A numerical simulation method for metal droplet formation in vacuum consumable arc melting process

Abstract

The present invention discloses a numerical simulation method for the formation of metal droplets in a vacuum consumable arc melting process, which can realize the numerical simulation of the electromagnetic field, temperature field and droplet formation process of the arc plasma zone in the VAR process, and explore the relationship between the melting voltage and the metal droplet formation rate. The method comprises the following steps: (1) establishing relevant mathematical models for calculating electromagnetic fields and fluid dynamics; (2) meshing the geometric model; (3) inputting relevant material properties; (4) setting relevant boundary conditions; (5) setting the calculation method and initializing the calculation conditions; (6) starting iterative calculation and tracking the flow of the metal liquid phase in the entire calculation domain; (7) calculating the current density, magnetic induction intensity, Lorentz force, Joule heat, etc.; (8) calculating the required mass, momentum, energy transfer, etc.; (9) judging the convergence conditions, entering the next time step if the convergence conditions are met, and entering the next cycle if the convergence conditions are not met, until the simulation results are obtained.

Description

Technical Field

[0001] The invention relates to the technical field of metal forming, and in particular to a numerical simulation method for metal droplet formation in a vacuum consumable arc melting process. Background Art

[0002] Vacuum consumable arc melting (VAR) is currently the main method for producing titanium alloy ingots. The macro segregation produced during the melting process cannot be removed during mechanical processing, which has a significant impact on the quality of the produced components. It is necessary to control defects such as macro segregation during the melting process. The heat transfer and electromagnetic field of the arc plasma zone and the droplet dripping of the consumable electrode during the melting process have an important influence on the melting process. The energy of the arc zone is related to the dripping rate of the metal droplet and the superheat of the molten pool, which affects the quality of the ingot by affecting the morphology of the molten pool and the solidification structure.

[0003] By studying the influence of process parameters such as current and voltage on electrode melting rate, arc plasma zone temperature field and electromagnetic field, combined with subsequent macro-segregation calculation simulation, the process parameters of the smelting process are optimized, which has important guiding significance for the actual production process. At present, there is no systematic and accurate understanding of the influence of process parameters on ingot quality in VAR smelting. Limited by the high dissection cost of large titanium alloy ingots and the lack of suitable real-time observation methods, it is impossible to experimentally determine the relationship between process parameters such as current and voltage and arc plasma zone temperature field, electromagnetic field, and metal droplet formation rate. The process parameters can only be determined by experience. Although many scholars at home and abroad have used numerical simulation methods to establish models to study the vacuum consumable arc melting process and explore the influence of electromagnetic fields on molten pool flow. However, the research methods at home and abroad have the following problems: (1) There is no systematic study on the temperature field and electromagnetic field of the arc plasma zone; (2) The correlation between process parameters such as current and voltage and droplet formation rate and molten pool temperature field has not been established, and no suggestions for improvement have been put forward, which has little guiding effect on actual production.

[0004] Therefore, technicians in this field are committed to developing a numerical simulation method for metal droplet formation in a vacuum consumable arc melting process. Summary of the invention

[0005] In view of the above-mentioned defects of the prior art, the technical problem to be solved by the present invention is to simulate the electromagnetic field, temperature field and molten droplet dripping process in the arc plasma zone, obtain the correlation between voltage and metal droplet formation rate, and provide a basis for guiding actual production and optimizing the process in the smelting process.

[0006] To achieve the above object, the present invention provides a numerical simulation method for metal droplet formation in a vacuum consumable arc melting process, characterized in that it comprises the following steps:

[0007] S1: Establish relevant mathematical models for computational electromagnetic fields and fluid dynamics;

[0008] S2: Meshing the geometric model;

[0009] S3: Input the relevant material properties of plasma and molten metal;

[0010] S4: Setting relevant boundary conditions, including electric field boundary conditions, magnetic field boundary conditions, convection heat transfer coefficient between plasma and molten metal, convection heat transfer coefficient between plasma and crucible, etc.;

[0011] S5: Set the calculation method and initialize the calculation conditions, including the initial temperature and the initial position and content of each phase;

[0012] S6: Start iterative calculation to track the flow of liquid metal in the entire calculation domain;

[0013] S7: Calculate current density, magnetic induction intensity, Lorentz force, Joule heat, etc. through relevant equations of electromagnetic fields;

[0014] S8: Substitute the electromagnetic force and Joule heat calculated by the electromagnetic field related equations into the fluid dynamics related equations to calculate the mass, momentum and energy transfer process;

[0015] S9: Determine the convergence condition. If the convergence condition is met, enter the next time step. If the convergence condition is not met, enter the next cycle until the calculation is completed.

