A simulation method for predicting the solidification process of vacuum consumable melting ingot

Abstract

The present invention discloses a simulation method for predicting the solidification process of vacuum consumable arc melting ingots, which relates to the technical field of vacuum consumable arc melting. By establishing relevant mathematical models of electromagnetic fields and flow fields, the geometric model is meshed, and the Eulerian-Eulerian method is adopted to set three phases: molten metal, equiaxed dendrites, and columnar crystals, obtain relevant material properties, set relevant boundary conditions and relevant dynamic grid parameters, and simulate the flow and solidification of molten metal during vacuum consumable arc melting, as well as the distribution of electromagnetic fields and solidification structures. The present invention simulates the rise of the molten pool and the solidification process of the ingot during vacuum consumable arc melting, obtains the flow morphology of the molten metal during the solidification process, has the ability to predict the macroscopic segregation of the ingot, plays an important guiding role in optimizing the vacuum consumable arc melting process to obtain an ingot with uniform composition, and has important significance for actual production.

Description

Technical Field

[0001] The invention relates to the technical field of vacuum consumable arc melting, and in particular to a simulation method for predicting a vacuum consumable melting ingot solidification process. Background Art

[0002] Vacuum consumable arc melting is mainly used to prepare active metal ingots such as titanium and zirconium for the production of parts in the aerospace, military and other industrial fields. The process of vacuum consumable arc melting is: the consumable electrode melts into metal droplets under the action of the DC arc and falls into the water-cooled copper crucible. The liquid level of the molten pool in the crucible continues to rise, and the metal liquid in the molten pool gradually solidifies and finally forms an ingot. During the remelting process, the uneven distribution of solutes will lead to the occurrence of segregation, which affects the processing performance and use performance of parts or components produced by the ingot. The vacuum consumable arc melting process involves multiple physical processes such as temperature field, electromagnetic field, flow field, and concentration field. During the melting process, the temperature field, flow field, and electromagnetic field have an important influence on the solidification structure and macro-segregation of the ingot. In actual production, macro-segregation can only be obtained by dissecting the ingot, which has the disadvantages of high cost and long time. At present, using computational simulation technology to predict the formation and evolution of macro-segregation of ingots is an effective means.

[0003] At present, scholars at home and abroad mainly use numerical simulation methods to predict the macro-segregation of ingots, and have achieved certain results. However, there are still the following problems: there has been no systematic study on vacuum consumable arc melting, there is a lack of simulation methods to predict the macro-segregation of vacuum consumable arc melting ingots, and there is no research on the influence of electromagnetic fields on macro-segregation.

[0004] It can be seen that there is an urgent need for a simulation method that can accurately and efficiently predict the macrosegregation of vacuum consumable arc melting ingots.

[0005] Therefore, the technicians in this field are committed to developing a simulation method for predicting the solidification process of vacuum consumable melting ingots. Using the finite volume method and the Euler-Euler multiphase flow model, a three-phase mixed model of vacuum consumable alloy ingots is established, realizing and breaking through the coupling between the electric field, magnetic field, temperature field, flow field, and concentration field involved in the consumable melting and solidification process. The flow and solidification structure of the molten metal during vacuum consumable arc melting can be simulated, and the effects of the self-inductance magnetic field and the stirring magnetic field on the flow of the molten metal during the solidification process and the macro-segregation of the ingot after solidification are analyzed and discussed, and the problem of difficult to predict macro-segregation in actual production is solved, which is of great significance for adjusting the process parameters to obtain an ingot with uniform composition. Summary of the invention

[0006] In view of the above-mentioned defects of the prior art, the technical problem to be solved by the present invention is how to simulate the flow and solidification of molten metal during vacuum consumable arc melting, as well as the distribution of electromagnetic field and solidification structure, so as to solve the problem of predicting macrosegregation and shrinkage porosity in actual production. To achieve the above-mentioned purpose, the present invention provides a simulation method for predicting the solidification process of vacuum consumable melting ingot, comprising the following steps:

[0007] Step 1, establishing a mathematical model related to the electromagnetic field and the flow field, taking into account the electromagnetic field, the hot solute convection, the sedimentation of the equiaxed dendrites, and the CET transformation of the columnar crystals to the equiaxed dendrites;

[0008] Step 2: Use appropriate mesh size to mesh the geometric model;

[0009] Step 3, using the Eulerian-Eulerian method, setting three phases: molten metal, equiaxed dendrites and columnar crystals;

[0010] Step 4: Obtain relevant material properties;

[0011] Step 5: Set relevant boundary conditions;

[0012] Step 6, obtaining the speed of the molten pool surface moving upward through the relationship between the current and the metal droplet formation rate, and setting relevant dynamic grid parameters;

