Numerical simulation method for vacuum distillation process of metal indium

Abstract

The application provides a numerical simulation method for a metal indium vacuum distillation process, comprising the following steps: drawing a three-dimensional model of a high-temperature vacuum equipment structure and internal components used for metal indium vacuum distillation; dividing the drawn model according to a polyhedral grid; assigning corresponding materials to the high-temperature vacuum equipment and the internal components in the model, setting basic assumptions and control equations for temperature field numerical simulation and flow field numerical simulation in the metal indium vacuum distillation process; setting boundary conditions for the temperature field numerical simulation and assigning initial values, and obtaining a temperature field numerical simulation result in the high-temperature vacuum equipment based on control equation calculation; based on the obtained temperature field numerical simulation result, setting boundary conditions for the flow field numerical simulation and assigning initial values, and obtaining a flow field numerical simulation result in the high-temperature vacuum equipment based on control equation calculation. The application can accurately simulate the metal indium vacuum distillation process, and can be used to further guide non-ferrous metal vacuum distillation purification and separation practice.

Description

Technical Field

[0001] This invention relates to the field of numerical simulation, and more specifically, to a numerical simulation method for the vacuum distillation process of metallic indium. Background Technology

[0002] Currently, high-purity metal preparation technology is considered an important technological reserve for fields such as microelectronics integrated circuits and aerospace. Indium (In) is widely used in the microelectronics integrated circuit industry and high-end chip target materials, both of which require high purity. For example, in the semiconductor field, the purity requirement for In is generally above 6N. Currently, vacuum distillation is a relatively effective and clean green technology in the preparation and purification of high-purity indium.

[0003] The temperature field and metal vapor distribution (i.e., flow field) within a vacuum furnace are crucial to the purity and direct yield of high-purity metals. However, a vacuum furnace is like a "black box," as the precise temperature field and metal vapor distribution within it are not clearly defined, making it impossible to accurately control the temperature and temperature gradient during practical operations. In experiments and production, people rely on experience or conduct numerous exploratory tests to make initial judgments, and then tentatively modify variable data based on the experimental results to obtain satisfactory parameter settings. However, this method leads to lengthy experimental research and production processes, and increased resource and energy consumption.

[0004] Numerical simulation is currently a relatively effective means and method for reducing experimental production costs and improving the reliability of prediction results. By simulating reaction processes using computers, more accurate process data parameters and result predictions can be obtained, reducing the number of exploratory experiments and errors caused by experience-based judgments, and effectively guiding the production process. Therefore, clarifying the temperature and flow fields inside vacuum furnaces using simulation methods is urgently needed in the field of vacuum metallurgy. Summary of the Invention

[0005] In view of the shortcomings of the prior art, one of the objectives of this invention is to solve one or more problems existing in the prior art. For example, one objective of this invention is to provide a more accurate numerical simulation method for the vacuum distillation process of metallic indium, which can effectively reduce resource and energy consumption in experimental and production processes.

[0006] This invention provides a numerical simulation method for the vacuum distillation process of metallic indium, which may include the following steps: Step S1, drawing a three-dimensional model of the structure and internal components of the high-temperature vacuum equipment used for vacuum distillation of metallic indium, wherein the high-temperature vacuum equipment is provided with a cooling water inlet and a cooling water outlet, and the internal components include a heating element; Step S2, dividing the drawn model into a polyhedral mesh, and refining the boundary layer at the solid-solid and solid-fluid contact surfaces; Step S3, assigning corresponding materials to the high-temperature vacuum equipment and internal components in the model, and setting the basic assumptions and governing equations for the numerical simulation of the temperature field and the flow field during the vacuum distillation process of metallic indium; Step S4, setting the boundary conditions for the numerical simulation of the temperature field and assigning initial values, and obtaining the numerical simulation result of the temperature field inside the high-temperature vacuum equipment based on the governing equations; Step S5, based on the obtained numerical simulation result of the temperature field, setting the boundary conditions for the numerical simulation of the flow field and assigning initial values, and obtaining the numerical simulation result of the flow field inside the high-temperature vacuum equipment based on the governing equations.