[0016] Furthermore, in the steps S1 and S7, the current density is calculated according to the following electromagnetic field control equation: Magnetic induction intensity Lorentz force Joule heat (Q):

[0017]

[0018]

[0019]

[0020]

[0021]

[0022]

[0023]

[0024] in: is the electric potential, is the magnetic vector, σ is the conductivity, u 0is the magnetic permeability.

[0025] Furthermore, in step S8, the mass, momentum and energy of the plasma and the molten metal are calculated according to the following mass conservation equation, momentum conservation equation and energy conservation equation:

[0026] The mass conservation equation:

[0027]

[0028]

[0029] Where: q is the plasma density, ρ l is the density of the molten metal, u q is the plasma velocity, is the speed of the molten metal.

[0030] Momentum conservation equation:

[0031]

[0032]

[0033] Where: f q is the plasma volume fraction, f l is the metal liquid volume fraction, p is the pressure, is the gravity of the plasma, is the gravity of the molten metal, is the Lorentz force of plasma, is the Lorentz force of the molten metal

[0034] Energy conservation equation:

[0035]

[0036]

[0037] Where: k q is the thermal conductivity of the plasma, k l is the thermal conductivity of the molten metal, Q q is the Joule heat of plasma, Q l is the Joule heat of the liquid phase.

[0038] The relationship between the droplet melting rate and Joule heat is as follows:

[0039]

[0040] in: is the melting speed of the molten metal, ε is the electrical efficiency, h l is enthalpy.

[0041] Furthermore, in the step S2, in order to capture the molten droplets and improve the accuracy of the calculation, the grid size in the grid division is set to 0.1 mm.

[0042] Furthermore, in the step S3, the electrode material is Ti 2 For AlNb, the plasma atmosphere is pure argon. The parameters such as resistivity, density, thermal conductivity, viscosity, specific heat, etc. that vary with temperature are set. The electromagnetic parameters, including melting current, melting voltage, and stirring magnetic field, are set according to the parameters provided by the factory.

[0043] Furthermore, in the step S4, the boundary conditions of the electric field are that a certain voltage value is applied to the top of the smelting electrode, zero potential is applied to the surface of the anode molten pool, and the potential gradient of other surfaces in the vertical direction is 0;

[0044] Furthermore, in the step S4, the boundary condition of the magnetic field is that the magnetic vector is applied on the surface of the smelting electrode and the anode molten pool parallel to the boundary;

[0045] Furthermore, in the step S4, the flow field boundary condition is that during the melting process of the crystalline metal, the temperature will be maintained near the melting point. 2 The melting point value of AlNb and the volume fraction of the molten metal are calculated, and the convection heat transfer coefficient between the plasma and the copper crucible is calculated based on the cooling water flow rate and water temperature.

[0046] Furthermore, in the step S5, the initialization calculation conditions include: dividing the grid area into a plasma area and a molten pool area, and respectively giving the initial temperature, the volume fraction of the molten metal, and the volume fraction of the plasma to each area.

[0047] Furthermore, the convergence condition in step S9 is less than 1E-3. To ensure convergence of each iterative calculation, the time step is set to 0.001s.

[0048] Beneficial effects of the present invention:

[0049] (1) The present invention establishes an arc plasma model of a vacuum consumable arc melting process to obtain the distribution of the electromagnetic field and temperature field in the arc plasma zone, thereby solving the problem of unclear understanding of the distribution laws of the electromagnetic field and temperature field in the arc zone in actual production.

