A numerical simulation method for the effect of electron beam on ingot solidification during electron beam cold hearth melting

Abstract

The present invention discloses a numerical simulation method for the effect of electron beam on ingot solidification during electron beam cold hearth melting, and belongs to the field of simulation of metal ingot solidification process. The method of the present invention is based on finite element numerical simulation software, establishes a numerical model of electron beam cold hearth melting (EBCHM), uses CFD (computational fluid dynamics) model to realize the simulation of flow field of electron beam cold hearth melting, establishes melting and solidification model, approximates electron beam with Gaussian heat source, writes UDF (user-defined function) by C language combined with Fluent specific macro, loads UDF on the upper surface of molten pool for operation, changes various process parameters of Gaussian heat source by UDF, and finally uses fluent to calculate the temperature change of the upper surface as electron beam scans, and then processes and analyzes the data to obtain the influence law of electron beam scanning on solidification. The method of the present invention has very important guiding significance for how to adjust process parameters of electron beam when electron beam cold hearth melting is used.

Description

Technical Field

[0001] The invention relates to a numerical simulation method for the influence of electron beam on ingot solidification during electron beam cold hearth smelting, and belongs to the field of simulation of metal ingot solidification process. Background Art

[0002] Electron beam cold hearth melting has become one of the main methods for melting titanium alloys because it can melt large-sized ingots of various shapes, the cooling bed structure can separate high and low density inclusions, and has high material utilization. Although EBCHM has the above advantages, it still faces many challenges, one of which is: the electron beam cold hearth melting process is carried out in a vacuum chamber, and the melt needs to stay in the cooling bed for a period of time, which makes some volatile alloy elements with high saturated vapor pressure easy to escape and cause certain burning losses. In addition, condensates are easily generated at the top of the vacuum chamber and may fall into the cooling bed or the crystallizer molten pool. Especially in the melting of titanium alloys containing aluminum elements, the falling phenomenon can be clearly observed, forming defects, and the rust of the furnace and the wear of the feed channel will also introduce impurities; through research, it is found that alloy elements with high saturated vapor pressure are positively correlated with temperature, so controlling the temperature field homogenization on the surface of the crystallizer molten pool becomes an effective method to reduce element volatilization and optimize ingot casting, and the homogenization of the surface temperature field is closely related to the scanning of the electron beam.

[0003] At present, it is very time-consuming, labor-intensive and costly to explore the electron beam scanning of the upper surface of the molten pool with different process parameters through experimental means. Therefore, technical personnel in this field are committed to developing a numerical simulation method for the influence of electron beam on ingot solidification during electron beam cold hearth smelting, so as to provide guidance for actual production through numerical simulation and reduce the loss of financial and material resources. Summary of the invention

[0004] In view of the deficiencies of the above-mentioned prior art, the purpose of the present invention is to provide a numerical simulation method for the influence of electron beam on the solidification of ingots during electron beam cold hearth melting. Based on finite element numerical simulation software, a numerical model of electron beam cold hearth melting (EBCHM) is established, and the flow field simulation of electron beam cold hearth melting is realized by using CFD (computational fluid dynamics) model, a melting and solidification model is established, and a Gaussian heat source is used to approximate the electron beam. A UDF (user defined function) is written by combining C language with Fluent's specific macros, and the UDF is loaded onto the upper surface of the molten pool for operation. Various process parameters of the Gaussian heat source are changed by UDF, and finally the temperature change of the upper surface as the electron beam scans is obtained by Fluent calculation. Then, the data is processed and analyzed to obtain the influence of electron beam scanning on solidification. This has very important guiding significance for how to adjust the process parameters of the electron beam during electron beam cold hearth melting.

[0005] To achieve the above object, the technical solution of the present invention is as follows:

[0006] A numerical simulation method for the effect of electron beam on ingot solidification during electron beam cold hearth smelting comprises the following steps:

[0007] (1) Determination of model parameters: According to the actual production process of electron beam cold hearth melting, the crystallizer size parameters and production process parameters (common process parameters, generally including casting speed, pouring speed, pouring temperature and heat transfer coefficient) are collected.