[0007] Furthermore, the basic assumptions for the numerical simulation of temperature field and flow field in the vacuum distillation process of metallic indium include: constant temperature of the heating element, constant inlet flow rate and temperature of cooling water, no backflow at the outlet of cooling water, and gas density following the Boussinesq assumption.

[0008] Furthermore, the governing equations may include:

[0009] Mass continuity equation:

[0010]

[0011] Momentum continuity equation:

[0012] x direction

[0013] y direction

[0014] z direction

[0015] Energy conservation equation:

[0016]

[0017] Where ρ represents mass density, t represents time, u, v, w are velocity vectors in the x, y, and z directions, respectively, in m / s; ρu, ρv, ρw represent mass fluxes in the x, y, and z directions, respectively; f x f is the x-component of the volume force f acting on a unit mass fluid element; y f is the y-component of f; z τ is the z-component of f; xxτ yy τ zz Let Pa and τ be the stress tensors on the plane perpendicular to x, y, and z, respectively, with the stress direction in the same direction as the normal direction. xy The stress component τ acts on a plane perpendicular to x, pointing towards y; Pa; xz The stress component τ acts on a plane perpendicular to x, pointing towards z; Pa; yx The stress component τ acts on a plane perpendicular to y, pointing towards x; Pa; yz The stress component acts on a plane perpendicular to y, pointing towards z, Pa; τ zx The stress component τ acts on a plane perpendicular to z, pointing towards x; Pa. zy denoted as σz, representing the stress component acting on a plane perpendicular to z, pointing towards y, in Pa; e is the internal energy per unit mass generated by the random motion of molecules, in J; p is the pressure, in Pa; and T is the temperature, in K. is the volumetric heating rate per unit mass, J / kg·K; k is the thermal conductivity, W / m·K.

[0018] Furthermore, step S3 also includes setting the thermal radiation model to a surface-to-surface model in the numerical simulation of the temperature field, with the following governing equations:

[0019] J k =E k +ρ k q in,k

[0020] Among them, J k E represents radiation emitted from a surface. k ρ represents the self-radiation of surface k; k Represents reflectivity; q in,k It represents the incident radiant heat flow emitted from surrounding objects.

[0021] Furthermore, setting the boundary conditions and assigning initial values ​​for the numerical simulation of the temperature field includes: setting the boundary conditions as follows: the cooling water inlet is set as a velocity inlet, the cooling water outlet is set as a pressure outlet, and the remaining boundaries are all set as adiabatic walls;

[0022] Assigning initial values ​​includes setting the operating pressure, cooling water flow rate, and heating element operating temperature.

[0023] Furthermore, the operating pressure is set to 1 Pa; the cooling water flow rate is set to 2 m / s; of course, the operating temperature of the heating element can be set according to actual conditions; the relationship between the saturation temperature of indium and the pressure is:

[0024] lgP = -12580T -1 -0.45lgT+11.91.

[0025] Furthermore, setting the boundary conditions and assigning initial values ​​for the flow field numerical simulation includes:

[0026] The boundary conditions are set as follows: the cooling water inlet is set as a velocity inlet, the cooling water outlet is set as a pressure outlet, and all other boundaries are set as adiabatic walls.

[0027] The initial values ​​include: setting the operating pressure, cooling water flow rate, and the height of liquid indium in the device during initialization.

[0028] Furthermore, the height of the liquid indium inside the device is 4 mm during initialization.

