall of the crystallizer is expressed in W.m^-2•K^-1；T ₃-T ₄Denotes the temperature gradient between the solidified ingot and the inner wall of the crystallizer, in K, where T₃The temperature of the solidified ingot close to the side of the crystallizer is expressed in units of K and T₄The temperature of the inner wall of the crystallizer is indicated in K.

According to the method, the conduction and radiation heat transfer of the helium are used as heat transfer boundary conditions between the solidified ingot and the inner wall of the crystallizer, the heat transfer boundary conditions and the definite conditions are the space interval, the heat conductivity coefficient of the helium and the radiation heat exchange coefficient in the space, and the heat transfer condition between the solidified ingot and the inner wall of the crystallizer can be accurately calculated.

Preferably, the model of conduction heat transfer between the inner wall and the outer wall of the crystallizer is shown in the following formulas (1-7):

（1-7）；

in the formula (1-7), the compound,λ _{copper (Cu)}Represents the heat conductivity coefficient of the copper crystallizer and has the unit of W.m^-1•K^-1；d_{Copper (Cu)}Represents the thickness of the copper crystallizer and has the unit of m;T ₄-T ₅denotes the temperature gradient of the crystallizer in K, where T₄Denotes the temperature of the inner wall of the crystallizer in units of K, T₅The temperature of the outer wall of the crystallizer is indicated in K.

Preferably, the model of the convective heat transfer between the outer wall of the crystallizer and the cooling circulation water is shown in the following formulas (1-8):

（1-8）；

in the formula (1-8),T ₅-T ₆the temperature gradient between the outer wall of the crystallizer and the cooling circulation water is expressed in K, wherein T₅Denotes the temperature of the outer wall of the crystallizer in K, T₆Represents the temperature of the cooling circulating water, and has the unit of K;h ₅the heat convection coefficient between the outer wall of the crystallizer and the cooling circulating water is expressed in W.m^-2•K^-1，h ₅The expression is shown in the following formula (1-9):

（1-9）；

in the formula (1-9), the metal oxide,λ _frepresents the heat conductivity coefficient of the cooling circulating water, and the unit is W.m^-1•K^-1；vRepresents the flow rate of the cooling circulation water in m.s^-1；μThe viscosity of the cooling circulating water is expressed in m²•s^-1；dThe equivalent diameter of the cooling circulation water flow is expressed in m; pr denotes the prandtl coefficient.

The heat transfer condition between the outer wall of the crystallizer and the cooling circulating water can be calculated more accurately by adopting the temperature of the cooling circulating water, the temperature of the outer wall of the crystallizer and the convective heat transfer coefficient of the cooling circulating water and the outer wall of the crystallizer as the boundary and the definite solution condition of convective heat transfer.

In the vacuum arc remelting simulation in the prior art, heat transfer between a molten alloy and a solidified ingot, heat transfer between the solidified ingot and a crystallizer, and heat transfer between the crystallizer and cooling circulating water are analyzed independently, and heat transfer by conduction in the solidified ingot and heat transfer by conduction between the inner wall and the outer wall of the crystallizer are ignored, so that an integral macroscopic model is incomplete, and a simulation result is not complete. In the method, the heat transfer processes of the molten alloy, the solidified ingot, the crystallizer and the cooling water in the vacuum arc remelting process are analyzed from five aspects of convective heat transfer between the molten alloy and the solidified ingot, conductive heat transfer inside the solidified ingot, heat transfer between the solidified ingot and the inner wall of the crystallizer, conductive heat transfer between the inner wall and the outer wall of the crystallizer and convective heat transfer between the outer wall of the crystallizer and the cooling circulating water, so that the simulation process and the result are more comprehensive and systematic. Specifically, the temperature value q of the boundary node is calculated by the equations (1-4) to (1-8)₁、q₂、q₃、q₄、q₅Then the value of q is used as the initial condition for solving the internal node temperature₁、q₂、q₃、q₄、q₅The heat source term Q is not limited to the above temperature values, and is a heat source for transferring heat to a part of the heat source term Q.

Preferably, the smelting process parameter model is shown as the following formula (1-10):

（1-10）；

in the formula (1-10), the metal oxide,Trepresents the surface temperature of the molten metal bath in K;T _Lrepresents the liquidus temperature of the alloy in K; j represents the smelting current in KA; d_iRepresenting the ingot diameter in m.

In the vacuum arc remelting process, smelting process parameters such as smelting electric arc, alloy solid-liquid phase line temperature, ingot casting diameter and the like all affect the temperature of the surface of the metal molten pool, so that the surface temperature of the metal molten pool can be theoretically calculated by adopting the smelting process parameter model, and the calculation is facilitated to obtain the temperature condition of the surface of the metal molten pool.

Preferably, the microscopic heat transfer model is represented by the following formula (1-11):

（1-11）；

in the formula (1-14), the metal oxide,ρexpressed as density in kg.m^-3；λDenotes the coefficient of thermal conductivity in W.m^-1•K^-1；CpThe specific heat capacity at constant pressure is expressed in kJ^-1•K^-1；

Represents the laplacian operator; t represents the temperature field of the calculation area and has the unit of K;

represents the heat released by the latent heat of solidification and has a unit of W.m^-2；f _sRepresents the solid phase fraction; tau represents time with unit of s, and concretely represents the calculation simulation time of simulation software, the time step length of the simulation, the number of simulation steps and the convergence precision of each stepCorrelation, namely a gradual change process;

the mass transfer model is shown in the following formula (1-12):

（1-12）；

in the formula (1-12), the metal oxide,C _irepresents solute concentration in%;

represents the laplacian operator;D _irepresents the solute diffusion coefficient; subscriptiS is s or l, s represents a solid phase and l represents a liquid phase;

indicating the discharged solute of the ingot changing from solid phase to liquid phase,f _srepresents the solid phase fraction; tau represents time with unit s, specifically represents the calculation simulation time of simulation software, and is a gradual change process related to the simulation time step length, the simulation step number and the convergence precision of each step.

Based on the above equations (1-11) and (1-12), to drive dendrite growth, the temperature field T and solute field C (x, y, τ) of the calculation domain must satisfy the initial condition and the solid-liquid interface boundary condition, x and y are the positions of the cells in the rectangular coordinate system, and τ is time. The microcosmic calculation is based on the fact that after the temperature field is calculated in the early stage, secondary calculation is carried out by using the temperature field data.

The heat transfer model and the mass transfer model can present information such as ingot dendritic spacing, solidification structure and the like, realize visualization of the vacuum arc remelting superalloy process, and ensure proper vacuum arc remelting process condition parameters through the microstructure of the solidified ingot.

Preferably, the crystal plane curvature model consists of a macroscopic supercooling degree delta T at a solid-liquid interface₀And the microcosmic supercooling degree delta T at the solid-liquid interface and the macroscopic supercooling degree delta T at the solid-liquid interface₀As shown in the following formulae (1-13):

（1-13）；

in the formula (1-13), ΔT _cRepresenting the degree of supercooling of the component; deltaT _rRepresents the degree of curvature supercooling; deltaT _tRepresenting the degree of supercooling of the temperature; deltaT _kRepresenting the degree of kinetic supercooling; wherein, Delta T_kThe dynamic supercooling degree is obvious only when the rapid solidification is carried out, and the conventional solidification can ignore the dynamic supercooling degree;

the micro supercooling degree Δ T at the solid-liquid interface is shown by the following formula (1-14):

（1-14）；

in the formula (1-17), the metal oxide,T _Lrepresents the liquidus temperature in K;Trepresents the temperature at the solid-liquid interface in K;C ₀denotes initial concentration in%;mrepresents the slope of the liquidus;

representing the Gibbs-Thomson coefficient; k represents the average curvature at the solid-liquid interface;

representing the interfacial anisotropy function;

represents the included angle between the normal direction of the solid-liquid interface and the horizontal direction;

indicating the preferred growth direction of the dendrite; wherein the mean curvature K at the solid-liquid interface can be calculated from the cell-adjacent cell solid fraction of the interface as shown in the following formula (1-15):

（1-15）；

in the formula (1-15), the metal oxide,N _nrepresents the number of neighbor cells; deltaxRepresenting the size of the cells, wherein the cells participating in counting can select neighbor cells including a nearest neighbor, a next neighbor and a third neighbor;f _s(i) the solid phase fraction is indicated.