[0013] Step 7: Initialize the calculation conditions, set the initial temperature conditions based on the relationship between current and superheat, and start iterative calculation;

[0014] Step 8, the dendrite structure of the equiaxed dendrite is processed with a simplified dendrite model, and the nucleation of the equiaxed dendrite and the growth of the columnar crystal and the equiaxed dendrite are calculated;

[0015] Step 9, derive the relevant electromagnetic field equations according to the Maxwell equations, and solve the current density, the magnetic induction intensity of the self-induced magnetic field, the Lorentz force of the self-induced magnetic field, the Lorentz force of the stirring magnetic field and the Joule heat;

[0016] Step 10: By using the flow dynamics related equations, the mass, momentum, solute and energy transfer in the smelting process are explicitly solved to obtain the distribution area and mass of the molten metal, the columnar crystals and the equiaxed dendrites, as well as the flow morphology of the molten metal and the solute distribution of the ingot.

[0017] Furthermore, by establishing an electromagnetic field model, the current density is calculated. The magnetic induction intensity (B θ ), the Lorentz force of the self-induced magnetic field, the Lorentz force of the stirring magnetic field and the Joule heat (Q):

[0018] By defining the scalar potential and the magnetic vector Invisibly solve the current density and the magnetic induction intensity of the self-inductance magnetic field:

[0019]

[0020]

[0021]

[0022]

[0023]

[0024] Where σ is the electrical conductivity, u0 is the magnetic permeability, J r and J z are the radial and axial current densities, A r and A z They are radial and axial magnetic vectors respectively, z is axial and r is radial.

[0025] Since the magnetic induction intensity in the radial and tangential directions is 0 under the stirring magnetic field, it has a constant value only in the axial direction. z )for:

[0026] B z = constant

[0027] The expression of the Lorentz force of the self-induced magnetic field is as follows:

[0028]

[0029] The expression of the Lorentz force of the stirring magnetic field is as follows:

[0030]

[0031] According to Ohm's law, the Joule heat (Q) formula is as follows:

[0032]

[0033] in, is the electric field strength.

[0034] Furthermore, the relevant material properties in step 4 are obtained through experiments.

[0035] Furthermore, the boundary conditions in step 5 include boundary conditions related to electric field, magnetic field and flow field.

[0036] Furthermore, in step 8, the nucleation of the equiaxed dendrites is calculated by Gaussian distribution heterogeneous nucleation theory, and the growth of the equiaxed dendrites and the columnar crystals is calculated by solute diffusion driven growth theory.

[0037] Furthermore, the nucleation calculation equation of the equiaxed dendrite is:

[0038]

[0039]

[0040] Supplementary equations:

[0041]

[0042]

[0043] Where: n is the grain density, n max is the maximum nucleation density, N e is the equiaxed dendrite growth rate, is the movement speed of the equiaxed dendrite, t is the time, f env is the volume fraction of equiaxed dendrites inside the envelope, Γ env is the growth rate of the equiaxed dendrite, S env is the surface density of the equiaxed dendrite, v tip is the growth rate of the equiaxed dendrite tip, ΔT is the supercooling, and ΔT N is the average nucleation undercooling corresponding to the maximum nucleation rate, ΔT σ is the Gauss distribution deviation.

[0044] Furthermore, the mass transfer equation in step 10 is:

[0045]

[0046]

[0047]

[0048] The mass (M) of the metal liquid phase transferred to the solid phase in the equiaxed dendrite per unit volume and per unit time is le )for:

[0049]

[0050] The mass (M) of the metal liquid phase transferred to the root region of the columnar dendrite per unit volume and per unit time lc )for:

[0051]

[0052] The growth rate of the equiaxed dendrite According to the diffusion model,

[0053]

[0054] The growth rate of the columnar dendrite root

[0055]

[0056] Where: n is the grain density, f e 、f c and f l are the volume fractions of the equiaxed dendrites, the columnar crystals, and the metal liquid phase, respectively, and are the velocities of the equiaxed dendrite and the metal liquid phase, ρ e , c and ρ l are the densities of the equiaxed dendrite, the columnar crystal and the metal liquid phase, λ1 is the primary dendrite spacing, R e and R c are the radii of the equiaxed dendrite and the columnar crystal, R f，e and R f，c are the maximum radii of the equiaxed dendrite and the columnar crystal allowed in the control volume, d e and d c are the equivalent diameters of the equiaxed dendrite and the columnar crystal, t is the time, D l and D s are the diffusion coefficients of the metal liquid phase and the solid phase, respectively, and are the solute concentrations of the metal liquid phase and the solid phase at the solidification interface, respectively, l and c s are the solute concentrations of the metal liquid phase and the solid phase, respectively, imp It is the Avrami factor.