[0029] Furthermore, obtaining the numerical simulation results of the temperature field within the high-temperature vacuum equipment also includes: after the calculation stabilizes, extracting the temperature monitoring point values ​​within the equipment and comparing them with the actual measured values ​​at the monitoring points within the equipment. If the compared values ​​do not match, the thermal conductivity and coefficient of thermal expansion of the gas material are modified, and the calculation is recalculated. Based on the new numerical simulation of the temperature field, the temperature monitoring point values ​​within the equipment are extracted and compared with the actual measured values ​​at the monitoring points within the equipment. If the compared values ​​match, a reliable numerical simulation result of the temperature field is considered to have been obtained. In the above, the gas material mainly refers to the atmosphere within the equipment.

[0030] Furthermore, if the values ​​do not match after comparison, the thermal conductivity of the gas material is modified to 8–9 W / m·K, and the coefficient of thermal expansion is modified to 0.006–0.008 / K for recalculation.

[0031] Compared with the prior art, the beneficial effects of the present invention include at least the following: the simulation method of the present invention can perform relatively accurate numerical simulation of the vacuum distillation process of metallic indium, which can be used to further guide the practice of vacuum distillation purification and separation of non-ferrous metals, and effectively reduce the consumption of resources and energy in the experimental and production processes. Attached Figure Description

[0032] The above and other objects and features of the present invention will become clearer from the following description taken in conjunction with the accompanying drawings, in which:

[0033] Figure 1 A model diagram of the high-temperature vacuum equipment used for vacuum distillation of metallic indium, as shown in Embodiment 1 of the present invention.

[0034] Figure 2 This is a comparison chart of the simulated and measured values ​​of the temperature measurement point in Embodiment 1 of the present invention.

[0035] Figure 3 This is a flow field distribution diagram of the vacuum distillation process of metallic indium in Embodiment 1 of the present invention.

[0036] Explanation of reference numerals in the attached figures:

[0037] Figure 1 1. Condensation plate; 2. Crucible; 3. Heating element; 4. Graphite insulation felt; (i) First temperature measuring point; (ii) Second temperature measuring point; (iii) Third temperature measuring point; (iv) Fourth temperature measuring point; (v) Fifth temperature measuring point. Detailed Implementation

[0038] In the following, a numerical simulation method for a vacuum distillation process of metallic indium according to the present invention will be described in detail with reference to the accompanying drawings and exemplary embodiments.

[0039] Specifically, the numerical simulation method of this invention is based on reasonable fundamental assumptions and real experimental conditions. It couples the control equations with parameters to achieve a relatively accurate numerical simulation of the temperature and flow fields during the vacuum distillation process of metallic indium, which agrees well with experimental results. This method provides a relatively accurate prediction of the temperature field and metal vapor flow field distribution during vacuum distillation, and can be used to further guide the practice of vacuum distillation purification and separation of non-ferrous metals.

[0040] This invention provides a numerical simulation method for the vacuum distillation process of metallic indium, which may include the following steps:

[0041] Step S1: Create a 3D model of the structure and internal components of the high-temperature vacuum equipment used for indium vacuum distillation. The high-temperature vacuum equipment includes a cooling water inlet and a cooling water outlet, and the internal components include a heating element. The internal components may include insulation material inside the high-temperature vacuum equipment, a crucible containing the indium-containing raw material, and a condenser plate, among other components.

[0042] Step S2 involves dividing the drawn model into a polyhedral mesh and refining the boundary layers at solid-solid and solid-fluid contact surfaces. For example, three boundary layer refinements can be performed.

[0043] Step S3: Assign corresponding materials to the high-temperature vacuum equipment and internal components in the model, and set the basic assumptions and control equations for the numerical simulation of the temperature field and the numerical simulation of the flow field during the vacuum distillation process of metallic indium.

[0044] Step S04: Set the boundary conditions for the numerical simulation of the temperature field and assign initial values. After calculation, obtain the numerical simulation results of the temperature field inside the high-temperature vacuum equipment.

[0045] Step S05: Based on the obtained numerical simulation results of the temperature field, set the boundary conditions for the numerical simulation of the flow field and assign initial values, and then calculate the numerical simulation results of the flow field inside the high-temperature vacuum equipment.