[0008] (2) Geometric model creation: A geometric model is established based on the mold size parameters and process parameters collected in step (1), and the unit type is defined for the established model, and material physical property parameters are assigned and the mesh is divided.

[0009] (3) Establish a turbulence model: Use the Ke model to calculate the flow field distribution of the fluid domain in the crystallizer.

[0010] (4) Establishing a melting and solidification model: The molten pool morphology during continuous casting solidification is calculated using the Solidification and Melting model.

[0011] (5) Use Gaussian heat source to approximate the electron beam, write UDF (user defined function) by using C language combined with Fluent specific macros, load UDF onto the upper surface of the molten pool and run it, change various process parameters of the Gaussian heat source through UDF, and finally use Fluent to calculate the temperature change of the upper surface as the electron beam scans, and use the post-processing software Tecplot to analyze the influence of various process parameters on the upper surface.

[0012] Preferably, the specific process of step (3) of the present invention is: using the Euler method to establish a turbulence model, the flow of metal titanium in the crystallizer can be characterized by the balance of mass, momentum and energy, and this balance is described by the mass conservation equation, momentum conservation equation and energy conservation equation:

[0013] ①Mass conservation equation:

[0014]

[0015] in represents the unit velocity; ρ is the density.

[0016] ② Momentum conservation equation:

[0017]

[0018] in represents the thermo-solute buoyancy; is the stress tensor; p represents the static pressure; is the acceleration due to gravity, Indicates momentum sinking in the mushy zone; are the unit vectors of the three coordinate axes x, y, and z; ρ is the density.

[0019]

[0020] Among them B T is the coefficient of thermal expansion, T represents temperature, T liq represents the liquidus temperature, C c,i is the expansion coefficient, Y i,1iq represents the local average concentration of solute element i in the liquid phase, Y0 represents the mass fraction of the initial solute i, and represents the momentum sink in the mushy region and has the following form:

[0021]

[0022] Among them, A mushy is the mushy region constant, β is the liquid volume fraction, and Indicates the continuous casting speed, Indicates unit speed;

[0023] ③Energy conservation equation:

[0024]

[0025] in, represents the energy of heat conduction; H represents enthalpy, h represents sensible enthalpy, ΔH represents latent heat, and ΔH f represents the heat of fusion of pure solvent, C p represents specific heat, h ref represents the reference enthalpy, T ref represents the reference temperature; k represents the thermal conductivity, Represents a source term.

[0026] In order to better simulate the flow in the metallic state, the turbulent kinetic energy K and the turbulent energy dissipation rate ε are introduced here to constrain and improve the model with mathematical equations; so that it can be used to predict medium-intensity swirls.

[0027] ④The turbulent kinetic energy K is given by the following formula:

[0028]

[0029] ⑤The turbulent energy dissipation rate ε is given by the following formula:

[0030]

[0031] Among them, u j is the instantaneous velocity component in the direction of coordinate j; x jrepresents the coordinate value component in the direction of coordinate j; μ represents the dynamic viscosity coefficient of the metal liquid, μ t is the turbulent viscosity; G K Turbulent kinetic energy caused by mean velocity gradient; G b is the turbulent kinetic energy due to buoyancy; Y M is the contribution of pulsation expansion in compressible turbulence; S K and S ε is the source term; σ K and σ ε is the turbulent Prandtl number; S ij is the average strain rate; v is the velocity; the turbulence model constant is: C 1ε =1.44, C2=1.9, σ K =1.0,σ ε =1.2; for the flow velocity in the same direction as gravity, C 3ε =1, for the flow direction perpendicular to the gravity direction C 3ε =0.

[0032] By solving equations ① to ⑤, we can obtain the velocity, pressure, temperature, turbulent kinetic energy, and turbulent energy dissipation rate of each unit fluid in the fluid domain in the crystallizer at any time. The flow field distribution of the entire fluid domain can be calculated using the fluid simulation software FLUENT.

[0033] Preferably, the specific process of step (4) of the present invention is as follows: Fluent directly determines whether a substance is in a liquid or solid state by temperature, so the liquid phase volume fraction β in the melting process has the following equation:

[0034]

[0035] Among them, T solidus is the solidus temperature of titanium metal; T liquidus is the liquidus temperature of titanium metal; T is the temperature of titanium metal.

