Simulation method and device for directional crystallization purification process of high-purity gallium

Abstract

The embodiment of the application provides a simulation method and device for a high-purity gallium directional crystallization purification process, the simulation method comprising: constructing a thermophysical property database and embedding the simulation software preprocessing module, the thermophysical property database comprising function relationships of different thermophysical property parameters of high-purity gallium changing with temperature; constructing a three-dimensional geometric model of the high-purity gallium directional crystallization purification and importing the simulation software; configuring a dynamic grid system in the calculation domain, the grid node position of the dynamic grid system being capable of being adaptively adjusted or reconstructed along with the movement of the stirring rod; setting preset conditions of the high-purity gallium directional crystallization purification process and activating a plurality of preset physical models in the solver, and calling the thermophysical property database by the solver to perform transient simulation calculation on the high-purity gallium directional crystallization purification process to obtain a simulation result. The technical scheme of the embodiment of the application can improve the simulation precision of the high-purity gallium directional crystallization purification process, and the simulation result can quickly meet the quick optimization demand of the process parameters in actual production.

Description

Technical Field

[0001] This application relates to the field of simulation technology, and more specifically, to a simulation method and apparatus for the high-purity gallium directional crystallization purification process. Background Technology

[0002] Currently, the research and optimization of high-purity gallium directional crystallization purification processes mainly rely on experimental trial and error. Researchers conduct successive crystallization experiments by adjusting equipment parameters, sampling and testing purity, and then adjusting the parameters again based on the results, repeating this process until the target purity is achieved. However, this method suffers from long cycles and high costs. Because the crystallization process takes place in a closed system, the temperature distribution inside the furnace is not visible, and the progress of the crystallization interface and the local enrichment of impurities are difficult to directly observe and quantitatively analyze through experimental means. This results in a lack of clear physical basis for adjusting process parameters, leading to low optimization efficiency.

[0003] In recent years, simulation technology has been gradually introduced into the field of crystallization and purification processes, using computer simulations to assist in the selection and optimization of process parameters. However, existing simulation schemes still have the following shortcomings: First, the high-purity gallium thermal properties used in the simulation are fixed constants. In reality, gallium's specific heat capacity, density, thermal conductivity, viscosity, and other thermal properties all change with temperature. The existing simulation scheme uses fixed constant values, which cannot reflect the actual changes in gallium's thermal properties with temperature. This results in a large deviation between the simulation input parameters and the actual physical behavior, leading to insufficient simulation accuracy.

[0004] Secondly, the simulation calculation mode is a steady-state calculation, which can only obtain a single static crystallization result. It cannot obtain dynamic evolution information of temperature field, flow field and solid fraction over time during the crystallization process, cannot track the migration path of the crystallization interface, and makes it difficult to perform dynamic analysis and process optimization of the crystallization process.

[0005] Due to the aforementioned shortcomings, the accuracy of existing simulation technologies in optimizing high-purity gallium directional crystallization purification processes is limited, making it difficult to meet the actual production requirements for rapid optimization of process parameters. Summary of the Invention

[0006] The embodiments of this application provide a simulation method and apparatus for the high-purity gallium directional crystallization purification process. Based on the technical solution provided in this application, the simulation accuracy of the high-purity gallium directional crystallization purification process can be improved, and the simulation results can quickly meet the actual production requirements for rapid optimization of process parameters.

[0007] Other features and advantages of this application will become apparent from the following detailed description, or may be learned in part from practice of this application.

[0008] According to a first aspect of the embodiments of this application, a simulation method for a high-purity gallium directional crystallization purification process is provided. The simulation method includes: constructing a thermal property database and embedding it into a preprocessing module of simulation software; the thermal property database includes functional relationships of different thermal property parameters of high-purity gallium changing with temperature, and functional relationships of the solid fraction of high-purity gallium changing with temperature; constructing a three-dimensional geometric model of high-purity gallium directional crystallization purification according to the structure of actual production equipment and importing it into the simulation software; the three-dimensional geometric model includes at least a crystallization tank for holding high-purity gallium, a cooling water tank for cooling high-purity gallium, and a stirring device for stirring high-purity gallium. A stirring rod is used; a dynamic mesh system is configured within the computational domain, and the mesh node positions of the dynamic mesh system can be adaptively adjusted or reconstructed as the stirring rod moves; preset conditions for the high-purity gallium directional crystallization purification process are set in the solver, and multiple preset physical models are activated. The solver calls the thermophysical property database to perform transient simulation calculations on the high-purity gallium directional crystallization purification process and obtain simulation results; the simulation results include at least one of the following: temperature distribution, flow field distribution, phase distribution, thermophysical property parameters, and solid fraction distribution of each mesh at each transient moment; the simulation results are used to analyze the crystallization law of high-purity gallium directional crystallization purification and / or optimize process parameters.