[0046] In some implementations, the specific process for step S03 may include:

[0047] Step S31: Assign corresponding materials to the high-temperature vacuum equipment and its internal components in the model. For example, set the heating element, condenser plate, and crucible inside the high-temperature vacuum equipment to graphite, set the insulation material to graphite felt, and set the furnace body of the equipment to steel.

[0048] Step S32: Set the basic assumptions for the numerical simulation of the temperature field and the flow field during the vacuum distillation process of metallic indium. The basic assumptions may include: (1) the temperature of the heating element is constant; (2) the inlet flow rate and temperature of the cooling water are constant, and there is no backflow at the outlet of the cooling water; (3) the gas density follows the Boussinesq assumption, i.e.

[0049] (ρ-ρ0)g≈-ρ0β(T-T0)g

[0050] Where ρ represents air density; ρ0 is the air density at a known temperature T0, in kg / m³. 3 β is the coefficient of thermal expansion of air, 1 / K; g represents the acceleration due to gravity, m / s². 2 .

[0051] Step S33: Set the governing equations for the numerical simulation of the temperature field and the numerical simulation of the flow field during the vacuum distillation process of metallic indium. The governing equations may include:

[0052] Mass continuity equation:

[0053]

[0054] Momentum continuity equation:

[0055] x direction

[0056] y direction

[0057] z direction

[0058] Energy conservation equation:

[0059]

[0060] Where ρ represents mass density, t represents time, u, v, w are velocity vectors in the x, y, and z directions, respectively, in m / s; ρu, ρv, ρw represent mass fluxes in the x, y, and z directions, respectively; f x f is the x-component of the volume force f acting on a unit mass fluid element; y f is the y-component of f; z τ is the z-component of f; xx τ yy τ zzLet Pa and τ be the stress tensors on the plane perpendicular to x, y, and z, respectively, with the stress direction in the same direction as the normal direction. xy The stress component τ acts on a plane perpendicular to x, pointing towards y; Pa; xz The stress component τ acts on a plane perpendicular to x, pointing towards z; Pa; yx The stress component τ acts on a plane perpendicular to y, pointing towards x; Pa; yz The stress component acts on a plane perpendicular to y, pointing towards z, Pa; τ zx The stress component τ acts on a plane perpendicular to z, pointing towards x; Pa. zy denoted as σz, representing the stress component acting on a plane perpendicular to z, pointing towards y, in Pa; e is the internal energy per unit mass generated by the random motion of molecules, in J; p is the pressure, in Pa; and T is the temperature, in K. is the volumetric heating rate per unit mass, J / kg·K; k is the thermal conductivity, W / m·K.

[0061] Step S34: In the numerical simulation of the temperature field, the thermal radiation model is set to a surface-to-surface model, and its governing equations are:

[0062] J k =E k +ρ k q in,k ;

[0063] Among them, J k E represents radiation emitted from a surface. k ρ represents the self-radiation of surface k; k Represents reflectivity; q in,k It represents the incident radiant heat flow emitted from surrounding objects.

[0064] In the numerical simulation of the temperature field, since the simulation is based on a vacuum state, the main heat transfer mechanism within the device is thermal radiation. When a temperature difference exists within the gas, the heat transfer mechanism is gas thermal conduction. The optical thickness of the medium is crucial for the radiation and refractive indices of a semi-transparent medium. A vacuum state means that the fluid in the computational domain is nearly transparent to the wavelength range of thermal radiation; therefore, this invention employs a surface-to-surface model.