[0050] (2) The present invention simulates the process of droplet formation and dripping during the consumable electrode melting process by coupling the Euler and VOF methods, and reveals for the first time the droplet dripping process during vacuum consumable arc melting, which is consistent with the actual theory.

[0051] (3) The present invention obtains the correlation between voltage and droplet formation rate and molten pool superheat, which provides a theoretical basis for the subsequent study of the effects of smelting parameters on the solidification behavior and macrosegregation of vacuum consumable arc melting ingots, and can be used to optimize the actual smelting production process.

[0052] (4) The present invention is suitable for studying the influence of process parameters such as current and voltage on the droplet formation rate of ingots of different materials produced by vacuum consumable arc melting, and can be used to guide the production of different high-temperature alloy ingots by vacuum consumable arc melting, thereby saving experimental costs and playing an important guiding role in actual production.

[0053] 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

[0054] Figure 1 It is the process of formation and dripping of molten metal droplets;

[0055] Figure 2 This is the current density distribution diagram when the melting voltage is 25V;

[0056] Figure 3 This is the current density distribution diagram at 35V melting voltage;

[0057] Figure 4 This is the current density distribution diagram at 45V melting voltage;

[0058] Figure 5 This is the Lorentz force distribution diagram when the melting voltage is 25V;

[0059] Figure 6 This is the Lorentz force distribution diagram at 35V melting voltage;

[0060] Figure 7 This is the Lorentz force distribution diagram at 45V melting voltage;

[0061] Figure 8 This is the temperature distribution diagram when the melting voltage is 25V;

[0062] Fig. 9 This is the temperature distribution diagram when the melting voltage is 35V;

[0063] Fig.10 This is the temperature distribution diagram at 45V melting voltage;

[0064] Fig.11 It is a graph showing the relationship between droplet formation rate and melting voltage. DETAILED DESCRIPTION

[0065] 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.

[0066] In the drawings, components with the same structure are indicated by the same numerical reference numerals, and components with similar structures or functions are indicated by similar numerical reference numerals. The size and thickness of each component shown in the drawings are arbitrarily shown, and the present invention does not limit the size and thickness of each component. In order to make the illustration clearer, the thickness of the components is appropriately exaggerated in some places in the drawings.

[0067] As shown in the figure, Figure 1 The formation and dripping process of molten metal droplets is shown. Figure 2 This is the process of the consumable electrode melting to form molten droplets. The figure shows the process of three molten droplets from formation to dripping. Analysis shows that the molten droplets are pushed toward the center of the electrode and drip under the action of the self-induced Lorentz force. The molten droplet formed in the center of the electrode is the largest. Figure 2-4 These are the current density distribution diagrams of the arc plasma zone at melting voltages of 25V, 35V, and 45V respectively. It can be seen from the figure that the current flowing into the ingot flows horizontally in the contact area between the ingot and the crucible, and converges to the electrode through the arc zone. This phenomenon is the same as in actual production. Analysis shows that as the melting voltage increases, the maximum current density increases accordingly, and the maximum current density is at the bottom of the electrode. Figure 5-7 The following are the distribution diagrams of the Lorentz force in the arc plasma zone under the melting voltages of 25V, 35V and 45V respectively. It can be seen from the figure that the direction of the Lorentz force under the self-inductance magnetic field points to the central axis, giving the molten drop a radial pulling force, and the maximum value of the Lorentz force increases with the increase of the melting voltage; Figure 8-10 It is the temperature distribution diagram of the arc plasma zone obtained by solving the energy equation at melting voltages of 25V, 35V, and 45V respectively. During the gas direct current (DC) discharge process, the charged particles are accelerated between the two poles by the electromagnetic field. The strong bombardment of high-speed electrons makes the surface of the anode molten pool tend to be white-hot, and the temperature rises sharply. The temperature of the anode molten pool surface is the highest. At the same time, it is found that the maximum temperature of the arc plasma zone increases with the increase of the melting voltage. Fig.11 It is a relationship diagram between the droplet formation rate and the melting voltage. Analysis shows that the droplet formation rate increases with the increase of the melting voltage.