[0036] Substituting the liquid phase volume fraction β into the energy equation ③, and then calculating with Fluent, we can obtain the solid phase region, mushy region and liquid phase region of the ingot in the crystallizer during the continuous casting process, thereby establishing a melting and solidification model for electron beam cold hearth melting.

[0037] The electron beam is approximated by using a Gaussian heat source, where the Gaussian heat source formula is as follows:

[0038]

[0039] Among them, η eb P is the efficiency of converting the kinetic energy of electron beam electrons impacting the melt surface into heat energy; ebis the power of the electron gun; σ is the radius of the electron beam; (x, y) is the coordinate of any point on the top surface; (x0, y0) is the coordinate of the center of the electron beam; q eb (x,y) is the heat flux at the position (x,y).

[0040] The beneficial effects of the present invention are:

[0041] (1) The present invention ingeniously uses a Gaussian heat source to approximate the simulation of the electron beam, and uses UDF to simulate the operation of the electron beam, providing a method for studying the influence of electron beam process parameters on solidification in electron beam cold hearth melting.

[0042] (2) The present invention studies the temperature change of the upper surface of the molten pool in the crystallizer when the Gaussian heat source is in operation, which is of great significance for studying the control of the melt surface temperature and thus the control of the composition uniformity in actual production.

[0043] (3) The present invention helps to understand how different electron beam process parameters affect the melt surface temperature, helps to solve the element volatilization problem caused by local overheating during electron beam cold hearth melting, and has a reference role in optimizing the ingot casting process of electron beam cold hearth melting.

[0044] (4) The present invention is applicable to predicting the melt surface temperature of various materials melted by electron beam cold furnace, and has applicability, and can reduce the experimental cost in the initial stage of production through simulation method. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 The present invention is a flow chart of a method for numerically simulating the effect of electron beam on ingot solidification during electron beam cold hearth smelting.

[0046] Figure 2 Dimension diagram and boundary conditions of the model established in the embodiment of the present invention.

[0047] Figure 3 Flow field diagram and molten pool morphology diagram in the model established in the embodiment of the present invention.

[0048] Figure 4 This is a diagram of the running trajectory of the Gaussian heat source in the model established in the embodiment of the present invention.

[0049] Figure 5 A five-point position diagram of the melt surface in the model established in the embodiment of the present invention.

[0050] Figure 6 This is the temperature field cloud diagram under different Gaussian heat source powers in production condition one.

[0051] Figure 7The temperature variation diagrams of five points on the melt surface in production condition 1. (a), (b), (c), and (d) are the temperature variation diagrams of point 1 and point 5, point 2, point 3, and point 4 during the period of 2000s-2050s, respectively.

[0052] Figure 8 This is the temperature field cloud diagram under different Gaussian heat source diameters in production condition 2.

[0053] Fig. 9 The temperature variation diagrams of five points on the melt surface in production condition 2. (a), (b), (c), and (d) are the temperature variation diagrams of point 1 and point 5, point 2, point 3, and point 4 during the period of 2000s-2050s, respectively.

[0054] Fig.10 This is the temperature field cloud diagram under different Gaussian heat source scanning circles in production condition three.

[0055] Fig.11 The temperature variation diagrams of five points on the melt surface in production condition three, (a), (b), (c), and (d) are the temperature variation diagrams of point 1 and point 5, point 2, point 3, and point 4 during the period of 2000s-2050s, respectively.

[0056] Fig.12 It is the temperature field cloud diagram under different Gaussian heat source frequencies in four production conditions.

[0057] Fig.13 The temperature variation diagrams of five points on the melt surface are taken for the production conditions. (a), (b), (c), and (d) are the temperature variation diagrams of point 1 and point 5, point 2, point 3, and point 4 during the period of 2000s-2050s, respectively. Specific implementation methods

[0058] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments, but the protection scope of the present invention is not limited to the contents described above.