The microstructure such as the dendritic crystal spacing, the crystal nucleus number, the tissue morphology and the like of the alloy cast ingot is calculated and represented through the crystal face curvature model, and the microstructure is a basic model and an auxiliary model in the microstructure; so as to feed back the microscopic morphology of the cast ingot under the corresponding process condition through the microstructure, and further regulate and control more suitable process condition parameters.

Preferably, in the grain nucleation model, a continuous rather than discrete distribution function is used, assuming that the number of crystal nuclei and the supercooling degree keep a continuous dependency relationshipdn/d(ΔT) To describe the variation of the grain density, as shown in the following formulas (1-16):

（1-16）；

in the formula (1-16), the metal oxide,dn/d（ΔT) Indicating an increase in supercooling degreed（ΔT) The resulting increase in grain densitydn；n _maxRepresents the maximum nucleation particle density in m^-3；ΔT _σ-standard deviation supercooling degree, in units of K; deltaT _maxRepresenting the maximum nucleation supercooling degree in K.

Using the above-described grain nucleation model, the nucleation process of a solidified ingot can be characterized in a continuous manner at a given supercooling ΔTUnder the condition, the total density n (delta T) of the nucleated crystal grains can be given by the integral of the distribution, which is beneficial to presenting the information of the metal molten pool appearance and average depth, the ingot casting dendrite spacing, the solidification structure and the like, realizing the visualization of the vacuum arc remelting superalloy process, and ensuring the proper vacuum arc remelting process condition parameters through the microstructure of the solidified ingot casting.

Preferably, the secondary dendrite spacing model is represented by the following formula (1-17):

（1-17）；

in the formula (1-17), the metal oxide,M(t) A constant representing a property of the alloy;t _Lrepresents the coagulation time of a certain spatial position, and the unit is s; wherein the content of the first and second substances,M(t) Represented by the following formulae (1 to 18):

（1-18）；

in the formula (1-18), the metal oxide,σ _slrepresents the solid-liquid interfacial energy in units of J;D _lrepresents the diffusion coefficient of the solute in the alloy liquid;T _Mrepresents the melting point of the pure substance in K;Lrepresents latent heat of fusion in W.m^-3；kRepresents the equilibrium partition coefficient;mrepresents the liquidus slope of the alloying element;C _l(t) Represents the concentration of liquid phase solute at the time t, and the unit is%;C _l,0expressed as the nominal concentration of solute in the liquid phase in%.

In the vacuum arc remelting 3D model, the distribution condition of secondary dendrite spacing in the solidified ingot can be calculated and described through the formulas (1-17) and (1-18), so that the information of the dendrite spacing, the solidification structure and the like of the ingot can be presented, and the visualization of the vacuum arc remelting superalloy process is realized.

Preferably, the dendrite growth kinetic model is represented by the following formula (1-19):

（1-19）；

in the formula (1-19), Δ T represents the degree of microcosmic supercooling at the solid-liquid interface,ɑ ₂、ɑ ₃the growth coefficients are respectively as follows:

（1-20）；

in the formula (1-20), the compound,c ₀the mass fraction of each element in the alloy is expressed, and can be deduced according to the content of each element in the alloy; ρ represents the density of the superalloy in kg.m^-3；mRepresents the slope of the liquidus;krepresents the solute equilibrium partition coefficient;Drepresents the solute self-diffusion coefficient; Γ denotes the Gibbs-Thomson coefficient.

In the process of simulating the microstructure of the cast ingot, the growth speeds of columnar crystals and equiaxed crystals of the cast ingot are described by adopting the dendrite growth dynamics (KGT) model, so that the information of the appearance and the average depth of a metal molten pool, the dendrite spacing and the solidification structure of the cast ingot and the like can be presented, and the visualization of the vacuum arc remelting superalloy process is realized.

Based on the construction of the solidification heat transfer macro model, the solidification ingot casting micro model and the smelting process parameter model of the vacuum arc remelting high-temperature alloy, the physical property parameters and the boundary conditions of the vacuum arc remelting high-temperature alloy are set, the obtained physical property parameters and the boundary condition results are coupled into the vacuum arc remelting 3D model, numerical simulation iteration solution is carried out, and then a plurality of groups of smelting process condition simulation values are obtained.

For setting physical parameters, based on chemical components of the high-temperature alloy, physical parameters such as conductivity, density and enthalpy of the high-temperature alloy under different temperature conditions are calculated by utilizing a thermodynamic database of a plurality of groups of phase alloys in Thermal-Calc software, a Scheil-Gulliver equation and an alloy material database of Procast software, and the obtained results are coupled to a vacuum arc remelting 3D model.

For setting the boundary conditions, because the high-temperature alloy and the pure copper used by the crystallizer are two different alloy materials in the vacuum arc remelting 3D model, the interface nodes of the copper crystallizer and the high-temperature alloy are subjected to double treatment in order to ensure the accuracy of a numerical simulation result and distinguish the temperatures at two ends of the interface by considering that the two different alloys are on the same interface and the temperature drop exists.

The method comprises the steps of controlling the cooling boundary conditions of the ingot such as the adding quality, the temperature and the rising rate of a molten metal pool and the like by writing and adding an external control equation through Visual Studio software, simultaneously comprising and calling mathematical expressions in aspects of remelting duration, the rising rate of the liquid level of the molten metal pool, remelting duration and the height of the ingot, the heat transfer coefficient of the side wall of a crystallizer and the contact area of the ingot, helium pressure and the height of the ingot, the heat transfer coefficient of the bottom of the crystallizer and the height of the ingot and the like, and jointly coupling the mathematical expressions to a vacuum arc remelting 3D model to enable the vacuum arc remelting 3D model to have the characteristics of continuity, mobility, gradual change and the like.

And finally, carrying out numerical simulation iterative solution on the vacuum arc remelting 3D model through Procast, Visual Studio and other simulations. In the numerical simulation calculation operation process, the time step length is set to be 1 s; calculating the stopping condition that the solid phase rate of the vacuum arc remelting 3D model reaches 100% or the maximum calculation step number is reached; the convergence accuracy of the simulation calculation was set to 1 × 10^-5(ii) a The output frequency of the simulation result is set to 1; the maximum filling rate of the numerical model is set to 1.

In a second aspect, the application provides a vacuum arc remelting control method for reducing segregation of high-temperature alloy, which adopts the following technical scheme:

a vacuum arc remelting control method for reducing segregation of high-temperature alloy comprises the following steps:

step A, establishing a model: establishing a solidification heat transfer macro model, a solidification ingot casting micro model and a smelting process parameter model of the vacuum arc remelting high-temperature alloy by adopting a computer numerical simulation method;

b, simulating process parameters: setting a plurality of groups of melting rate values according to the performance of the high-temperature alloy, combining the plurality of groups of melting rate values into a solidification heat transfer macro model, a solidification ingot casting micro model and a smelting process parameter model, and iterating to obtain a plurality of groups of smelting process condition simulation values;

step C, simulating a smelting process: analyzing the appearance and average depth of a metal molten pool, the dendrite spacing of an ingot and solidification structure information under the corresponding melting rate according to a plurality of groups of smelting process condition simulation values, and formulating suitable smelting condition parameters of the vacuum arc remelting superalloy;

step D, smelting high-temperature alloy: and smelting the high-temperature alloy according to the smelting condition parameters obtained by the model simulation.