[0057] Furthermore, the momentum transfer equation in step 10 is:

[0058]

[0059]

[0060] Pressure Tensor u q is the metal liquid phase (u l ) and the equiaxed dendrite phase (u e ) viscosity, the viscosity of the equiaxed dendrite phase ue It can be deduced from the effective viscosity, that is:

[0061]

[0062] The Boussinesq method is used to calculate the thermal-solute buoyancy (F l ) is as follows:

[0063] F l =f l ·ρ l ·g·[β T ·(T ref -T l )+β c ·(c ref -c l )]

[0064] For the equiaxed dendrite phase, the buoyancy force (F e ) is caused by the density difference between the equiaxed dendrite phase and the metal liquid phase, so:

[0065] F e =f e ·(ρ e -ρ l )·g

[0066] Where: p is the pressure, and are respectively the momentum exchange rates between the metal liquid phase and the equiaxed dendrites, the metal liquid phase and the columnar crystals, and the columnar crystals and the equiaxed dendrites, and are the stress-strain tensors of the equiaxed dendrite and the metal liquid phase, respectively, is the packing limit of the equiaxed dendrite, g is the gravitational acceleration, β c and β T are the solute expansion coefficient and thermal expansion coefficient, c ref and T ref are the reference composition and reference temperature, T l and c l are respectively the temperature of the metal liquid phase and the solute concentration in the metal liquid phase;

[0067]

[0068] is the momentum exchange caused by phase change, and the specific expression is:

[0069]

[0070] It is the momentum exchange between the metal liquid phase and the equiaxed dendrite phase due to the relative motion, and the specific expression is:

[0071]

[0072] Where K le It is obtained based on the solid-liquid interface drag force model;

[0073]

[0074] The momentum exchange caused by the phase change is The presence of the metal liquid phase and the columnar crystal phase causes a momentum exchange of The drag coefficient is K is the permeability factor;

[0075] Same as above, Since there is no mass exchange between the columnar crystals and the equiaxed dendrites, The drag coefficient of the two phases is:

[0076]

[0077] Furthermore, the solute transport equation in step 10 is:

[0078]

[0079]

[0080]

[0081] in D e , D l and D c are the diffusion coefficients of the equiaxed dendrite, the metal liquid phase, and the columnar crystal, respectively, c e 、c l and c c are the concentrations of the equiaxed dendrite, the metal liquid phase, and the columnar crystal, respectively, and k is the equilibrium distribution coefficient.

[0082] Furthermore, the energy transfer equation in step 10 is:

[0083]

[0084]

[0085]

[0086] in The heat exchange caused by the phase transformation between the molten metal and the equiaxed dendrite is: The two-phase energy exchange caused by heat transfer is (T l -T e );

[0087] in The heat exchange caused by the transformation of the metal liquid phase to the equiaxed dendrite phase is The two-phase energy exchange caused by heat transfer is

[0088] in The heat exchange caused by the transformation of the metal liquid phase to the equiaxed dendrite phase is The two-phase energy exchange caused by heat transfer is

[0089] Among them, h l 、h e and h c are the enthalpy of the metal liquid phase, the equiaxed dendrite, and the columnar crystal, respectively, k l , k e and k c are the thermal conductivities of the metal liquid phase, the equiaxed dendrites, and the columnar crystals, respectively; Q is the Joule heat, Q (e , Q lc and Q ce are the energy exchanges between the metal liquid phase and the equiaxed dendrites, the metal liquid phase and the columnar crystals, and the columnar crystals and the equiaxed dendrites, respectively, T l , T e and T c are the temperatures of the metal liquid phase, the equiaxed dendrites, and the columnar crystals, respectively, H * is the volume heat transfer coefficient.

[0090] The present invention is suitable for accurately predicting the macro-segregation of vacuum consumable arc melting ingots of different materials, obtaining the influence of electromagnetic field on the flow and composition distribution of molten metal, guiding the actual production of vacuum consumable arc melting, and providing a basis for optimizing process parameters to obtain ingots with uniform composition.

[0091] Compared with the prior art, the present invention has the following technical effects:

[0092] 1. The present invention simulates the rise of the molten pool and the solidification process of the ingot during vacuum consumable arc melting by setting dynamic grid conditions, and obtains the flow pattern of the molten metal during the solidification process, which is of great significance to actual production.

[0093] 2. The present invention is suitable for accurately predicting the macro-segregation of vacuum consumable melting ingots of different materials, and plays an important guiding role in optimizing the VAR process to obtain ingots with uniform composition.

[0094] 3. The present invention successfully simulates the distribution of the electromagnetic field by establishing an electromagnetic field model, and solves the research problem of the influence of the self-inductance magnetic field and the stirring magnetic field on the flow and macro-segregation of the molten metal.