[0059] The attached drawings of the present invention show temperature variation diagrams of five points on the upper surface of the melt during the period of 2000s-2050s under four different working conditions; in actual production, because the sizes of the ingots produced are different, it is necessary to adjust the various process parameters of the electron beam according to different production sizes when using an electron beam cold furnace to melt the ingots. For such situations, a large number of simulations are required for different ingot production sizes. The present invention only provides a simple and feasible numerical simulation method. The purpose of providing this implementation method is to provide a more thorough and comprehensive understanding of the disclosed content of the present invention.

[0060] Since electron beam cold hearth melting is carried out in a high temperature and vacuum environment, the traditional method is to manually use the electron gun software system to adjust the electron beam parameter control for the production of ingots, and the melt surface temperature is measured by a temperature measuring instrument. The optimal electron beam process parameters for producing ingots are obtained through continuous experiments. Such a method consumes a lot of manpower, financial resources and time. However, with the development of computer technology, the finite element numerical simulation method provides an important means for studying the influence of electron beam process parameters on solidification in electron beam cold hearth melting. The present invention is described in detail with molten TA10 titanium alloy as the implementation object. The molten TA10 titanium alloy flows into the calculation domain from the inlet at a constant casting speed of 0.0295m / s and a pouring temperature of 2273K; the heat transfer coefficient between the water-cooled copper mold and the molten metal is 2000W / m 2 / K; It should be noted that the present invention is not only applicable to the smelting of TA10 alloy, but also applicable to a series of other metals smelted using electron beam cold hearth.

[0061] Example 1

[0062] The present embodiment provides a numerical simulation method for the effect of electron beam on ingot solidification during electron beam cold hearth melting. Figure 1 As shown, the following steps are included:

[0063] Step 1: Determine model parameters: According to the actual production process of electron beam cold hearth melting, collect the mold size parameters and basic production process parameters.

[0064] The size of the crystallizer in this embodiment is: R130mm×300mm; Figure 2 shown.

[0065] Step 2: Geometric model creation: Establish a geometric model based on the mold size parameters and process parameters collected in step (1), define the unit type for the established model and assign material physical property parameters; divide the grid; set boundary conditions, as shown in Figure 2.

[0066] Step 3: Because the study is on the fluid region inside the crystallizer, the Euler method is used to establish a turbulence model. The flow field can be characterized by the balance of mass, momentum and energy. This balance is described by the mass conservation equation, momentum conservation equation and energy conservation equation:

[0067] ①Mass conservation equation:

[0068]

[0069] in represents the unit velocity; ρ is the density.

[0070] ② Momentum conservation equation:

[0071]

[0072] in represents the thermo-solute buoyancy; is the stress tensor; p represents the static pressure; is the acceleration due to gravity, Indicates momentum sinking in the mushy zone; are the unit vectors of the three coordinate axes x, y, and z; ρ is the density.

[0073]

[0074] Among them B T is the coefficient of thermal expansion, T represents temperature, T liq represents the liquidus temperature, C c,i is the expansion coefficient, Y i,1iq represents the local average concentration of solute element i in the liquid phase, Y0 represents the mass fraction of the initial solute i, and represents the momentum sink in the mushy region and has the following form:

[0075]

[0076] Among them, A mushy and β are the mushy zone constants, and Indicates the conversion speed, Indicates the unit speed.

[0077] ③Energy conservation equation:

[0078]

[0079] in, Represents the energy of heat conduction; H represents enthalpy, h represents sensible enthalpy, ΔH represents latent heat, ΔH f represents the heat of fusion of pure solvent, C p represents specific heat, h ref represents the reference enthalpy, T ref represents the reference temperature; k represents the thermal conductivity, Represents a source term.

[0080] In order to simulate the flow better, the turbulent kinetic energy K and the turbulent energy dissipation rate ε are introduced here to constrain and improve the model with mathematical equations, so that it can be used to predict medium-intensity swirls.