Simulating a plurality of groups of smelting condition parameters through a vacuum arc remelting 3D model, analyzing information such as the appearance and average depth of a metal molten pool, the dendrite spacing of an ingot and a solidification structure in each group of simulation results based on a plurality of groups of smelting process condition simulation values, formulating more suitable smelting process parameters of the vacuum arc remelting high-temperature alloy, and then smelting the high-temperature alloy to realize a simulation process of multi-dimensional, multi-phase, multi-scale and multi-physical fields, thereby facilitating the control of the internal segregation problem of the alloy.

Preferably, the specific steps of smelting the high-temperature alloy comprise the following steps:

casting and molding the high-temperature alloy to prepare a high-temperature alloy consumable electrode, welding the high-temperature alloy consumable electrode and a transition electrode, then putting the high-temperature alloy consumable electrode into a crystallizer, sealing the furnace, vacuumizing until the vacuum degree in the furnace is less than 3Pa, and performing power transmission smelting;

according to the parameters of the smelting conditions obtained by model simulation, a metal molten pool is established, and voltage and current are controlled to regulate and control the smelting rate so as to smelt the high-temperature alloy;

when the weight of the solidified ingot is 250-350kg, helium is filled into the vacuum arc remelting furnace, the pressure of the helium in the furnace is maintained at 200-350Pa, and the ingot is smelted at a constant smelting rate;

when the residual weight of the high-temperature alloy consumable electrode is 75-175kg, stopping helium filling, and reducing the melting rate until the melting is finished;

and cooling the solidified ingot in a vacuum arc remelting furnace for 60-120min, and taking out the solidified ingot after breaking the hollow to obtain the high-temperature alloy solidified ingot.

The high-temperature alloy is smelted through the steps, and the smelting process parameters obtained by combining the vacuum arc remelting 3D model simulation can be used for analyzing information such as the appearance and the average depth of a metal molten pool, the dendrite spacing of an ingot and a solidification structure in a simulation result, so that the more suitable appearance and macro-microstructure of the metal molten pool are determined, and the more suitable smelting process parameters of the vacuum arc remelting high-temperature alloy are further obtained, so that the aims of reducing alloy segregation and improving the metallurgical quality are fulfilled.

In the vacuum arc remelting process, the weight of the consumable electrode of the high-temperature alloy refers to the weight of the electrode which is not subjected to vacuum arc remelting, and the weight of the solidified ingot refers to the weight of the ingot formed by vacuum arc remelting. In the vacuum arc remelting process, helium is refilled after a certain weight of solidified ingot is formed; and in the final cooling process of the solidified ingot, the solidified ingot is naturally cooled in a vacuum arc remelting furnace in vacuum, the whole smelting process is finished in vacuum, only power-off treatment is carried out after the smelting is finished, no interference factor exists in the cooling process, the vacuum degree is broken subsequently, and the solidified ingot is taken out.

In summary, the present application has the following beneficial effects:

1. the heat transfer model of the vacuum arc remelting high-temperature alloy is formed by combining a convection heat transfer model between a molten alloy and a solidified ingot, a conduction heat transfer model inside the solidified ingot, a heat transfer model between the solidified ingot and the inner wall of a crystallizer, a conduction heat transfer model between the inner wall and the outer wall of the crystallizer and a convection heat transfer model between the outer wall of the crystallizer and cooling circulating water, so that the heat transfer link of the vacuum arc remelting high-temperature alloy can be comprehensively characterized, and the vacuum arc remelting 3D model with the characteristics of continuity, mobility, gradual change and the like can be constructed.

2. The method is characterized in that a heat transfer model, a mass transfer model, a crystal face curvature model, a crystal grain nucleation model, a secondary dendrite spacing model and a dendrite growth dynamics model are combined to form a solidification ingot microscopic model so as to simulate a solidification ingot microscopic structure in a vacuum arc remelting process, so that the vacuum closed arc remelting high-temperature alloy process is visualized, information such as the shape and the average depth of a metal molten pool, the ingot dendrite spacing and the solidification structure can be fed back conveniently, and the method is combined with a solidification heat transfer macroscopic model of the vacuum arc remelting high-temperature alloy, and is helpful for establishing a multidimensional, multiscale and multiphase field coupled vacuum arc remelting 3D model.

3. The method is based on the smelting characteristics, the control flow and the computer simulation technology of the actual industrial vacuum arc remelting process, and is characterized in that a multidimensional, multi-scale and multi-phase field coupling vacuum arc remelting 3D model is constructed, and comprises a solidification heat transfer macro model, a solidification ingot casting micro model and a smelting process parameter model of vacuum arc remelting high-temperature alloy, so that the vacuum closed vacuum arc remelting smelting process can be converted into visual operation, the macro-micro structure of the solidification ingot casting can be visually represented, and theoretical basis and engineering guidance are provided for adjustment and matching of smelting process parameters, and control of the solidification ingot casting structure and smelting quality;

4. by setting a plurality of groups of smelting process parameters of the vacuum arc remelting superalloy and comparing and analyzing information such as the metal bath morphology and average depth, the ingot casting dendrite spacing, the solidification structure and the like in a simulation result of a model simulation process, a more suitable metal bath morphology and an ingot casting macro-microstructure are determined, and then more suitable smelting process parameters of the vacuum arc remelting superalloy are formulated, so that the aims of reducing alloy segregation and improving metallurgical quality are fulfilled, a large amount of financial resources, material resources, research and development time and the like consumed by a traditional trial and error method are avoided, and the homogenization degree and metallurgical quality of the ingot casting are improved.

Drawings

FIG. 1 is a schematic heat transfer diagram of a vacuum arc remelting process according to the present application;

FIG. 2 is a graph of the change in the topography of the molten metal pool for a plurality of sets of melting rates for examples 1 through 4;

FIG. 3 is a graph of data for average depth of molten metal pool at multiple sets of melting rates for examples 1 through 4;

FIG. 4 is a schematic diagram of the distribution of the primary dendrite spacing of the ingot at multiple sets of melting rates of examples 1 to 4;

FIG. 5 is a graph of data for ingot primary dendrite spacing for multiple sets of melt rates for examples 1-4;

FIG. 6 is a schematic diagram showing the distribution of the secondary dendrite spacing of the ingot at multiple sets of melting rates of examples 1 to 4;

FIG. 7 is a graph of data for ingot secondary dendrite spacing for multiple sets of melt rates for examples 1-4;

FIG. 8 is a schematic view showing the distribution of solidification structures of ingots at a plurality of sets of melting rates in examples 1 to 4;

FIG. 9 is a set of graphs of the change in the topography of the molten metal pool for a plurality of sets of melting rates for examples 5 through 9;

FIG. 10 is a graph of data for average depth of molten metal pool at multiple sets of melting rates for examples 5 through 9;

FIG. 11 is a schematic diagram showing the distribution of primary dendrite spacing of an ingot at multiple sets of melting rates of examples 5 to 9;

FIG. 12 is a graph of data for ingot primary dendrite spacing for multiple sets of melt rates for examples 5-9;

FIG. 13 is a schematic diagram showing the distribution of secondary dendrite spacing of the ingot at multiple sets of melting rates of examples 5 to 9;

FIG. 14 is a graph of data for ingot secondary dendrite spacing for multiple sets of melt rates for examples 5-9;

FIG. 15 is a schematic view showing the distribution of solidification structures of ingots in a plurality of sets of melting rates of examples 5 to 9;

FIG. 16 is a graph showing the changes in the morphology of the molten metal bath for the sets of cooling cycle water flow rates of examples 10 to 12;

FIG. 17 is a schematic view showing the distribution of primary dendrite spacing of ingots at a plurality of cooling circulation water flows of examples 10 to 12;

FIG. 18 is a schematic view showing the distribution of secondary dendrite spacing of ingots at a plurality of cooling circulation water flows of examples 10 to 12;

FIG. 19 is a schematic view showing the distribution of solidification structures of ingots in a plurality of sets of cooling circulation water flows of examples 10 to 12;

description of the drawings: 1. a molten metal bath; 2. solidifying and casting ingots; 3. a gap; 4. a crystallizer; 5. and cooling the circulating water.