[0009] In some embodiments of this application, based on the aforementioned scheme, the computational domain is divided into a liquid gallium phase, a cooling water phase, and an air phase, with the air phase filling the gap region between the stirring rod and the crystallization tank and the cavity region above the liquid surface in the crystallization tank.

[0010] In some embodiments of this application, based on the foregoing scheme, the functional relationship between the solid fraction of high-purity gallium and temperature is as follows:

[0011] Among them, C ps For the constant-voltage specific heat capacity of solid-state gallium, T m is the melting point of gallium, and L is the latent heat of fusion of gallium.

[0012] In some embodiments of this application, based on the aforementioned scheme, a dynamic mesh system is configured within the computational domain, including: defining the movement trajectory of the stirring rod through a user-defined function; loading the dynamic mesh model in the simulation software and configuring the dynamic mesh parameters through a user-defined function, the dynamic mesh parameters including the dynamic mesh relaxation factor, mesh reconstruction threshold, elastic smoothing parameter, and local reconstruction parameter; dividing the computational domain into meshes, and performing quality checks and dynamic mesh motion pre-performance verification on the divided meshes, so as to configure the dynamic mesh system within the computational domain.

[0013] In some embodiments of this application, based on the aforementioned scheme, the grid density of the first region in the computational domain is greater than that of the second region. The first region includes the inner wall of the crystallization tank and the solid-liquid phase transition interface of high-purity gallium. The second region includes the far-field region of the cooling water tank and the region in the computational domain that is far from the solid-liquid phase transition interface and the flow core region.

[0014] In some embodiments of this application, based on the aforementioned scheme, multiple preset physical models include: VOF multiphase flow model, convection-thermal coupling model and solidification-melting phase change model.

[0015] In some embodiments of this application, based on the aforementioned scheme, a solver calls a thermal property database to perform transient simulation calculations on the high-purity gallium directional crystallization purification process, obtaining simulation results, including: for each transient moment of the transient simulation calculation, a user-defined function calculates the position data of the stirring rod at that transient moment based on the moving trajectory of the stirring rod; the dynamic mesh model updates the mesh nodes based on the position data of the stirring rod at that transient moment; the updated flow field distribution and phase distribution of each mesh at that transient moment are obtained by solving the VOF multiphase flow model; the updated temperature distribution of each mesh at that transient moment is obtained by solving the convection-conduction coupling model; the updated solid fraction distribution and thermal property parameters of each mesh at that transient moment are obtained by solving the solidification-melting phase change model based on the thermal property database; and the flow field distribution, phase distribution, temperature distribution, solid fraction distribution, and thermal property parameters at each transient moment are used as simulation results.

[0016] In some embodiments of this application, based on the aforementioned scheme, multiple preset physical models also include a standard k-ε turbulence model, which is used to solve for turbulent viscosity, and the turbulent viscosity is used to determine the input data of the convection-conduction coupling model.

[0017] In some embodiments of this application, based on the foregoing scheme, the simulation method further includes: adjusting at least one parameter in the preset conditions, and / or adjusting at least one model parameter in a plurality of preset physical models, and / or adding a preset physical model, and repeatedly performing transient simulation calculations to obtain multiple sets of simulation results; the parameters in the preset conditions include at least one of the initial temperature of high-purity gallium, the surface temperature of the stirring rod, the cooling water temperature, and the stirring speed.

[0018] According to a second aspect of the embodiments of this application, a simulation device for a high-purity gallium directional crystallization purification process is provided. A first construction unit is configured to construct a thermal property database and embed it into the preprocessing module of the simulation software. The thermal property database includes functional relationships between different thermal property parameters of high-purity gallium and temperature, and a functional relationship between the solid fraction of high-purity gallium and temperature. A second construction unit is configured to construct a three-dimensional geometric model of the high-purity gallium directional crystallization purification process according to the structure of actual production equipment and import it into the simulation software. The three-dimensional geometric model includes at least a crystallization tank for holding high-purity gallium, a cooling water tank for cooling high-purity gallium, and a stirring rod for stirring high-purity gallium. The configuration unit is used to configure a dynamic mesh system within the computational domain. The mesh node positions of the dynamic mesh system can be adaptively adjusted or reconstructed as the stirring rod moves. The solution unit is used to set preset conditions for the high-purity gallium directional crystallization purification process in the solver and activate multiple preset physical models. The solver calls the thermophysical property database to perform transient simulation calculations on the high-purity gallium directional crystallization purification process and obtain simulation results. The simulation results include at least one of the following: temperature distribution, flow field distribution, phase distribution, thermophysical property parameters, and solid fraction distribution of each mesh at each transient moment. The simulation results are used to analyze the crystallization law of high-purity gallium directional crystallization purification and / or optimize process parameters.