[0095] 4. The present invention is a three-phase model, which has the ability to predict the phase distribution of the ingot by solving the mass, momentum, energy, and transmission related equations and considering the interaction between columnar crystals and equiaxed dendrites.

[0096] The concept, specific structure and technical effects of the present invention will be further described below in conjunction with the accompanying drawings to fully understand the purpose, characteristics and effects of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0097] Figure 1 is a current density distribution diagram in an ingot of a preferred embodiment of the present invention;

[0098] Figure 2 is a Lorentz force vector diagram of the self-induced magnetic field in an ingot of a preferred embodiment of the present invention;

[0099] Figure 3 is a Lorentz force vector diagram of a stirring magnetic field in an ingot of a preferred embodiment of the present invention;

[0100] Figure 4 It is a preferred embodiment of the present invention, which is a vector diagram of the flow rate of the molten metal in the ingot at 500s;

[0101] Figure 5 It is a preferred embodiment of the present invention and is a vector diagram of the flow rate of the molten metal in the ingot at 1500s;

[0102] Figure 6 It is a preferred embodiment of the present invention, a vector diagram of the flow rate of the molten metal in the ingot at 2500s;

[0103] Figure 7 It is a final segregation distribution diagram of the ingot of a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0104] The following describes several preferred embodiments of the present invention with reference to the drawings in the specification, so that the technical content is clearer and easier to understand. The present invention can be embodied in many different forms of embodiments, and the protection scope of the present invention is not limited to the embodiments mentioned in the text.

[0105] Example

[0106] A simulation method for predicting macrosegregation of vacuum consumable melting ingots comprises the following steps:

[0107] Step 1: Establish the relevant mathematical models of electromagnetic field and flow field, taking into account the electromagnetic field, hot melt convection, sedimentation of equiaxed dendrites, and CET transformation of columnar crystals to equiaxed dendrites.

[0108] Step 2: Use appropriate mesh size to mesh the geometric model.

[0109] Step 3: Using the Eulerian-Eulerian method, set up three phases: molten metal, equiaxed dendrites, and columnar crystals.

[0110] Step 4: Obtain relevant material properties through experiments.

[0111] Step 5: Set relevant boundary conditions, including electric field, magnetic field, and flow field boundary conditions.

[0112] Step 6. Obtain the upward movement speed of the molten pool surface through the relationship between current and metal liquid formation rate, and set relevant dynamic grid parameters.

[0113] Step 7: Initialize the calculation conditions. According to the relationship between current and superheat, set the initial temperature conditions and start iterative calculation.

[0114] Step 8: Process the dendrite structure of the equiaxed dendrite with a simplified dendrite model, calculate the nucleation of the equiaxed dendrite by Gaussian distribution heterogeneous nucleation theory, and calculate the growth of columnar crystals and equiaxed dendrites by solute diffusion driven growth theory.

[0115] Step 9. According to Maxwell's equations, the relevant electromagnetic field equations are derived, and the current density, the magnetic induction intensity of the self-induced magnetic field, the Lorentz force of the self-induced magnetic field, the Lorentz force of the stirring magnetic field and the Joule heat are solved invisible.

[0116] Step 10: By using the flow dynamics related equations, the mass, momentum, solute and heat transfer in the smelting process are explicitly solved to obtain the distribution areas of the molten metal, columnar crystals, equiaxed dendrites, the flow pattern of the molten metal and the solute distribution of the ingot.

[0117] Step 11: produce an ingot by a vacuum consumable arc furnace, cut, polish and etch it to obtain the ingot microstructure distribution of the cross section, and use ICP to analyze the composition to obtain the composition distribution on the center line of the ingot.

[0118] Step 12: Compare the simulation results with the experimental results, including the molten pool morphology, phase distribution, and macro-segregation distribution, to verify the reliability and accuracy of this simulation method and prepare for guiding actual production.

[0119] The mathematical model is as follows:

[0120] (1) Electromagnetic field model

[0121] There are two forms of current and magnetic field in the vacuum consumable arc melting process. Due to the arc discharge, a melting current is generated on the ingot and the crucible, which in turn generates a self-induced magnetic field. The radially distributed melting current interacts with the self-induced magnetic induction intensity to produce a self-induced Lorentz force. The stirring current flowing in the coil wrapped around the outer wall of the crucible generates an upward magnetic field along the axis inside the crucible. This magnetic field interacts with the melting current to produce a stirring Lorentz force. The electromagnetic stirring in the vacuum consumable arc melting process is to add a stirring magnetic field to the original self-induced magnetic field to generate two electromagnetic forces that drive the movement of the molten pool. By establishing an electromagnetic field model, the applied remelting current density, the magnetic induction intensity of the self-induced magnetic field, the Lorentz force of the self-induced magnetic field, the Lorentz force of the stirring magnetic field and the Joule heat can be calculated.