[0068] A numerical simulation method for metal droplet formation in a vacuum consumable arc melting process, characterized in that it comprises the following steps:

[0069] S1: Establish relevant mathematical models for computational electromagnetic fields and fluid dynamics;

[0070] S2: Meshing the geometric model;

[0071] S3: Input the relevant material properties of plasma and molten metal;

[0072] S4: Setting relevant boundary conditions, including electric field boundary conditions, magnetic field boundary conditions, convection heat transfer coefficient between plasma and molten metal, convection heat transfer coefficient between plasma and crucible, etc.;

[0073] S5: Set the calculation method and initialize the calculation conditions, including the initial temperature and the initial position and content of each phase;

[0074] S6: Start iterative calculation to track the flow of liquid metal in the entire calculation domain;

[0075] S7: Calculate current density, magnetic induction intensity, Lorentz force, Joule heat, etc. through relevant equations of electromagnetic fields;

[0076] S8: Substitute the electromagnetic force and Joule heat calculated by the electromagnetic field related equations into the fluid dynamics related equations to calculate the mass, momentum and energy transfer process;

[0077] S9: Determine the convergence condition. If the convergence condition is met, enter the next time step. If the convergence condition is not met, enter the next cycle until the calculation is completed.

[0078] The specific equations of the mathematical model for calculating the electromagnetic field, temperature field, and flow field are as follows:

[0079] 1) Electromagnetic field related equations

[0080] Maxwell's equations describe the theory of electromagnetic fields. They are simplified by defining the scalar potential and the magnetic vector The electric field and magnetic field are separated to form independent electric field equations and magnetic field equations, which are applied to the simplified Maxwell equations. After calculation and derivation, the electric field partial differential equations and the magnetic field partial differential equations are obtained. Then, the current density and magnetic induction intensity can be obtained through invisible calculation, and the Lorentz force and Joule heat can be solved.

[0081] The derived electromagnetic field control equation is as follows:

[0082]

[0083]

[0084]

[0085] Where: σ is the conductivity, u 0 is the magnetic permeability, is the current density.

[0086] The relationship between current density and potential is as follows:

[0087]

[0088] Magnetic induction intensity The relationship between and magnetic vector is as follows:

[0089]

[0090] Lorentz force The vector expression of is as follows:

[0091]

[0092] From Ohm's law, the formula for Joule heat (Q) is as follows:

[0093]

[0094] 2) The mass, momentum and energy of the plasma phase (q) and the metal liquid phase (l) are explicitly calculated through the mass conservation equation, momentum conservation equation and energy conservation equation.

[0095] The mass conservation equation:

[0096]

[0097]

[0098] Where: q is the plasma density, ρ l is the density of the molten metal, u q is the plasma velocity, is the speed of the molten metal.

[0099] Momentum conservation equation:

[0100]

[0101]

[0102] Where: f q is the plasma volume fraction, f l is the metal liquid volume fraction, p is the pressure, is the gravity of the plasma, is the gravity of the molten metal, is the Lorentz force of plasma, is the Lorentz force of the molten metal

[0103] Energy conservation equation:

[0104]

[0105]

[0106] Where: k q is the thermal conductivity of the plasma, k l is the thermal conductivity of the molten metal, Q q is the Joule heat of plasma, Q l is the Joule heat of the liquid phase.

[0107] 3) The relationship between the droplet melting rate and Joule heat is as follows:

[0108]

[0109] in: is the melting speed of the molten metal, ε is the electrical efficiency, h l is enthalpy.