[0019] According to a third aspect of the embodiments of this application, a computer-readable storage medium is provided, characterized in that the computer-readable storage medium stores at least one piece of program code, the at least one piece of program code being loaded and executed by a processor to perform the operations performed by the method described in any of the first aspects above.

[0020] According to a fourth aspect of the present application, an electronic device is provided, including one or more processors and one or more memories, wherein at least one piece of program code is stored in the one or more memories, the at least one piece of program code being loaded and executed by the one or more processors to perform the operation as described in any of the first aspects above.

[0021] The technical solution of this application, in the simulation of the high-purity gallium directional crystallization purification process, firstly, constructs a thermal property database and embeds it into the preprocessing module of the simulation software. The thermal property database includes functional relationships between different thermal property parameters of high-purity gallium and temperature, as well as a functional relationship between the solid fraction of high-purity gallium and temperature. Secondly, according to the structure of the actual production equipment, a three-dimensional geometric model of high-purity gallium directional crystallization purification is constructed and imported into the simulation software. The three-dimensional geometric model includes at least a crystallization tank for holding high-purity gallium, a cooling water tank for cooling high-purity gallium, and a stirring rod for stirring high-purity gallium. Thirdly, in A dynamic mesh system is configured within the computational domain, and the mesh node positions of the dynamic mesh system can be adaptively adjusted or reconstructed as the stirring rod moves. Finally, preset conditions for the high-purity gallium directional crystallization purification process are set in the solver, and multiple preset physical models are activated. The solver calls the thermophysical property database to perform transient simulation calculations on the high-purity gallium directional crystallization purification process, and the simulation results are obtained. The simulation results include at least one of the following: temperature distribution, flow field distribution, phase distribution, thermophysical property parameters, and solid fraction distribution of each mesh at each transient moment. The simulation results are used to analyze the crystallization law of high-purity gallium directional crystallization purification and / or optimize process parameters.

[0022] Based on the technical solution of this application, at least the following technical effects can be achieved: 1. By constructing a thermal property database containing functional relationships between different thermal properties of high-purity gallium and temperature, and embedding it into the preprocessing module of simulation software, each mesh cell can dynamically assign thermal property parameters based on its current temperature during the simulation process. Compared with the fixed constant assignment method used in existing technologies, this application can accurately reflect the actual changes in thermal properties such as specific heat capacity, density, thermal conductivity, and viscosity of high-purity gallium with temperature, eliminating simulation deviations caused by inaccurate property parameters and significantly improving simulation accuracy.

[0023] 2. By activating multiple preset physical models in the solver and performing transient simulation calculations, the temperature distribution, flow field distribution, phase distribution, and solid fraction distribution of each grid at each transient moment during the crystallization process can be obtained, realizing dynamic simulation of the entire process from the fully liquid state to the completion of crystallization. Compared with the steady-state calculations of existing technologies, this application can track the migration path of the crystallization interface and the evolution of the solid fraction over time, providing complete transient information support for the optimization of process parameters.

[0024] 3. By configuring a dynamic mesh system within the computational domain, the mesh node positions can be adaptively adjusted or reconstructed as the stirring rod moves, avoiding mesh distortion and negative volume problems caused by the movement of the stirring rod, ensuring the stability and accuracy of the simulation calculation, and making the simulation boundary conditions highly consistent with the actual working conditions.

[0025] In summary, the simulation method for high-purity gallium directional crystallization purification process provided in this application can provide high-precision simulation results covering the entire process for optimizing process parameters, thereby effectively reducing the trial-and-error costs in process development.