[0081] ④The turbulent kinetic energy K is given by the following formula:

[0082]

[0083] ⑤The turbulent energy dissipation rate ε is given by the following formula:

[0084]

[0085] Among them, u j is the instantaneous velocity component in the direction of coordinate j; x j represents the coordinate value component in the direction of coordinate j; μ represents the dynamic viscosity coefficient of the metal liquid, μ t is the turbulent viscosity; G K Turbulent kinetic energy caused by mean velocity gradient; G b is the turbulent kinetic energy due to buoyancy; Y M is the contribution of pulsation expansion in compressible turbulence; S K and S ε is the source term; σ K and σ ε is the turbulent Prandtl number; S ij is the average strain rate; v is the velocity, and the turbulence model constant is: C 1ε =1.44, C2=1.9, σ K =1.0,σ ε =1.2; for the flow velocity in the same direction as gravity, C 3ε =1, for the flow direction perpendicular to the gravity direction C 3ε =0.

[0086] By solving equations ① to ⑤, we can obtain the velocity, pressure, temperature, turbulent kinetic energy, and turbulent energy dissipation rate of each unit fluid in the fluid domain at any time in the crystallizer. The flow field distribution of the entire fluid domain can be obtained by calculation using fluid simulation software, such as Figure 3 As shown;

[0087] Step 4: Establish a melting and solidification model: Use the Solidification and Melting model to calculate the molten pool morphology during continuous casting solidification; Fluent directly determines whether the material is in liquid or solid state by temperature, so the liquid phase volume fraction β in the melting process has the following equation:

[0088]

[0089] Among them, T solidus is the solidus temperature of titanium metal; T liquidus is the liquidus temperature of titanium metal; T is the temperature of titanium metal.

[0090] Substituting the liquid phase volume fraction β into the energy equation ③, and then calculating with Fluent, we can obtain the solid phase region, mushy region and liquid phase region of the ingot in the crystallizer during the continuous casting process, thereby establishing a melting and solidification model for electron beam cold hearth melting.

[0091] The mass conservation, momentum conservation, energy conservation, turbulent kinetic energy, turbulent energy dissipation rate equations and solid-liquid phase equation of the molten metal flow are solved by the phase coupling algorithm in the fluent software to simulate the continuous casting process.

[0092] Step 5: Select a suitable Gaussian heat source to approximate the electron beam. The Gaussian heat source formula is as follows:

[0093]

[0094] Among them, η eb P is the efficiency of converting the kinetic energy of electron beam electrons impacting the melt surface into heat energy; eb is the power of the electron gun; v is the radius of the electron beam; (x, y) is the coordinate of any point on the top surface; (x0, y0) is the coordinate of the center of the electron beam; q eb (x,y) is the heat flux at the position (x,y).

[0095] Due to the complex electron beam motion trajectory in electron beam cold bed melting, the model built into Fluent cannot complete the above model solution. Fluent needs to be redeveloped to complete the above simulation work. Formula (11) is written into a UDF (user-defined function) by using C language combined with Fluent's specific macros. The UDF is loaded into the top surface of the molten pool in Fluent and run, as shown in the following example: Figure 4 As shown in the figure; by changing the various process parameters of the Gaussian heat source through UDF, the top surface temperature changes under four different working conditions are simulated respectively, and the temperature cloud map of the top surface when the smelting reaches a steady state is obtained. Then 5 points are selected on the top surface, and the positions are as follows Figure 5 As shown in the figure, the temperature change data of 5 points are collected. Point 1 and point 5 are symmetrical so the temperature at each moment is almost the same. The post-processing software Tecplot is used to analyze the change diagram of the influence of different process parameters on the temperature of each point on the top surface, as shown in the figure. Figure 6 , 7 , 8, and 9, where (a) is the temperature change diagram of point 1 and point 5, (b) is point 2, (c) is point 3, and (d) is point 4 during the period of 2000s-2050s. Through comparative analysis, the influence of different electron beam process parameters on the solidification of ingot is finally obtained.