[0122] By defining the scalar potential and the magnetic vector Invisible solution for current density and the magnetic induction intensity of the self-induced magnetic field (B θ ):

[0123]

[0124]

[0125]

[0126]

[0127]

[0128] Since the magnetic induction intensity in the radial and tangential directions is 0 under the stirring magnetic field, it has a constant value only in the axial direction. z )for:

[0129] B z = constant

[0130] The expression of the Lorentz force of the self-induced magnetic field is as follows:

[0131]

[0132] The expression of the Lorentz force of the stirring magnetic field is as follows:

[0133]

[0134] From Ohm's law, the formula for Joule heat (Q) is as follows:

[0135]

[0136] Where σ is the electrical conductivity, u0 is the magnetic permeability, J r and J z are the radial and axial current densities, A r and A z are the radial and axial magnetic vectors respectively, z is the axial direction, r is the radial direction, is the electric field strength.

[0137] (2) The mass, momentum, energy, and solute transport equations between the liquid metal phase, equiaxed dendrite phase, and columnar crystal phase are solved in a coupled manner to obtain the distribution areas of the three phases, the flow pattern of the liquid metal, and the solute distribution of the ingot. The nucleation of equiaxed dendrites is calculated using the Gaussian distribution heterogeneous nucleation theory, and the growth of columnar crystals and equiaxed dendrites is calculated using the solute diffusion driven growth theory.

[0138] Nucleation and transport equations for equiaxed dendrites:

[0139]

[0140]

[0141] Supplementary equations:

[0142]

[0143]

[0144] Where: n is the grain density, n max is the maximum nucleation density, N e is the equiaxed dendrite growth rate, is the movement speed of the equiaxed dendrite, t is the time, f env is the volume fraction of equiaxed dendrites inside the envelope, Γ env is the growth rate of equiaxed dendrites, S env is the surface density of equiaxed dendrites, v tip is the growth rate of the equiaxed dendrite tip, ΔT is the supercooling, and ΔT N is the average nucleation undercooling corresponding to the maximum nucleation rate, ΔT σ is the Gauss distribution deviation.

[0145] Mass transfer equation:

[0146]

[0147]

[0148]

[0149] The mass transfer from the liquid phase to the solid phase in the equiaxed dendrite per unit volume and per unit time (M le )for:

[0150]

[0151] The mass of liquid phase transferred to the columnar crystal in the root area of ​​dendrite per unit volume and per unit time (M lc )for:

[0152]

[0153] Growth rate of equiaxed dendrites According to the diffusion model,

[0154]

[0155] Growth rate of columnar dendrite root

[0156]

[0157] Where: n is the grain density, f e 、f c and f l are the volume fractions of the equiaxed dendrites, the columnar crystals, and the metal liquid phase, respectively, and are the velocities of the equiaxed dendrite and the metal liquid phase, ρ e , c and ρ l are the densities of the equiaxed dendrite, the columnar crystal and the metal liquid phase, λ1 is the primary dendrite spacing, R e and R c are the radii of the equiaxed dendrite and the columnar crystal, R f，e and R f，c are the maximum radii of the equiaxed dendrite and the columnar crystal allowed in the control volume, d e and d c are the equivalent diameters of the equiaxed dendrite and the columnar crystal, t is the time, D l and D s are the diffusion coefficients of the metal liquid phase and the solid phase, respectively, and are the solute concentrations of the liquid phase and the solid phase at the solidification interface, respectively, l and c s are the solute concentrations of the metal liquid phase and the solid phase, respectively, imp is the Avrami factor. Momentum control equation

[0158]

[0159]

[0160] Pressure Tensor u q is the metal liquid phase (u l ) and the equiaxed dendrite phase (u e ) viscosity, the viscosity of the equiaxed dendrite phase u e It can be deduced from the effective viscosity, that is:

[0161]

[0162] The Boussinesq method is used to calculate the thermal-solute buoyancy (F l ) is as follows:

[0163] F l =f l ·ρ l ·g·[β T ·(T ref -T l )+β c ·(c ref -c l )]

[0164] For the equiaxed dendrite phase, the buoyancy force (F e ) is caused by the density difference between the equiaxed dendrite phase and the metal liquid phase, so:

[0165] F e =f e ·(ρ e -ρ l )·g

[0166] Where: p is the pressure, and are respectively the momentum exchange rates between the metal liquid phase and the equiaxed dendrites, the metal liquid phase and the columnar crystals, and the columnar crystals and the equiaxed dendrites, and are the stress-strain tensors of the equiaxed dendrite and the metal liquid phase, respectively, is the packing limit of the equiaxed dendrite, g is the gravitational acceleration, β c and β T are the solute expansion coefficient and thermal expansion coefficient, c ref and T ref are the reference composition and reference temperature, Tl and c l are respectively the temperature of the metal liquid phase and the solute concentration in the metal liquid phase;

[0167]

[0168] is the momentum exchange caused by phase change, and the specific expression is:

[0169]

[0170] It is the momentum exchange between the metal liquid phase and the equiaxed dendrite phase due to the relative motion, and the specific expression is:

[0171]

[0172] Where K le It is obtained based on the solid-liquid interface drag force model.

[0173]

[0174] The momentum exchange caused by the phase change is The presence of the metal liquid phase and the columnar crystal phase causes a momentum exchange of The drag coefficient is K is the permeability factor.

[0175] Same as above, Since there is no mass exchange between the columnar crystals and the equiaxed dendrites, The drag coefficient of the two phases is:

[0176]

[0177] Solute transport equation:

[0178]

[0179]

[0180]

[0181] in D e , D l and D c are the diffusion coefficients of the equiaxed dendrite, the metal liquid phase, and the columnar crystal, respectively, c e 、c l and c c are the concentrations of the equiaxed dendrite, the metal liquid phase, and the columnar crystal, respectively, and k is the equilibrium distribution coefficient.

[0182] Energy governing equation:

[0183]

[0184]

[0185]

[0186] in The heat exchange caused by the transformation of the metal liquid phase to the equiaxed dendrite phase is The two-phase energy exchange caused by heat transfer is

[0187] in The heat exchange caused by the transformation of the metal liquid phase to the equiaxed dendrite phase is The two-phase energy exchange caused by heat transfer is

[0188] in The heat exchange caused by the transformation of the metal liquid phase to the equiaxed dendrite phase is The two-phase energy exchange caused by heat transfer is

[0189] Among them, h l 、h e and h c are the enthalpy of the metal liquid phase, the equiaxed dendrite, and the columnar crystal, respectively, k l , k e and k c are the thermal conductivities of the metal liquid phase, the equiaxed dendrites, and the columnar crystals, respectively; Q is the Joule heat, Q le , Q lc and Q ce are the energy exchanges between the liquid phase and the equiaxed dendrites, the metal liquid phase and the columnar crystals, and the columnar crystals and the equiaxed dendrites, respectively, T l , T e and T c are the temperatures of the metal liquid phase, the equiaxed dendrites, and the columnar crystals, respectively, H * is the volume heat transfer coefficient.

[0190] Figure 1 is a current density distribution diagram of an ingot in a preferred embodiment of the present invention, from Figure 1 It can be seen from the figure that the simulated current flow is the same as the flow path of the actual production process of vacuum consumables: the current flows from the crucible into the ingot, flows laterally to the inside of the ingot at the contact area between the ingot and the crucible, and converges to the arc area, and reaches the electrode after passing through the arc area, forming a complete current loop; at the same time, it can be seen from the figure that the current density inside the ingot decreases along the longitudinal direction, there is almost no current in the lower part of the ingot, and the current density is the largest at the cross section of the molten pool. Figure 2The Lorentz force distribution diagram under the self-inductance magnetic field of a preferred embodiment of the present invention is shown in FIG. Figure 2 It can be seen that the self-induced Lorentz force points obliquely downward to the central axis of the ingot, and can be divided into a radial force pointing to the axis and a downward axial force. Analysis shows that the self-induced Lorentz force can not only make the melt at the edge of the ingot move radially, but also make the melt in the top molten pool move downward. Figure 3 This is a Lorentz force distribution diagram under a stirring magnetic field of a preferred embodiment of the present invention. It can be seen from the figure that the stirring magnetic field generates a tangential Lorentz force, which can cause the fluid in the molten pool to rotate in the horizontal direction, thereby stirring the molten pool. Figure 4-6 The vector diagrams of the flow rate of the molten metal in the ingot at 500s, 1500s and 2500s of the preferred embodiment of the present invention respectively show that the surface of the molten pool rises while the ingot solidifies, and the fluid moves clockwise (the left half of the ingot), forming a vortex in the upper part of the molten pool, bringing the fluid at the edge of the ingot to the center of the ingot, and then moving toward the bottom of the ingot, forming a clockwise circulation, and also drawing heat from the top of the molten pool to the bottom of the molten pool, deepening the depth of the molten pool. During the solidification process, the flow of molten metal is affected by five different driving forces: (1) vertical downward thermal buoyancy; (2) vertical upward solute buoyancy; (3) downward drag force caused by the sedimentation of equiaxed dendrites; (4) self-induced Lorentz force pointing obliquely downward toward the center of the ingot; and (5) tangential stirring Lorentz force. When the two magnetic fields act together, the self-induced Lorentz force and the stirring Lorentz force play a dominant role in the flow. The fluid not only rotates in the vertical direction but also forms a clockwise vortex. The flow vortex in the molten pool moves toward the surface of the molten pool. The flow in the cross section of the molten pool is rapid, and the flow in the lower part of the molten pool is not obvious. Figure 7 This is a final segregation distribution diagram of the ingot of a preferred embodiment of the present invention. Analysis shows that the central area of ​​the ingot centerline is a negative segregation area, and the area away from the center is a positive segregation area.