[0065] In some implementations, for step S04, setting the boundary conditions and assigning initial values ​​for the temperature field numerical simulation, and obtaining the temperature field numerical simulation results within the high-temperature vacuum equipment based on the control equations, may include: setting the boundary conditions as follows: the cooling water inlet is set as a velocity inlet (boundary type: velocity inlet), the cooling water outlet is set as a pressure outlet (boundary type: pressure outlet), and all other boundaries are set as adiabatic walls. Assigning initial values ​​includes setting the operating pressure, cooling water flow velocity, and operating temperature of the heating element. For example, in the assigned initial values, the operating pressure for indium vacuum distillation can be set to 0.8–12 Pa; the cooling water flow velocity can be set to 2 m / s. For example, the operating pressure can be set to 1 Pa; the cooling water flow velocity can be set to 2 m / s. The relationship between the indium saturation temperature and the pressure can be set as follows:

[0066] lgP = -12580T -1 -0.45lgT+11.91;

[0067] Where P represents pressure and T represents the saturation temperature of indium.

[0068] In some implementations, step S04, which calculates the numerical simulation results of the temperature field within the high-temperature vacuum equipment based on the governing equations, may include: after setting the boundary conditions and initial values ​​for the numerical simulation of the temperature field, substituting the initial values ​​into the governing equations, and obtaining the numerical simulation results of the temperature field through iterative calculation. For example, the Fluent fluid simulation software under the Ansys software package can be used to calculate the temperature field during the vacuum distillation of metallic indium. After setting the boundary conditions and initial values ​​for the numerical simulation of the temperature field, the results can be obtained through calculation using the Fluent fluid simulation software.

[0069] In some implementations, step S05, setting the boundary conditions for the flow field numerical simulation and assigning initial values ​​based on the obtained temperature field numerical simulation results, may include:

[0070] The boundary conditions are set as follows: the cooling water inlet is set as a velocity inlet, the cooling water outlet is set as a pressure outlet, and all other boundaries are set as adiabatic walls.

[0071] Assigning initial values ​​includes setting the operating pressure, cooling water flow rate, and the height of liquid indium inside the device at initialization. For example, the height of liquid indium inside the device at initialization is 4 mm.

[0072] In some implementations, the VOF multiphase flow model can be used to track the phase interface changes during indium evaporation in step S05 during the process numerical simulation. Specifically, this may include:

[0073] In step (1), during the evaporation of metallic indium, the liquid-gas phase mass transfer is controlled by the gas phase transport equation:

[0074]

[0075] Where v represents the gas phase; α v ρ is the gas phase volume fraction; v This refers to the gas phase density. This refers to the gas phase velocity. These represent the mass transfer rates of evaporation and condensation, respectively, in kg / s·m. -3 In this step, the VOF multiphase flow model introduces a volume fraction for each cell of each phase, and all attributes within this cell are determined by the weighted volume fraction.

[0076] Step (2) defines the evaporation mass transfer rate as a positive value and the condensation mass transfer rate as a negative value. The mass transfer rates of evaporation and condensation are calculated using the saturation temperature.

[0077] When T l >T sat Time (evaporation process):

[0078]

[0079] When T l <T sat Time (condensation process):

[0080]

[0081] Where coeff is the adjustment coefficient, in units of 1 / s; α and ρ are the phase volume fraction and density, respectively, with l representing the liquid phase and v representing the gas phase in the subscripts; T sat Let K be the saturation temperature.

[0082] In some implementations, step S05, which calculates the flow field numerical simulation results within the high-temperature vacuum equipment based on the governing equations, may include: setting the boundary conditions for the flow field numerical simulation and assigning initial values, then substituting these initial values ​​and obtaining the flow field numerical simulation results through iterative calculation of the governing equations. For example, the Fluent fluid simulation software under the Ansys software package can be used to calculate the flow field during the vacuum distillation of metallic indium. After setting the boundary conditions and initial values ​​for the flow field numerical simulation, the results can be obtained through calculation using the Fluent fluid simulation software.

[0083] In some implementations, the Fluent fluid simulation software under the Ansys software package can be used to perform numerical simulations of the temperature and flow fields. Before initialization, the Coupled pressure-velocity coupling method can be used. This method employs pressure-based transient calculations and selects a time step. The time step can be 10... -5 s.