[0096] Production Condition 1: By changing the power of the Gaussian heat source (similar to the electron beam) through UDF, the temperature cloud diagrams on the top surface under the electron beam power of 20KW, 40KW, 60KW, and 80KW and the temperature change diagrams at 5 points under different powers were obtained, as shown in Figure 1. Figures 6-7As shown; it can be seen from the figure: when the power is 20KW and 40KW, although the central local overheating is not obvious, the temperature at points 1, 2, and 5 shows a downward trend, which means that the electron beam at this power cannot ensure the steady state of the molten pool, which is not conducive to continuous casting; but with the increase of power, the temperature at points 1, 2, and 5 increases, which means that increasing the electron beam power is helpful to maintain the stability of the molten pool, but with the increase of power, the local overheating phenomenon at point 3 gradually intensifies, and the temperature fluctuation also intensifies. The temperature change at point 4 is not obvious because it is close to the inlet.

[0097] Production Condition 2: Based on Production Condition 1, the diameter of the Gaussian heat source (approximately the electron beam) was changed through UDF, and the temperature cloud diagrams on the top surface under the electron beam diameters of 20mm, 40mm, 60mm, and 80mm and the temperature change diagrams at 5 points under different electron beam diameters were obtained, as shown in Figure 2. Figures 8-9 As shown; it can be seen from the figure: with the increase of the electron beam diameter, the temperature fluctuations at points 1, 2, and 5 gradually become gentle and decrease, and at the same time, the central local temperature gradually decreases, which shows that the increase in the electron beam diameter is conducive to the uniformity of the top surface temperature, and the reduction in temperature fluctuations is conducive to reducing the volatilization of volatile elements; the temperature change at point 4 is not obvious because it is close to the inlet.

[0098] Production Condition 3: Based on Production Conditions 1 and 2, the number of scans of the Gaussian heat source (approximately the electron beam) was changed through UDF, and the temperature cloud maps on the top surface were obtained when the electron beam scanned 20, 18, 16, and 14 times, and the temperature change maps at 5 points under different scans were obtained, as shown in Figure 3. Figures 10-11 As shown; it can be seen from the figure: with the reduction of the number of scanning circles, the temperatures at points 1, 2, 3, and 5 have dropped significantly and the temperature fluctuation has become more gentle, and the phenomenon of local overheating has been significantly improved, which shows that appropriately reducing the number of electron beam scanning circles is helpful to reduce the volatilization of volatile elements while maintaining the steady state of the molten pool, which is beneficial to the optimization of the ingot; the temperature change at point 4 is not obvious because it is close to the inlet.

[0099] Production Condition 4: Based on Production Conditions 1 and 2, the frequency of the Gaussian heat source (approximately the electron beam) was changed through UDF, and the temperature cloud map on the top surface under the electron beam frequency of 5HZ, 10HZ, 20HZ, and 40HZ and the temperature change map of 5 points at different frequencies were obtained, as shown in Figure 4. Figures 12-13As shown; it can be seen from the figure: with the increase of the electron beam scanning frequency, we can obviously see that the temperature fluctuation at each point is greatly reduced, but when the scanning frequency is increased from 20HZ to 40HZ, it can be found by comparison that the temperature change is no longer obvious. This is mainly because the increase in frequency shortens the residence time of the electron beam at each point on the surface. Therefore, the appropriate increase in the electron beam frequency is still helpful to reduce the temperature fluctuation caused by electron beam scanning, help to homogenize the top surface temperature field and stabilize the molten pool morphology, and thus help to improve the destined production quality.