Detailed Description

The present application is described in further detail below with reference to figures 1-19 and examples.

Examples

Example 1

In the embodiment, the vacuum arc remelting treatment is carried out on the high-temperature alloy GH4169 with the diameter of 508 mm.

At present, when domestic enterprises remelt 508mm high-temperature alloy GH4169 in vacuum arc, the melting rate of the alloy fluctuates within the range of 3.0 +/-0.05 kg/min; the flow rate of the cooling circulation water fluctuates within the range of 700-800L/min. Therefore, in the embodiment, both the flow rate and the melting rate of the cooling circulation water are processed by taking intermediate values, namely the flow rate and the melting rate of the cooling circulation water are set to 750L/min, the melting rate is set to 3.0kg/min, the rising rate of the liquid level of the metal molten pool is reversely deduced through the known melting rate, the interface heat exchange coefficient of the whole model can be calculated through the pressure of the cooling water flow rate and the helium gas and the combination of an internal empirical formula or constant, the simulation is carried out through the combination of a solidification heat transfer macro model, a solidification ingot casting micro model and a smelting process parameter model of the vacuum arc remelting high-temperature alloy, an external control equation is coupled, and the gradual change and the continuity of the boundary conditions are realized through the time and position change.

In the numerical simulation calculation operation process, the time step length is set to be 1 s; calculating the stop condition as the number of calculation steps that the solid phase rate of the vacuum arc remelting 3D model reaches 100%; the convergence accuracy of the simulation calculation was set to 1 × 10^-5(ii) a The output frequency of the simulation result is set to 1; the maximum filling rate of the numerical model is set to 1.

Example 2

This embodiment differs from embodiment 1 described above in that: the melting rate was set to 3.5 kg/min.

Example 3

This embodiment differs from embodiment 1 described above in that: the melting rate was set to 4.0 kg/min.

Example 4

This embodiment differs from embodiment 1 described above in that: the melting rate was set to 4.5 kg/min.

The simulation parameter settings for the above examples 1-4 are shown in table 1 below:

TABLE 1 simulation parameter set-up for vacuum arc remelting 508mm diameter superalloy GH4169 of examples 1-4

Through the simulation results and the combination of the attached figures 2 to 8, the changes of the shape and the average depth of a metal molten pool under the condition of a plurality of groups of melting rates and the distribution conditions of the dendrite spacing and the solidification structure of the cast ingot are contrastively analyzed, and the smelting process parameter range of the high-temperature alloy GH4169 with the more suitable vacuum arc remelting diameter of 508mm is screened, so that the purposes of reducing alloy segregation and improving the metallurgical quality are achieved.

TABLE 2 simulation results of vacuum arc remelting 508mm diameter superalloy GH4169 for examples 1-4

Wherein, fig. 2 shows the change situation of the molten metal pool morphology under the condition of a plurality of groups of melting rates when the cooling circulation water flow is 750L/min, as can be known from fig. 2, the pictures of the molten metal pool morphology under the condition of a plurality of groups of melting rates are composed of two parts, the left part of each group of pictures represents the temperature field distribution of the molten metal pool and the solidified ingot in the melting stable state in the vacuum arc remelting process, and the right part represents the solid phase ratio of the molten metal pool and the solidified ingot at the same time as the left part. When the melting rate is increased from 3.0kg/min to 4.5kg/min, the appearance of the metal molten pool is gradually transited from a shallow U shape to a U shape and then to a deep U shape.

FIG. 3 is a graph showing the change of the average depth of the molten metal bath at a plurality of sets of melting rates when the flow rate of the cooling circulation water is 750L/min; as can be seen from FIG. 3 in combination with Table 2, the average depth of the molten metal bath gradually increased from 145.4 + -0.4 mm to 191.1 + -0.4 mm as the melting rate was increased from 3.0kg/min to 4.5kg/min when the cooling circulation water flow rate was 750L/min.

As can be seen from FIGS. 4 to 5 and Table 2, the primary dendrite spacing at the core of the ingot is reduced from 12758 μm to 11734 μm; as can be seen from FIGS. 6 to 7, the secondary dendrite spacing at the core of the ingot is reduced from 266.7 μm to 234.2 μm; it can be seen from fig. 8 that the uniformity of the dendrite spacing distribution of the solidified ingot is significantly improved when the melting rate is increased from 3.0kg/min to 4.0kg/min, but the uniformity of the dendrite spacing distribution of the solidified ingot is reduced when the melting rate is increased from 4.0kg/min to 4.5 kg/min. In addition, the deflection angle formed by the inverted V-shaped columnar crystals in the solidified structure in the ingot and the total number of crystal grains in the solidified ingot are both greatly increased.

According to the microstructure of the solidified ingot, when the high-temperature alloy GH4169 with the diameter of 508mm is remelted by vacuum arc, the solidified structure in the ingot is gradually thinned along with the increasing of the melting rate, which is beneficial to the control of alloy segregation and metallurgical quality, but along with the increasing of the melting rate, the appearance of a metal molten pool is changed, the average depth of the metal molten pool is increased, and the probability of forming 'black spot' defects in the ingot due to the 'density inversion' of the alloy is increased.

In summary, when the high-temperature alloy GH4169 with the diameter of 508mm is vacuum arc remelting, the melting rate is preferably 3.5-4.0kg/min when the cooling circulation water flow is 750L/min, and the segregation of the alloy is much smaller than that of the existing alloy with the melting rate of 3.0kg/min, i.e. when the cooling circulation water flow is 750L/min, the ingot formed with the melting rate of 3.5-4.0kg/min has a higher homogenization degree than that of the ingot formed with the melting rate of 3.0 kg/min.

The embodiment 1 to the embodiment 4 are combined with a vacuum arc remelting 3D model, so that a simulation result of the vacuum arc remelting high-temperature alloy GH4169 with the diameter of 508mm can be obtained, a series of vacuum arc remelting process condition parameters corresponding to a proper melting rate can be obtained, and the actual production of the vacuum arc remelting high-temperature alloy can be guided from the aspects of multi-dimension, multi-scale, multi-phase fields and the like.

Example 5

In the embodiment, the vacuum arc remelting treatment is carried out on the high-temperature alloy GH4720Li with the diameter of 508 mm.

At present, when domestic enterprises remelt 508mm high-temperature alloy GH4720Li in vacuum arc, the melting rate is selected to fluctuate within the range of 3.2 +/-0.05 kg/min; the cooling circulation water flow fluctuates within the range of 850-950L/min. Therefore, in the embodiment, both the flow rate and the melting rate of the cooling circulation water are processed by taking intermediate values, namely the flow rate and the melting rate of the cooling circulation water are set to 900L/min, the melting rate is set to 3.2kg/min, the rising rate of the liquid level of the metal molten pool is reversely deduced through the known melting rate, the interface heat exchange coefficient of the whole model can be calculated through the pressure of the cooling water flow rate and the helium gas and the combination of an internal empirical formula or constant, the simulation is carried out through the combination of a solidification heat transfer macro model, a solidification ingot casting micro model and a smelting process parameter model of the vacuum arc remelting high-temperature alloy, an external control equation is coupled, and the gradual change and the continuity of the boundary conditions are realized through the time and position change.

Example 6

This embodiment differs from embodiment 5 described above in that: the melting rate was set to 3.5 kg/min.

Example 7

This embodiment differs from embodiment 5 described above in that: the melting rate was set to 3.8 kg/min.

Example 8

This embodiment differs from embodiment 5 described above in that: the melting rate was set to 4.1 kg/min.