[0084] To better understand the present invention, specific examples are provided below to further illustrate the content of the present invention, but the content of the present invention is not limited to the examples below.

[0085] Example 1

[0086] A numerical simulation method for the vacuum distillation process of metallic indium may include the following steps:

[0087] Step S01: Using Solidworks software, a geometric model of the actual high-temperature vacuum equipment is drawn at a 1:1 scale. The geometric model is as follows: Figure 1 As shown, the high-temperature vacuum equipment is a vertical vacuum furnace, including a condenser plate 1, a crucible 2, a heating element 3, and graphite insulation cotton 4. The condenser plate 1 has a total of 9 condenser plates. The crucible 2 is used to hold the indium-containing raw material. The crucible 2 can be a high-purity graphite crucible. The heating element 3 is located inside the equipment and is used to heat the equipment. Five temperature measuring points are set on the outer wall of the condenser plates at stages 1, 3, 5, 7, and 9, respectively, designated as (i), (ii), (iii), (iv), and (v), with heights of 93 mm, 143 mm, 193 mm, 243 mm, and 293 mm. Graphite insulation felt 4 is placed around and at the bottom of the heating element, and circulating cooling water flows through the furnace lid, furnace shell, and furnace bottom. The furnace body is made of steel, and all other solid components are made of high-purity graphite. Metallic indium is used as the experimental raw material. The main dimensions of the vertical vacuum distillation furnace are shown in Table 1.

[0088] Table 1 Main Dimensions of Vertical Vacuum Distillation Furnace

[0089]

[0090] Step S02: Divide the model into polyhedral meshes and refine the boundary layers at the solid-solid and solid-fluid contact surfaces with three layers, resulting in a total of approximately 2.77 million meshes.

[0091] Step S03: Assign appropriate materials to each part of the model, including setting the heating element, condenser plate, and crucible to graphite, the insulation material to graphite felt, and the furnace body to steel. Establish the basic assumptions for simulating the vacuum distillation flow field of metallic indium, including:

[0092] First: It is assumed that the temperature of the heating element is constant.

[0093] Second: It is assumed that the inlet velocity and temperature of the cooling water are constant, and that no backflow occurs at the outlet of the cooling water.

[0094] Third: Gas density follows the Boussinesq assumption.

[0095] Step S04, setting boundary conditions and initial conditions, including:

[0096] (1) Calculate the temperature field

[0097] The initial values ​​are: initial air temperature of 300K, initial heating element temperature of 1473K, operating pressure P = 1Pa, and cooling water flow velocity v = 2m / s.

[0098] Boundary conditions: The cooling water inlet is set to a velocity inlet with a speed of 2 m / s; the cooling water outlet is set to a pressure outlet with backflow suppressed. All other boundaries of the model are adiabatic walls.

[0099] The calculation is considered to have converged when the temperature monitoring point fluctuation is less than 1K.

[0100] (2) Calculate the flow field

[0101] The initial values ​​are: the initial temperature of the heating element is 1473K; a region with a height of 4mm is set in the crucible, and the liquid volume fraction of metallic indium in this region is set to 1; the operating pressure is P = 1Pa; and the height of liquid indium in the crucible is 4mm at the time of initialization.

[0102] Boundary conditions: The cooling water inlet is set to a velocity inlet with a speed of 2 m / s; the cooling water outlet is set to a pressure outlet with backflow suppressed. All other boundaries of the model are adiabatic walls.

[0103] When the calculated residual is less than 10 -6 When the computation is considered to have converged.

[0104] The material parameters of metallic indium are shown in Table 2.

[0105] Table 2 Material parameters of indium

[0106]

[0107]

[0108] The temperature and flow fields during the vacuum distillation of indium were numerically calculated using Fluent fluid simulation software under the Ansys software package. Pressure-based transient calculations were employed, using the Coupled pressure-velocity coupling method with a time step of 10. - 5 The temperature field and flow field distribution during the vacuum distillation process of metallic indium were calculated.