[0110] 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 numerical simulation method for metal droplet formation in a vacuum consumable arc melting process, characterized in that: The steps include: S1: Establish relevant mathematical models for computational electromagnetic fields and fluid dynamics; S2: Mesh the geometric model; S3: Input the relevant material properties of plasma and molten metal; S4: setting relevant boundary conditions, including electric field boundary conditions, magnetic field boundary conditions, convection heat transfer coefficient between plasma and molten metal, and convection heat transfer coefficient between plasma and crucible; S5: Set the calculation method and initialize the calculation conditions, including the initial temperature and the initial position and content of each phase; S6: Start iterative calculation to track the flow of liquid metal in the entire calculation domain; S7: Calculate current density, magnetic induction intensity, Lorentz force, and Joule heat through relevant equations of electromagnetic fields; S8: Substitute the electromagnetic force and Joule heat calculated by the electromagnetic field related equations into the fluid dynamics related equations to calculate the mass, momentum and energy transfer process; S9: Determine the convergence condition. If the convergence condition is met, enter the next time step. If the convergence condition is not met, enter the next cycle until the calculation is completed. In the steps S1 and S7, the current density is calculated according to the following electromagnetic field control equation: Magnetic induction intensity Lorentz force Joule heat Q, the temperature field and electromagnetic field distribution of the arc plasma zone are obtained, the direction and magnitude of the current density and the Lorentz force are the same as the actual theory, and the influence of the melting voltage on the electromagnetic field and temperature field of the arc plasma is analyzed: in: is the electric potential, is the magnetic vector, σ is the electrical conductivity, u0 is the magnetic permeability; In step S8, the mass, momentum and energy of the plasma and the molten metal are calculated according to the following mass conservation equation, momentum conservation equation and energy conservation equation, and the continuous process of the consumable electrode melting to form a molten droplet falling into the molten pool is successfully simulated, and the relationship between the smelting voltage and the metal droplet formation rate is analyzed: The mass conservation equation: Where: q is the plasma density, ρ l is the density of the molten metal, u q is the plasma velocity, is the speed of the liquid metal; Momentum conservation equation: Where: f q is the plasma volume fraction, f l is the metal liquid volume fraction, p is the pressure, is the gravity of the plasma, is the gravity of the molten metal, is the Lorentz force of plasma, is the Lorentz force of the molten metal; Energy conservation equation: Where: k q is the thermal conductivity of the plasma, k l is the thermal conductivity of the molten metal, D q is the Joule heat of plasma, Q l is the Joule heat of the liquid phase; The relationship between the droplet melting rate and Joule heat is as follows: in: is the melting speed of the molten metal, ε is the electrical efficiency, h l is enthalpy.

2. A numerical simulation method for metal droplet formation in a vacuum consumable arc melting process according to claim 1, characterized in that: In the step S2, the grid size in the grid generation is 0.1 mm.

3. The numerical simulation method for metal droplet formation in a vacuum consumable arc melting process according to claim 1, characterized in that: In the step S3, the electrode material is Ti2AlNb, the plasma atmosphere is pure argon, the parameter settings include the resistivity, density, thermal conductivity, viscosity, and specific heat of the plasma that vary with temperature, and the factors affecting the electromagnetic parameter settings include melting current, melting voltage, and stirring magnetic field.

4. The numerical simulation method for metal droplet formation in a vacuum consumable arc melting process according to claim 1, characterized in that: In the step S4, the boundary conditions of the electric field are set to apply a certain voltage value on the top of the smelting electrode, apply zero potential on the surface of the anode molten pool, and the potential gradient of other surfaces in the vertical direction is 0.

5. The numerical simulation method for metal droplet formation in vacuum consumable arc melting process according to claim 1, characterized in that: In the step S4, the boundary condition of the magnetic field is set to apply a magnetic vector parallel to the boundary on the surface of the smelting electrode and the anode molten pool.

6. The numerical simulation method for metal droplet formation in a vacuum consumable arc melting process according to claim 1, characterized in that: In the step S4, the flow field boundary condition is set under the condition that the melting point value of Ti2AlNb and the volume fraction of the molten metal are given by the electrode, and the convection heat transfer coefficient between the plasma and the copper crucible is calculated according to the cooling water rate and water temperature.

7. The numerical simulation method for metal droplet formation in vacuum consumable arc melting process according to claim 1, characterized in that: In the step S5, the initialization calculation conditions include: dividing the grid area into a plasma area and a molten pool area, and respectively giving the initial temperature, the volume fraction of the molten metal, and the volume fraction of the plasma to each area.

8. The numerical simulation method for metal droplet formation in vacuum consumable arc melting process according to claim 1, characterized in that: The convergence condition in step S9 is less than 1E-3, and the time step is set to 0.001s.

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