Example 9

This embodiment differs from embodiment 5 described above in that: the melting rate was set to 4.4 kg/min.

The specific simulation parameter settings for the above examples 5-9 are shown in table 3 below.

TABLE 3 simulation parameter settings for vacuum arc remelting 508mm diameter superalloy GH4720Li of examples 5-9

Through the simulation results and the combination of the attached figures 9 to 15, the changes of the metal molten pool morphology and the average depth under the condition of multiple groups of melting rates and the distribution conditions of ingot casting dendrite spacing and solidification structures are contrastively analyzed when the cooling circulation water flow is 900L/min, and the smelting process parameter range of the high-temperature alloy GH4720Li with the more suitable vacuum arc remelting diameter of 508mm is screened, so that the purposes of reducing alloy segregation and improving the metallurgical quality are achieved.

TABLE 4 simulation results of vacuum arc remelting 508mm diameter superalloy GH4720Li from examples 5-9

Wherein, fig. 9 shows the change situation of the metal molten pool morphology under the condition of multiple groups of melting rates when the cooling circulation water flow is 900L/min, the pictures of the metal molten pool morphology under the condition of multiple groups of melting rates are composed of two parts, the left part of each group of pictures represents the temperature field distribution of the metal molten pool and the solidified ingot under the melting stable state in the vacuum arc remelting process, the right part represents the solid phase ratio of the metal molten pool and the solidified ingot at the same time as the left part, and as can be known from fig. 9, the metal molten pool morphology gradually changes from a shallow U shape to a U shape and then to a deep U shape as the melting rate is increased from 3.2kg/min to 4.4 kg/min.

FIG. 10 is a graph showing the change in average depth of molten metal pool at a plurality of sets of melting rates with a cooling circulation water flow rate of 900L/min; as can be seen from FIG. 10 in combination with Table 4, when the cooling circulation water flow rate was 900L/min, the average depth of the molten metal pool gradually increased from 146.2. + -. 0.4mm to 199.7. + -. 0.4mm as the melting rate was increased from 3.2kg/min to 4.4 kg/min.

As can be seen from fig. 11 to fig. 12 and table 4, the primary dendrite spacing at the core of the ingot is reduced from 11808 μm to 10472 μm; as can be seen from FIGS. 13 to 14, the secondary dendrite spacing at the core of the ingot is reduced from 267.8 μm to 243.6 μm; as can be seen from fig. 15, the uniformity of the dendrite spacing distribution in the solidified ingot is significantly improved when the melting rate is increased from 3.2kg/min to 3.8kg/min, but the uniformity of the dendrite spacing distribution in the solidified ingot is reduced when the melting rate is increased from 3.8kg/min to 4.4 kg/min. In addition, the deflection angle formed by the inverted V-shaped columnar crystals in the solidified structure in the ingot and the total number of crystal grains in the solidified ingot are both greatly increased.

According to the microstructure of the solidified ingot, when the high-temperature alloy GH4720Li with the diameter of 508mm is remelted by vacuum arc, the solidified structure in the ingot is gradually thinned along with the increase of the melting rate, which is beneficial to the control of alloy segregation and metallurgical quality, but the appearance of a metal molten pool is changed along with the increase of the melting rate, the average depth of the metal molten pool is increased, and the probability of forming 'black spot' defects in the ingot due to the 'density inversion' of the alloy is increased.

In summary, when the high-temperature alloy GH4720Li with the diameter of 508mm is vacuum arc remelted, the melting rate is preferably 3.5-4.1kg/min when the cooling circulation water flow is 900L/min, and the segregation of the alloy is much smaller than that of the alloy with the existing melting rate of 3.2kg/min, i.e. when the cooling circulation water flow is 900L/min, the homogenization degree of the ingot formed with the melting rate of 3.5-4.1kg/min is higher than that of the ingot formed with the melting rate of 3.2 kg/min.

In examples 5 to 9, a simulation result of the vacuum arc remelting 3D model can be obtained for the superalloy GH4720Li with the vacuum arc remelting diameter of 508mm, so that a series of vacuum arc remelting process condition parameters corresponding to a relatively high melting rate can be obtained, and the actual production of the vacuum arc remelting superalloy can be guided in the aspects of multi-dimensional, multi-scale, multi-phase fields and the like.

Example 10

In this example, a vacuum arc remelting process was performed on a 406mm diameter superalloy GH 4169.

At present, when domestic enterprises remelt 406mm high-temperature alloy GH4169 in vacuum arc, the melting rate of the alloy fluctuates within the range of 3.0 +/-0.05 kg/min; the cooling circulation water flow rate fluctuates within the range of 950-1050L/min. Therefore, in the embodiment, both the flow rate and the melting rate of the cooling circulation water are processed by taking intermediate values, namely the flow rate and the melting rate of the cooling circulation water are set to be 1000L/min, the melting rate is set to be 3.0kg/min, the rising rate of the liquid level of the metal molten pool is reversely deduced through the known melting rate, the interface heat exchange coefficient of the whole model can be calculated through the pressure of the cooling water flow rate and the helium gas and the combination of an internal empirical formula or a constant, the solidification heat transfer macro model, the solidification ingot casting micro model and the smelting process parameter model of the vacuum arc remelting high-temperature alloy are combined to carry out simulation, an external control equation is coupled, and the gradual change and the continuity of the boundary conditions are realized through the time and position change.

Example 11

This embodiment differs from embodiment 10 described above in that: the cooling circulation water flow rate was set to 900L/min.

Example 12

This embodiment differs from embodiment 10 described above in that: the flow rate of the cooling circulation water is set to 800L/min.

The specific simulation parameter settings for the above examples 10-12 are shown in table 5 below.

TABLE 5 simulation parameter settings for vacuum arc remelting 406mm diameter superalloy GH4169 for examples 10-12

Based on the simulation results, the average depth of the molten metal pool, the primary dendrite spacing and the secondary dendrite spacing of the ingot were subjected to data arrangement, and the results are shown in table 6. Meanwhile, with reference to the attached drawings 16-19, when the melting rate is 3.0kg/min, the changes of the metal molten pool morphology and the average depth under the condition of a plurality of groups of cooling circulating water flow rates and the distribution conditions of ingot casting dendrite spacing and solidification structures are contrastively analyzed, and a more proper smelting process parameter range of the high-temperature alloy GH4169 with the vacuum arc remelting diameter of 406mm is screened, so that the purposes of reducing alloy segregation and improving the metallurgical quality are achieved.

TABLE 6 simulation results of vacuum arc remelting 406mm diameter superalloy GH4169 for examples 10-12

Wherein, fig. 16 shows the change situation of the molten metal pool morphology under the condition of the flow rate of the multiple groups of cooling circulating water when the melting rate is 3.0kg/min, and as can be seen from fig. 16, the pictures of the molten metal pool morphology under the condition of the flow rate of the multiple groups of cooling circulating water are composed of two parts, the left part of each group of pictures represents the temperature field distribution of the molten metal pool and the solidified ingot in the melting stable state in the vacuum arc remelting process, and the right part represents the solid phase ratio of the molten metal pool and the solidified ingot at the same time as the left part. Meanwhile, as can be seen from Table 6, the shapes of the molten metal pools are basically the same and are all U-shaped when the flow rate of the cooling circulating water is decreased from 1000L/min to 800L/min. Although the average depth of the molten metal bath gradually decreases, the average depth decreases in the same stage and fluctuates within 160 + -1 mm.

As can be seen from fig. 17, fig. 18, and table 6, when the flow rate of the cooling circulation water is decreased from 1000L/min to 800L/min, the dendrite spacing distribution state of the solidified ingot is substantially the same, and the primary dendrite spacing and the secondary dendrite spacing at the core of the ingot both decrease in the same stage, and fluctuate within the ranges of 9741 ± 40 μm and 196 ± 1 μm, respectively. In addition, as can be seen from fig. 19, the deflection angle formed by the inverted "V" shaped columnar crystals in the solidification structure of the ingot at different cooling cycle water flow rates is substantially similar to the total number of crystal grains in the solidified ingot.