[0109] Considering computational efficiency, the steady-state temperature field is calculated first, and the transient flow field is calculated after obtaining the accurate temperature field distribution.

[0110] The temperature field calculation results are as follows:

[0111] Table 3 shows the temperature data of the measuring points on the straight line y = 0 mm and the straight line y = 40 mm at different set temperatures when steady state is reached. It shows that the average temperature difference ΔT between the inside and outside of the crucible is between 30 and 45 K. This is because the heat source of the fluid domain inside the crucible is the heat transferred to the surface of the crucible by the heating element through vacuum thermal radiation. However, the thermal emissivity of high-purity graphite is generally 0.85 to 0.95, causing some heat to be absorbed by the crucible and other devices. Therefore, the temperature of the fluid domain inside the crucible is generally lower than the temperature outside the crucible.

[0112] Table 3 Temperature data at temperature measurement points

[0113]

[0114]

[0115] Comparison of simulated and measured values ​​at temperature measurement points (e.g.) Figure 2 As shown in the figure, the error is approximately 5%. The error calculation formula is as follows:

[0116]

[0117] Among them, T S To simulate the temperature value, T E These are actual measured values.

[0118] The flow field calculation results are as follows:

[0119] After obtaining the accurate temperature distribution inside the condenser, the flow field distribution of metallic indium in vacuum distillation at 1473 K was calculated as follows: Figure 3 As shown.

[0120] Depend on Figure 3 It can be seen that the metal vapor diffuses continuously into the condenser pan against the temperature gradient in a cluster form. Most of the metal vapor accumulates in the crucible and the first-stage condenser pan. The metal vapor content in the second-stage condenser pan decreases and rapidly decreases until it reaches the fourth-stage condenser pan. This is because there is a temperature difference of about 33K between the inside and outside of the crucible. At the temperature measurement point (ii), the inside of the crucible is already below the saturated evaporation temperature, so it cannot move upwards in large quantities.

[0121] Table 4 compares the distribution of metal vapor in each condenser region in the simulation results at steady state at 1473 K with the experimental values ​​at 1473 K and 4 hours of holding time. Due to issues with the collection method and measurement accuracy, it was not possible to obtain experimental data on condensate in condenser pans of levels 6 to 9 for comparison with the simulated values. However, the table shows that the simulated values ​​in the crucible and each condenser pan are quite close to the existing experimental values, indicating that the existing simulation method is reliable.

[0122] Table 4 Comparison of simulation results and experimental values

[0123]

[0124] As shown in the chart, the simulation process described above is in good agreement with the results of the vacuum distillation experiment of metallic indium.

[0125] Although the invention has been described above in conjunction with exemplary embodiments, those skilled in the art will understand that various modifications and changes can be made to the exemplary embodiments of the invention without departing from the spirit and scope defined by the claims.