[0191] The preferred specific embodiments of the present invention are described in detail above. It should be understood that ordinary technicians in the field can make many modifications and changes based on the concept of the present invention without creative work. Therefore, all technical solutions that can be obtained by technicians in the technical field based on the concept of the present invention through logical analysis, reasoning or limited experiments on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A simulation method for predicting the solidification process of a vacuum consumable melting ingot, characterized in that: The method comprises the following steps: Step 1, establishing a mathematical model related to the electromagnetic field and the flow field, taking into account the electromagnetic field, the hot solute convection, the sedimentation of the equiaxed dendrites, and the CET transformation of the columnar crystals to the equiaxed dendrites; Step 2: Use appropriate mesh size to mesh the geometric model; Step 3, using the Eulerian-Eulerian method, setting three phases: molten metal, equiaxed dendrites and columnar crystals; Step 4: Obtain relevant material properties; Step 5: Set relevant boundary conditions; Step 6, obtaining the speed of the molten pool surface moving upward through the relationship between the current and the metal droplet formation rate, and setting relevant dynamic grid parameters; Step 7: Initialize the calculation conditions, set the initial temperature conditions based on the relationship between current and superheat, and start iterative calculation; Step 8, the dendrite structure of the equiaxed dendrite is processed by a simplified dendrite model, and the nucleation of the equiaxed dendrite and the growth of the columnar crystal and the equiaxed dendrite are calculated; the nucleation of the equiaxed dendrite is calculated by Gaussian distribution heterogeneous nucleation theory, and the growth of the equiaxed dendrite and the columnar crystal is calculated by solute diffusion driven growth theory; the nucleation calculation equation of the equiaxed dendrite is: Supplementary equations: Where: n is the grain density, n max is the maximum nucleation density, N e is the equiaxed dendrite growth rate, is the movement speed of the equiaxed dendrite, t is the time, f env is the volume fraction of equiaxed dendrites inside the envelope, Γ env is the growth rate of the equiaxed dendrite, S env is the surface density of the equiaxed dendrite, v tip is the growth rate of the equiaxed dendrite tip, ΔT is the supercooling, and ΔT N is the average nucleation undercooling corresponding to the maximum nucleation rate, ΔT σ is the Gauss distribution deviation; Step 9: According to Maxwell's equations, the relevant electromagnetic field equations are derived, and the current density, the magnetic induction intensity of the self-induced magnetic field, the Lorentz force of the self-induced magnetic field, the Lorentz force of the stirring magnetic field and the Joule heat are solved; by establishing an electromagnetic field model, the current density is calculated. The magnetic induction intensity B of the self-induced magnetic field θ , the Lorentz force of the self-inductance magnetic field, the Lorentz force of the stirring magnetic field and the Joule heat Q: By defining the scalar potential and the magnetic vector Invisibly solve the current density and the magnetic induction intensity B of the self-inductance magnetic field θ : Where σ is the electrical conductivity, u0 is the magnetic permeability, J r and J z are the radial and axial current densities, A r and A z are the radial and axial magnetic vectors respectively, z is the axial direction and r is the radial direction; Because in the stirring magnetic field, the radial and tangential components of the magnetic induction intensity are 0, and only the axial direction has a fixed value constant. The axial magnetic induction intensity B z for: B z =constant The expression of the Lorentz force of the self-induced magnetic field is as follows: The expression of the Lorentz force of the stirring magnetic field is as follows: According to Ohm's law, the Joule heat Q formula is as follows: in, is the electric field strength; Step 10, explicitly solving the mass, momentum, solute and energy transfer in the smelting process through the flow dynamics related equations, and obtaining the distribution areas of the metal liquid phase, the columnar crystals and the equiaxed dendrites, the flow morphology of the metal liquid, and the solute distribution of the ingot; The mass transfer equation is: The mass M of the metal liquid phase transferred to the solid phase in the equiaxed dendrite per unit volume and per unit time is le for: The mass M of the metal liquid phase transferred to the dendrite root region of the columnar crystal per unit volume and per unit time is lc for: The growth rate of the equiaxed dendrite According to the diffusion model, The growth rate of the dendrite root of the columnar crystal Where: n is the grain density, f e 、f c and f l are the volume fractions of the equiaxed