Claims

1. A numerical simulation method for the effect of electron beam on ingot solidification during electron beam cold hearth smelting, characterized in that: The specific steps include: (1) Model parameter determination: According to the actual production process of electron beam cold hearth melting, the crystallizer size parameters and production process parameters are collected; (2) Geometric model creation: A geometric model is established based on the mold size parameters and process parameters collected in step (1), and the unit type is defined for the established model, and material physical property parameters are assigned and the mesh is divided; (3) Establish turbulence model: Use the Ke model to calculate the flow field distribution of the fluid domain in the crystallizer; (4) Establishing a melting and solidification model: Using the Solidification and Melting model, the molten pool morphology during continuous casting solidification is calculated; (5) Use Gaussian heat source to approximate the electron beam, write a custom function by using C language combined with Fluent's specific macro, load the custom function onto the upper surface of the molten pool and run it, change the various process parameters of the Gaussian heat source through the custom function, and finally use Fluent to calculate the temperature change of the upper surface as the electron beam scans, and use the post-processing software Tecplot to analyze the influence of various process parameters on the upper surface; The specific process of step (3) is as follows: the turbulence model is established using the Euler method. The flow of metal in the crystallizer can be characterized by the balance of mass, momentum and energy. This balance is described by the mass conservation equation, momentum conservation equation and energy conservation equation: ①Mass conservation equation: in represents the unit velocity; ρ is the density; ② Momentum conservation equation: in represents the thermo-solute buoyancy; is the stress tensor; p represents the static pressure; is the acceleration due to gravity, Indicates momentum sinking in the mushy zone; They are the unit vectors of the three coordinate axes x, y, and z; Among them B T is the coefficient of thermal expansion, T represents temperature, T liq represents the liquidus temperature, C c,i is the expansion coefficient, Y i,1iq represents the local average concentration of solute element i in the liquid phase, Y0 represents the mass fraction of the initial solute i, and represents the momentum sink in the mushy region and has the following form: Among them, A mushy is the mushy region constant, β is the liquid volume fraction, and Indicates the continuous casting speed, Indicates unit speed; ③Energy conservation equation: in, represents the energy of heat conduction; H represents enthalpy, h represents sensible enthalpy, ΔH represents latent heat, and ΔH f represents the heat of fusion of pure solvent, C p represents specific heat, h ref represents the reference enthalpy, T ref represents the reference temperature; k represents the thermal conductivity, represents the source term; The turbulent kinetic energy K and turbulent energy dissipation rate ε are introduced to constrain and improve the model for predicting medium-intensity swirls. ④The turbulent kinetic energy K is given by the following formula: ⑤The turbulent energy dissipation rate ε is given by the following formula: Among them, u j is the instantaneous velocity component in the direction of coordinate j; x j represents the coordinate value component in the direction of coordinate j; μ represents the dynamic viscosity coefficient of the metal liquid, μ t is the turbulent viscosity; G K Turbulent kinetic energy caused by mean velocity gradient; G b is the turbulent kinetic energy due to buoyancy; Y M is the contribution of pulsation expansion in compressible turbulence; S K and S ε is the source term; σ K and σ ε is the turbulent Prandtl number; S ij is the average strain rate; v is the velocity; the turbulence model constant is: C 1ε =1.44, C2=1.9, σ K =1.0,σ ε =1.2; for the flow velocity in the same direction as gravity, C 3ε =1, for the flow direction perpendicular to the gravity direction C 3ε =0; By solving equations ① to ⑤, we can obtain the velocity, pressure, temperature, turbulent kinetic energy, and turbulent energy dissipation rate of each unit fluid in the fluid domain in the crystallizer at any time. The flow field distribution of the entire fluid domain can be calculated using the fluid simulation software FLUENT.

2. The method for numerically simulating the effect of electron beam on ingot solidification during electron beam cold hearth smelting according to claim 1, characterized in that: The specific process of step (4) is as follows: Fluent directly determines whether a substance is in liquid or solid state by temperature, so the liquid phase volume fraction β of the melting process has the following equation: Among them, T solidus is the solidus temperature of titanium metal; T liquidus is the liquidus temperature of titanium metal; T is the temperature of titanium metal; Substituting the liquid phase volume fraction β into the energy equation ③, and then calculating with Fluent, we can obtain the solid phase region, mushy region and liquid phase region of the ingot in the crystallizer during the continuous casting process, thereby establishing a melting and solidification model for electron beam cold hearth melting.

3. The method for numerically simulating the effect of electron beam on ingot solidification during electron beam cold hearth smelting according to claim 1 or 2, characterized in that: The electron beam is approximately simulated using a Gaussian heat source, where the Gaussian heat source formula is as follows: Among them, η eb P is the efficiency of converting the kinetic energy of electron beam electrons impacting the melt surface into heat energy; eb is the power of the electron gun; σ is the radius of the electron beam; (x, y) is the coordinate of any point on the top surface; (x0, y0) is the coordinate of the center of the electron beam; q eb (x,y) is the heat flux at the position (x,y).

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