Claims

1. A numerical simulation method for the vacuum distillation process of metallic indium, characterized in that, Includes the following steps: Step S1: Draw a three-dimensional model of the structure and internal components of the high-temperature vacuum equipment used for vacuum distillation of metallic indium. The high-temperature vacuum equipment is equipped with a cooling water inlet and a cooling water outlet, and the internal components include a heating element. Step S2: Divide the drawn model into a polyhedral mesh and refine the boundary layer at the solid-solid and solid-fluid contact surfaces; Step S3: Assign corresponding materials to the high-temperature vacuum equipment and internal components in the model, and set the basic assumptions and control equations for the numerical simulation of the temperature field and the numerical simulation of the flow field during the vacuum distillation process of metallic indium. Step S04: Set the boundary conditions for the numerical simulation of the temperature field and assign initial values, and calculate the numerical simulation results of the temperature field inside the high-temperature vacuum equipment. Step S05: Based on the obtained numerical simulation results of the temperature field, set the boundary conditions for the numerical simulation of the flow field and assign initial values, and calculate the numerical simulation results of the flow field inside the high-temperature vacuum equipment; wherein, The basic assumptions for the numerical simulation of temperature field and flow field in the vacuum distillation process of metallic indium include: constant temperature of the heating element, constant inlet flow rate and temperature of cooling water, no backflow at the outlet of cooling water, and gas density following the Boussinesq assumption. Setting the boundary conditions and assigning initial values ​​for the numerical simulation of the temperature field includes: The boundary conditions are set as follows: the cooling water inlet is set as a velocity inlet, the cooling water outlet is set as a pressure outlet, and all other boundaries are set as adiabatic walls. Assigning initial values ​​includes setting the operating pressure, cooling water flow rate, and heating element operating temperature; Setting boundary conditions and assigning initial values ​​for the flow field numerical simulation includes: The boundary conditions are set as follows: the cooling water inlet is set as a velocity inlet, the cooling water outlet is set as a pressure outlet, and all other boundaries are set as adiabatic walls. The initial values ​​include: setting the operating pressure, cooling water flow rate, and the height of liquid indium in the device during initialization.

2. The numerical simulation method for the vacuum distillation process of metallic indium according to claim 1, characterized in that, The governing equations include: Mass continuity equation: ； Momentum continuity equation: Energy conservation equation: ； Where ρ represents mass density and t represents time. , , The velocity vectors in the x, y, and z directions; , , These represent the mass flux in the x, y, and z directions, respectively. Let f be the x-direction component of the volume force f acting on a unit mass fluid element; Let f be the component in the y-direction; Let f be the component in the z-direction; These are the stress tensors on the planes perpendicular to x, y, and z, where the stress direction is the same as the normal direction; The stress component acts on a plane perpendicular to x, with its direction pointing to y; The stress component acts on a plane perpendicular to x, and its direction points to z; The stress component acts on a plane perpendicular to y, with its direction pointing to x; The stress component acts on a plane perpendicular to y, and its direction points to z; The stress component acts on a plane perpendicular to z, with its direction pointing to x; denoted as , where is the stress component acting on a plane perpendicular to z, pointing towards y; e is the internal energy per unit mass generated by the random motion of molecules; p is the pressure; and T is the temperature. Volumetric heating rate per unit mass; is the thermal conductivity.

3. The numerical simulation method for the vacuum distillation process of metallic indium according to claim 1 or 2, characterized in that, Step S3 also includes setting the thermal radiation model to a surface-to-surface model in the numerical simulation of the temperature field, with the following governing equations: ； in, Indicates radiation emitted from the surface. This represents the self-radiation of surface k; Indicates reflectivity; It represents the incident radiant heat flow emitted from surrounding objects.

4. The numerical simulation method for the vacuum distillation process of metallic indium according to claim 1 or 2, characterized in that, The numerical simulation results of the temperature field inside the high-temperature vacuum equipment also include: Once the calculation is stable, extract the temperature monitoring point values ​​inside the equipment and compare them with the actual measured monitoring point values ​​inside the equipment. If the values ​​do not match, modify the thermal conductivity and thermal expansion coefficient of the gas material and recalculate. Based on the new temperature field numerical simulation, extract the temperature monitoring point values ​​inside the equipment and compare them with the actual measured monitoring point values ​​inside the equipment. If the values ​​match, it is considered that a reliable temperature field numerical simulation result has been obtained.

5. The numerical simulation method for the vacuum distillation process of metallic indium according to claim 4, characterized in that, If the values ​​do not match after comparison, the thermal conductivity of the gas material is changed to 8~9 W / m·K and the coefficient of thermal expansion is changed to 0.006~0.008 / K, and then the calculation is repeated.

6. The numerical simulation method for the vacuum distillation process of metallic indium according to claim 1 or 2, characterized in that, In the flow field numerical simulation process of step S05, the VOF multiphase flow model is used to track the phase interface changes during the evaporation of metallic indium.

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