According to the analysis of the morphology of the metal molten pool, the average depth of the metal molten pool and the microstructure of the solidified ingot, when the high-temperature alloy GH4169 with the diameter of 406mm is remelted by vacuum arc, the distribution state of the morphology of the metal molten pool and the distribution state of the solidified structure of the ingot are basically similar along with the decreasing of the flow of cooling circulating water, but the average depth of the metal molten pool and the solidified structure in the ingot are fluctuated in a certain range and are reduced in the same stage. This shows that the influence of the vacuum arc remelting smelting process is small along with the decreasing of the cooling circulating water flow, but the vacuum arc remelting smelting process is in a gradually refined state on the solidification structure of the cast ingot, which is beneficial to the control of alloy segregation and metallurgical quality.

In summary, when the high-temperature alloy GH4169 with the diameter of 406mm is vacuum arc remelting, when the melting rate is 3.0kg/min, the suitable cooling circulation water flow rate is 800L/min, and the segregation condition of the alloy is smaller than that of the alloy formed by the existing cooling circulation water flow rate of 1000L/min, that is, when the melting rate is 3.0kg/min, the homogenization degree of the ingot formed by the fluctuation of the cooling circulation water flow rate in the range of 800L/min is higher than that of the ingot formed by the fluctuation of the cooling circulation water flow rate in the range of 1000L/min.

In examples 10 to 12, a simulation result of vacuum arc remelting of the high-temperature alloy GH4169 with a diameter of 406mm can be obtained by combining the vacuum arc remelting 3D model, so that a series of vacuum arc remelting process condition parameters corresponding to a relatively suitable cooling circulating water flow can be obtained, and the actual production of the vacuum arc remelting high-temperature alloy can be guided in the aspects of multi-dimensional, multi-scale, multi-phase fields and the like.

Application example

The following application examples 1 to 9 and the melting condition parameters (melting rate, cooling circulation water flow, melting voltage, melting current, time of filling nitrogen, nitrogen pressure, time of stopping filling helium, cooling time and the like) of the comparison application examples 1 to 3 all have a certain floating space, in actual process operation, specific parameter values obtained through simulation cannot be completely adopted, an operation window for regulating and controlling needs to be reserved for an operator, and the specific parameter values obtained through simulation are theoretically more suitable process conditions, so that theoretical basis and engineering guidance are provided for regulation and matching of the melting process parameters, solidification of ingot casting tissues and control of the melting quality.

Application example 1

Based on the simulation effects of the embodiments 1 to 4, the existing process parameters are optimized, the process condition parameters of the embodiment 2 are adopted to carry out vacuum arc remelting treatment on the high-temperature alloy GH4169 with the diameter of 508mm, wherein the melting rate is 3.5 +/-0.05 kg/min, and the cooling circulating water flow is 750 +/-50L/min; the specific vacuum arc remelting process comprises the following steps:

casting and molding a high-temperature alloy GH4169 to prepare a high-temperature alloy consumable electrode GH4169, welding the high-temperature alloy consumable electrode GH4169 with a transition electrode, then putting the welded high-temperature alloy consumable electrode GH4169 into a crystallizer, sealing the crystallizer, vacuumizing until the vacuum degree in the furnace is less than 3Pa, and performing power transmission smelting;

according to the parameters of the smelting conditions obtained by the model simulation of the embodiment 2, a metal melting pool is established, the smelting voltage is controlled to be 22.5 +/-2.5V, the smelting current is controlled to be 5.5 +/-1.0 KA, and the high-temperature alloy is smelted by regulating and controlling the smelting rate to be 3.5 +/-0.05 kg/min;

when the weight of the solidified ingot is 300 plus or minus 50kg, filling helium into the vacuum arc remelting furnace, maintaining the pressure of the helium in the furnace at 275 plus or minus 75Pa, and smelting at a constant melting rate;

when the residual weight of the high-temperature alloy consumable electrode is 125 +/-50 kg, stopping helium filling, and reducing the melting rate until the melting is finished;

and cooling the solidified ingot in a vacuum arc remelting furnace for 90 +/-30 min, and taking out the solidified ingot after breaking the hollow to obtain the high-temperature alloy solidified ingot.

Application example 2

The present application example differs from the above application example 1 in that: the melting rate was 3.7. + -. 0.05 kg/min.

Application example 3

The present application example differs from the above application example 1 in that: the melting rate was 3.9. + -. 0.05 kg/min.

Application example 4

Based on the simulation effects of the above embodiments 5 to 9, the existing process parameters are optimized, and the process condition parameters of the embodiment 6 are adopted to carry out vacuum arc remelting treatment on the high-temperature alloy GH4720Li with the diameter of 508mm, wherein the melting rate is 3.5 +/-0.05 kg/min, and the cooling circulation water flow is 900 +/-50L/min; the specific vacuum arc remelting process comprises the following steps:

casting and molding a high-temperature alloy GH4720Li to prepare a high-temperature alloy consumable electrode GH4720Li, welding the high-temperature alloy consumable electrode GH4720Li with a transition electrode, then putting the welded high-temperature alloy consumable electrode GH4720 into a crystallizer, sealing a furnace, vacuumizing until the vacuum degree in the furnace is less than 3Pa, and performing power transmission smelting;

according to the parameters of the smelting conditions obtained by the model simulation of the embodiment 6, a metal molten pool is established, the smelting voltage is controlled to be 22.5 +/-2.5V, the smelting current is controlled to be 5.5 +/-1.0 KA, and the high-temperature alloy is smelted by regulating and controlling the smelting rate to be 3.5 kg/min;

Application example 5

The present application example differs from the above application example 4 in that: the melting rate was 3.7. + -. 0.05 kg/min.

Application example 6

The present application example differs from the above application example 5 in that: the melting rate was 3.9. + -. 0.05 kg/min.

Application example 7

Based on the simulation effects of the above embodiments 10 to 12, the existing process parameters are optimized, and the process condition parameters of the embodiment 12 are adopted to carry out vacuum arc remelting treatment on the high-temperature alloy GH4169 with the diameter of 406mm, wherein the melting rate is 3.0 +/-0.05 kg/min, and the cooling circulation water flow is 830 +/-10L/min; the specific vacuum arc remelting process comprises the following steps:

according to the parameters of the smelting conditions obtained by the model simulation of the embodiment 12, a metal melting pool is established, the smelting voltage is controlled to be 22.3 +/-1.2V, the smelting current is controlled to be 5.2 +/-0.9 KA, and the high-temperature alloy is smelted by regulating and controlling the smelting rate to be 3.0 +/-0.05 kg/min;

when the weight of the solidified ingot is 200 plus or minus 50kg, filling helium into the vacuum arc remelting furnace, maintaining the pressure of the helium in the furnace at 225 plus or minus 75Pa, and smelting at a constant melting rate;

when the residual weight of the high-temperature alloy consumable electrode is 100 +/-50 kg, stopping helium filling, and reducing the melting rate until the melting is finished;

Application example 8

The present application example differs from the above application example 7 in that: the flow rate of the cooling circulating water is 800 +/-10L/min.

Application example 9

The present application example differs from the above application example 7 in that: the flow rate of the cooling circulating water is 770 +/-10L/min.

Comparative application example 1

The present comparative application example 1 differs from the above application example 1 in that: based on the existing technological condition parameters, the melting rate of the vacuum arc remelting high-temperature alloy GH4169 with the diameter of 508mm is controlled to be 3.0 +/-0.05 kg/min.