dendrites, the columnar crystals, and the metal liquid phase, respectively, and are the velocities of the equiaxed dendrite and the metal liquid phase, ρ e , c and ρ l are the densities of the equiaxed dendrite, the columnar crystal and the metal liquid phase, λ1 is the primary dendrite spacing, R e and R c are the radii of the equiaxed dendrite and the columnar crystal, R f,e and R f,c are the maximum radii of the equiaxed dendrite and the columnar crystal allowed in the control volume, d e and d c are the equivalent diameters of the equiaxed dendrite and the columnar crystal, t is the time, D l and D s are the diffusion coefficients of the metal liquid phase and the solid phase, respectively, and are the solute concentrations of the metal liquid phase and the solid phase at the solidification interface, respectively, l and c s are the solute concentrations of the metal liquid phase and the solid phase, respectively, imp It is the Avrami factor; The momentum transfer equation is: Pressure Tensor u q is the metal liquid phase u l and the equiaxed dendrite phase u e The viscosity of the equiaxed dendrite phase u e It can be deduced from the effective viscosity, that is: The Boussinesq method is used to calculate the thermal-solute buoyancy F of the metal liquid phase. l As shown below: F l =f k ·r l ·g·[β T ·(T ref -T l )+b c ·(c ref -c l )] For the equiaxed dendrite phase, the buoyancy F e It is caused by the density difference between the equiaxed dendrite phase and the metal liquid phase, so: F e =f e ·(r e -r l )·g Where: p is the pressure, and are respectively the momentum exchange rates between the metal liquid phase and the equiaxed dendrites, the metal liquid phase and the columnar crystals, and the columnar crystals and the equiaxed dendrites, and are the stress-strain tensors of the equiaxed dendrite and the metal liquid phase, respectively, e c is the packing limit of the equiaxed dendrite, g is the gravitational acceleration, β c and β T are the solute expansion coefficient and thermal expansion coefficient, c ref and T ref are the reference composition and reference temperature, T l and c l are respectively the temperature of the metal liquid phase and the solute concentration in the metal liquid phase; is the momentum exchange between the metal liquid phase and the equiaxed dendrite phase due to phase change, and the specific expression is: It is the momentum exchange between the metal liquid phase and the equiaxed dendrite phase due to the relative motion, and the specific expression is: Where K le It is obtained based on the solid-liquid interface drag force model; The momentum exchange between the metal liquid phase and the columnar crystal phase caused by phase change is: The momentum exchange caused by the metal liquid phase and the columnar crystal phase is: The drag coefficient is K is the permeability factor; Same as above, Since there is no mass exchange between the columnar crystals and the equiaxed dendrites, The drag coefficient of the two phases is: The solute transport equation is: in D e , D l and D c are the diffusion coefficients of the equiaxed dendrite, the metal liquid phase, and the columnar crystal, respectively, c e 、c l and c c are the concentrations of the equiaxed dendrite, the metal liquid phase, and the columnar crystal, respectively, and k is the equilibrium distribution coefficient; The energy transfer equation is: in The heat exchange caused by the transformation of the metal liquid phase to the equiaxed dendrite phase is The two-phase energy exchange caused by heat transfer is in The heat exchange caused by the transformation of the metal liquid phase to the equiaxed dendrite phase is The two-phase energy exchange caused by heat transfer is in The heat exchange caused by the transformation of the metal liquid phase to the equiaxed dendrite phase is The two-phase energy exchange caused by heat transfer is Among them, h l 、h e and h c are the enthalpy of the metal liquid phase, the equiaxed dendrite, and the columnar crystal, respectively, k l , k e and k c are the thermal conductivities of the metal liquid phase, the equiaxed dendrites, and the columnar crystals, respectively; Q is the Joule heat, Q le , Q lc and Q ce are the energy exchanges between the metal liquid phase and the equiaxed dendrites, the metal liquid phase and the columnar crystals, and the columnar crystals and the equiaxed dendrites, respectively, T l , T e and T c are the temperatures of the metal liquid phase, the equiaxed dendrites, and the columnar crystals, respectively, H * is the volume heat transfer coefficient.

2. The simulation method for predicting the solidification process of vacuum consumable melting ingot according to claim 1, characterized in that: The relevant material properties described in step 4 are obtained through experiments.

3. The simulation method for predicting the solidification process of vacuum consumable melting ingot according to claim 1, characterized in that: The boundary conditions in step 5 include boundary conditions related to electric field, magnetic field and flow field.

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