Comparative application example 2

The present comparative application example 2 differs from the above application example 4 in that: based on the existing process condition parameters, the melting rate of the high-temperature alloy GH4720Li with the vacuum arc remelting diameter of 508mm is controlled to be 3.2 +/-0.05 kg/min.

Comparative application example 3

The present comparative application example 3 differs from the above application example 7 in that: based on the existing technological condition parameters, the cooling circulating water flow of the high-temperature alloy GH4169 with the vacuum arc remelting diameter of 406mm is controlled to be 1000 +/-10L/min.

Performance test

Segregation coefficient experimental analysis was performed on each element of the solidified GH4169 ingots prepared by vacuum arc remelting of the high-temperature alloy GH4169 having a diameter of 508mm in the above application examples 1 to 3 and comparative application example 1. The analysis method comprises the following steps: and measuring the content distribution condition of each element in the dendrite trunk and interdendritic region by using an electronic probe and an energy spectrometer, sorting and analyzing the data, and calculating the segregation coefficient of each element. The test results are given in table 7 below:

TABLE 7 elemental segregation coefficients of solidified GH4169 ingots of application examples 1-3 and comparative application example 1

Item	Melting Rate (kg/min)	Al	Ti	Nb	Cr	Co
							Application example 1	3.5±0.05	1.12	1.42	2.06	0.94	0.95
Application example 2	3.7±0.05	1.09	1.39	2.03	0.96	0.96
							Application example 3	3.9±0.05	1.11	1.40	2.05	0.95	0.95
Comparative application example 1	3.0±0.05	1.43	2.07	2.84	0.81	0.83

The data in the table 7 show that when the high-temperature alloy GH4169 with the diameter of 508mm is remelted by vacuum arc, the segregation coefficient of Al in the ingot obtained by the optimized process compared with the original process parameters is reduced from 1.43 to 1.10, and is reduced by 23%; the segregation coefficient of Ti is reduced to 1.40 from 2.07, which is reduced by 32%; the segregation coefficient of Nb is reduced from 2.84 to 2.05, which is reduced by 28 percent; the segregation coefficient of Cr is increased from 0.81 to 0.95 and is reduced by 17 percent; the segregation coefficient of Co increased from 0.83 to 0.95, which decreased by 14%.

Further, segregation coefficient experimental analysis was performed on each of the solidified GH4720Li ingots produced by vacuum arc remelting of a high temperature alloy GH4720Li having a diameter of 508mm in the above application examples 4 to 6 and comparative application example 2, and the test results are shown in Table 8 below:

TABLE 8 elemental segregation coefficients of solidified GH4720Li ingots of application examples 4-6 and comparative application example 2

Item	Melting Rate (kg/min)	Al	Ti	Cr	Co
						Application example 4	3.5±0.05	1.11	2.12	0.95	0.94
Application example 5	3.7±0.05	1.09	2.10	0.96	0.96
						Application example 6	3.9±0.05	1.08	2.07	0.97	0.96
Comparative application example 2	3.2±0.05	1.27	2.63	0.75	0.79

The data in the table 8 show that when the high-temperature alloy GH4720Li with the diameter of 508mm is remelted by vacuum arc, the segregation coefficient of Al in the ingot obtained by the optimized process compared with the original process parameters is reduced from 1.27 to 1.09 by 14 percent; the segregation coefficient of Ti is reduced to 2.10 from 2.63, and is reduced by 20 percent; the segregation coefficient of Cr is increased from 0.75 to 0.96 and is reduced by 28 percent; the segregation coefficient of Co increased from 0.79 to 0.95, which was decreased by 21%.

Further, segregation coefficient experimental analysis was performed on each element of the solidified GH4169 ingots obtained by vacuum arc remelting of the high temperature alloy GH4169 having a diameter of 406mm in the above application examples 7 to 9 and comparative application example 3. The analysis method comprises the following steps: and measuring the content distribution condition of each element in the dendrite trunk and interdendritic region by using an electronic probe and an energy spectrometer, sorting and analyzing the data, and calculating the segregation coefficient of each element. The test results are given in table 9 below:

TABLE 9 elemental segregation coefficients for solidified GH4169 ingots of application examples 7-9 and comparative application example 3

Item	Cooling circulation water flow (L/min)	Al	Ti	Nb	Cr	Co
							Application example 7	830±10	1.05	1.32	1.87	0.97	0.98
Application example 8	800±10	1.04	1.32	1.86	0.97	0.98
							Application example 9	770±10	1.04	1.31	1.85	0.97	0.98
Comparative application example 3	1000±10	1.09	1.37	1.93	0.94	0.94

The data in the table 9 show that when the high-temperature alloy GH4169 with the diameter of 406mm is remelted by vacuum arc, the segregation coefficient of Al in the ingot obtained by the optimized process compared with the original process parameters is reduced from 1.09 to 1.04 by 5%; the segregation coefficient of Ti is reduced from 1.37 to 1.32, which is reduced by 4%; the segregation coefficient of Nb is reduced from 1.93 to 1.86, which is reduced by 4%; the segregation coefficient of Cr is increased from 0.94 to 0.97 and is reduced by 3 percent; the segregation coefficient of Co increased from 0.94 to 0.98, and decreased by 4%.

According to the segregation results of the three high-temperature alloys, the process condition parameters are simulated based on the vacuum arc remelting 3D model, the macro-microstructure of the solidified ingot is visually represented, the process condition parameters which are more suitable are determined through the microstructure, the smelting process parameters are further optimized, the alloy segregation can be effectively reduced, and the metallurgical quality is improved.

The present embodiment is only for explaining the present application, and it is not limited to the present application, and those skilled in the art can make modifications of the present embodiment without inventive contribution as needed after reading the present specification, but all of them are protected by patent law within the scope of the claims of the present application.

Claims

1. A method for establishing a vacuum arc remelting 3D model for controlling segregation of high-temperature alloy is characterized by comprising the following steps of: establishing a vacuum arc remelting 3D model by adopting a computer numerical simulation method, wherein the vacuum arc remelting 3D model comprises a solidification heat transfer macro model, a solidification ingot casting micro model and a smelting process parameter model of a vacuum arc remelting high-temperature alloy;

the solidification ingot casting micro model comprises a heat transfer model, a mass transfer model, a crystal face curvature model, a crystal grain nucleation model, a secondary dendrite spacing model and a dendrite growth dynamics model;

the convective heat transfer model between the molten alloy and the solidified ingot is shown as the following formula (1-4):

（1-4）；

in the formula (1-4), T₁-T₂Represents the temperature gradient of the alloy liquid and the solidified cast ingot, and has the unit of K, wherein T₁Expressed as the temperature of the alloy liquid in units of K, T₂The temperature of the solidified cast ingot close to one side of the alloy liquid is expressed in K; h is₁The heat convection coefficient between the molten alloy and the solidified cast ingot is expressed in W.m^-2•K^-1；

The conduction heat transfer model inside the solidified ingot is shown as the following formula (1-5):

（1-5）；

in the formula (1-5), the metal oxide,λ _{alloy (I)}The thermal conductivity of the solidified ingot is expressed in W.m^-1•K^-1；T ₂-T ₃Denotes the temperature gradient of the solidified ingot in K, where T₂The temperature of the solidified ingot close to the molten metal is expressed in units of K and T₃The temperature of the solidified ingot close to one side of the crystallizer is expressed in K; Δ d represents the thickness of the solidified ingot in m;

the heat transfer model between the solidified ingot and the inner wall of the crystallizer is shown as the following formula (1-6):

（1-6）；

in the formula (1-6),λ _{air conditioner}Denotes the thermal conductivity of helium in W.m^-1•K^-1；d_{Air conditioner}The space between the solidified cast ingot and the inner wall of the crystallizer is expressed as m; h is_radRepresents the radiant heat transfer coefficient of the air gap and has the unit of W.m^-1•K^-1；h₃The heat convection coefficient between the solidified ingot and the inner wall of the crystallizer is expressed in W.m^-2•K^-1；T ₃-T ₄Denotes the temperature gradient between the solidified ingot and the inner wall of the crystallizer, in K, where T₃The temperature of the solidified ingot close to the side of the crystallizer is expressed in units of K and T₄Represents the temperature of the inner wall of the crystallizer and has the unit of K;

the conduction heat transfer model between the inner wall and the outer wall of the crystallizer is shown as the following formula (1-7):

（1-7）；

in the formula (1-7), the compound,λ _{copper (Cu)}Represents the heat conductivity coefficient of the copper crystallizer and has the unit of W.m^-1•K^-1；d_{Copper (Cu)}Represents the thickness of the copper crystallizer and has the unit of m;T ₄-T ₅denotes the temperature gradient of the crystallizer in K, where T₄Denotes the temperature of the inner wall of the crystallizer in units of K, T₅Represents the temperature of the outer wall of the crystallizer in K;

the model of the convection heat transfer between the outer wall of the crystallizer and the cooling circulating water is shown as the following formula (1-8):

（1-8）；

in the formula (1-8),T ₅-T ₆the temperature gradient between the outer wall of the crystallizer and the cooling circulation water is expressed in K, wherein T₅Denotes the temperature of the outer wall of the crystallizer in K, T₆Represents the temperature of the cooling circulating water, and has the unit of K;h ₅indicating convection between the outer wall of the crystallizer and the cooling circulation waterThermal coefficient in W.m^-2•K^-1，h ₅The expression is shown in the following formula (1-9):

（1-9）；

in the formula (1-9), the metal oxide,λ _frepresents the heat conductivity coefficient of the cooling circulating water, and the unit is W.m^-1•K^-1；vRepresents the flow rate of the cooling circulation water in m.s^-1；μThe viscosity of the cooling circulating water is expressed in m²•s^-1；dThe equivalent diameter of the cooling circulation water flow is expressed in m; pr represents a Plantt coefficient;

the smelting process parameter model is shown as the following formula (1-10):

（1-10）；

in the formula (1-10), the metal oxide,T _{molten bath}Represents the surface temperature of the molten metal bath in K;T _Lrepresents the liquidus temperature of the alloy in K; j represents the smelting current in KA; d_{i-ingot casting}Represents the ingot diameter in m;

the microscopic heat transfer model is shown in the following formula (1-11):

（1-11）；

Representing Laplace algorithmA seed; t is_{Temperature field}Represents the temperature field of the calculation area, with the unit of K;

represents the heat released by the latent heat of solidification and has a unit of W.m^-2；f _sRepresents the solid phase ratio; τ represents time in units of s;

the mass transfer model is shown in the following formula (1-12):

（1-12）；

in the formula (1-12), the metal oxide,C _irepresents solute concentration in%;

represents the laplacian operator;D _{i-accommodation diffusion}Represents the solute diffusion coefficient; subscriptiS is s or l, s represents a solid phase and l represents a liquid phase;

indicating the discharged solute of the ingot changing from solid phase to liquid phase,f _srepresents the solid phase ratio; τ represents time in units of s;

the macroscopic supercooling degree delta T of the crystal face curvature model at the solid-liquid interface₀And the microcosmic supercooling degree delta T at the solid-liquid interface and the macroscopic supercooling degree delta T at the solid-liquid interface₀As shown in the following formulae (1-13):

（1-13）；

in the formula (1-13), ΔT _cRepresenting the degree of supercooling of the component; deltaT _rRepresents the degree of curvature supercooling; deltaT _tRepresenting the degree of supercooling of the temperature; deltaT _kRepresenting the degree of kinetic supercooling;

（1-14）；

in the formula (1-17), the metal oxide,T _Lrepresents the liquidus temperature in K;T _solid-liquidRepresents the temperature at the solid-liquid interface in K;C ₀denotes initial concentration in%;mrepresents the slope of the liquidus;

representing the interfacial anisotropy function;

（1-15）；

in the formula (1-15), the metal oxide,N _nrepresents the number of neighbor cells; deltaxRepresenting the size of the cells, wherein the cells participating in counting can select neighbor cells including a nearest neighbor, a next neighbor and a third neighbor;f _s(i) represents the solid phase ratio;

in the crystal grain nucleation model, continuous rather than discrete dependence relationship between the number of crystal grains and supercooling degree is assumedDistribution function of dispersiondn/d(ΔT) To describe the variation of the grain density, as shown in the following formulas (1-16):

（1-16）；

in the formula (1-16), the metal oxide,dn/d（ΔT) Indicating an increase in supercooling degreed（ΔT) The resulting increase in grain densitydn；n _maxRepresents the maximum nucleation particle density in m^-3；ΔT _σ-standard deviation supercooling degree, in units of K; deltaT _maxRepresents the maximum nucleation supercooling degree, and the unit is K;

the secondary dendrite spacing model is shown in the following formula (1-17):

（1-17）；

（1-18）；

in the formula (1-18), the metal oxide,σ _slrepresents the solid-liquid interfacial energy in units of J;D _lrepresents the diffusion coefficient of the solute in the alloy liquid;T _Mrepresents the melting point of the pure substance in K;Lrepresents latent heat of fusion in W.m^-3；kRepresents the equilibrium partition coefficient;mrepresents the liquidus slope of the alloying element;C _l(t) Represents the concentration of liquid phase solute at the time t, and the unit is%;C _l,0expressed as the nominal concentration of solute in the liquid phase in%;

the dendrite growth kinetic model is shown by the following formula (1-19):

（1-19）；

（1-20）；

in the formula (1-20), the compound,c ₀represents the mass fraction of each element in the alloy, and the unit is%; ρ represents the density of the superalloy in kg.m^-3；mRepresents the slope of the liquidus;krepresents the solute equilibrium partition coefficient;Drepresents the solute self-diffusion coefficient; Γ denotes the Gibbs-Thomson coefficient.

2. The method of claim 1, wherein the vacuum arc remelting 3D model for controlling superalloy segregation comprises: the solidification heat transfer macroscopic model is shown as the following formula (1-1);

（1-1）；

in the formula (1-1), ρ represents the density of the alloy in kg.m^-3(ii) a Cp represents the constant-pressure specific heat capacity of the alloy and has the unit of kJ/(kg.K); t is_{Conveying appliance}The heat transfer temperature of a heat transfer link in the vacuum arc remelting process is represented by K; t represents time in units of s; λ represents the thermal conductivity, in units of W/(m.k); q represents a heat source term in W.m^-3(ii) a And x, y and z represent three-dimensional coordinates of the heat transfer direction in the heat transfer link.

3. The method of claim 2 wherein said vacuum arc is established to control segregation of said superalloyA method of remelting a 3D model, characterized in that: the heat source term Q represents the heat released by the latent heat of solidification in the process of simulating the solidification of the ingot, and the solid phase ratio in unit volume and unit time is assumed to be

The heat released in the process of ingot solidificationQComprises the following steps:

（1-2）；

Represents the solid phase ratio;

（1-3）。

4. a vacuum arc remelting control method for reducing segregation of high-temperature alloy is characterized by comprising the following steps: the method comprises the following steps:

step A, simulating process parameters: setting a plurality of groups of melting rate values according to the performance of the high-temperature alloy, and combining the melting rate values into a vacuum arc remelting control model established by the method of any one of claims 1-3 according to the plurality of groups of melting rate values to iteratively obtain a plurality of groups of smelting process condition simulation values;

step B, simulating a smelting process: analyzing the appearance and average depth of a metal molten pool, the dendrite spacing of an ingot and solidification structure information under the corresponding melting rate according to a plurality of groups of smelting process condition simulation values, and formulating suitable smelting condition parameters of the vacuum arc remelting superalloy;

step C, smelting high-temperature alloy: and smelting the high-temperature alloy according to the smelting condition parameters obtained by the model simulation.