[0026] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and do not limit this application. Attached Figure Description

[0027] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application. It is obvious that the drawings described below are merely some embodiments of this application, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort. In the drawings: Figure 1 A schematic flowchart illustrating a simulation method for a high-purity gallium directional crystallization purification process according to an embodiment of this application is shown. Figure 2 A schematic diagram of a three-dimensional geometric model of high-purity gallium directional crystallization purification according to an embodiment of this application is shown; Figure 3 A detailed flowchart illustrating the configuration of a dynamic mesh system within a computational domain according to an embodiment of this application is shown. Figure 4 A schematic diagram of the temperature field distribution after 8 hours of crystallization according to an embodiment of this application is shown; Figure 5 A schematic diagram of the flow field distribution after 8 hours of crystallization according to an embodiment of this application is shown; Figure 6 A block diagram of a simulation apparatus for a high-purity gallium directional crystallization purification process according to an embodiment of this application is shown; Figure 7 A schematic diagram of the structure of an electronic device according to an embodiment of this application is shown. Detailed Implementation

[0028] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided to make this application more comprehensive and complete, and to fully convey the concept of the exemplary embodiments to those skilled in the art.

[0029] Furthermore, the described features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. Numerous specific details are provided in the following description to give a thorough understanding of embodiments of this application. However, those skilled in the art will recognize that the technical solutions of this application can be practiced without one or more of the specific details, or other methods, components, apparatuses, steps, etc., can be employed. In other instances, well-known methods, apparatuses, implementations, or operations are not shown or described in detail to avoid obscuring various aspects of this application.

[0030] The block diagrams shown in the accompanying drawings are merely functional entities and do not necessarily correspond to physically independent entities. That is, these functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0031] The flowcharts shown in the accompanying drawings are merely illustrative and do not necessarily include all content and operations / steps, nor do they necessarily have to be performed in the described order. For example, some operations / steps can be broken down, while others can be combined or partially combined; therefore, the actual execution order may change depending on the specific circumstances.

[0032] It should be noted that "multiple" in this article refers to two or more. "And / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A alone, A and B simultaneously, or B alone. The character " / " generally indicates that the preceding and following related objects have an "or" relationship.

[0033] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such uses of these terms can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in orders other than those illustrated or described.

[0034] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0035] It should be noted that high-purity gallium (≥99.999%), as a core raw material for the preparation of compound semiconductors such as gallium nitride and gallium arsenide, is widely used in 5G communications, LED lighting, radio frequency devices, and power electronics. Directional crystallization is one of the mainstream processes for preparing high-purity gallium. Its basic principle is to utilize the segregation effect of impurities in the solid and liquid phases during gallium solidification. By controlling the temperature gradient and crystallization rate, impurities are enriched in the liquid phase, thereby achieving gallium purification. This process involves the coordinated control of multiple parameters, such as cooling water temperature, stirring speed, and crystallization time, which are interconnected. Therefore, optimizing the process parameters for directional crystallization purification of high-purity gallium can effectively improve the crystallinity of high-purity gallium.

[0036] The following detailed description of some embodiments of this application will be provided in conjunction with the accompanying drawings. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0037] See Figure 1 The diagram illustrates a simulation method for a high-purity gallium directional crystallization purification process according to an embodiment of this application, specifically including the following steps 110 to 140: Step 110: Construct a thermal property database and embed it into the preprocessing module of the simulation software. The thermal property database includes functional relationships of different thermal property parameters of high-purity gallium as a function of temperature, and functional relationships of the solid fraction of high-purity gallium as a function of temperature.

[0038] In this embodiment, based on the publicly available data on the thermal properties of high-purity gallium, and for the temperature range where data is missing, the Debye model and hard sphere model are used to calculate and fit the data, thereby obtaining the functional relationships between different thermal property parameters of high-purity gallium and temperature, as well as the functional relationship between the solid fraction of high-purity gallium and temperature.

[0039] In this embodiment, the different thermophysical parameters of high-purity gallium include at least two of the following: density, specific heat capacity, thermal conductivity, viscosity, enthalpy, and entropy.

[0040] It should be noted that because the thermal properties of high-purity gallium change differently with temperature in liquid and solid states, when constructing a thermal property database for high-purity gallium, it is necessary to distinguish between the solid and liquid states of high-purity gallium, and to construct functional relationships between different thermal properties of high-purity gallium in liquid state and temperature, respectively.

[0041] In some implementations, when the thermal property parameter includes density, the density of liquid gallium as a function of temperature is expressed as Equation 1 below, and the density of solid gallium as a function of temperature is expressed as Equation 2 below: (T) = 6090 - 0.65(T - 302.91) (Formula 1) (T) = 5910 - 0.82(T - 302.91) (Formula 2) in, (T) represents the density of liquid gallium, and T represents the temperature. (T) represents the density of solid gallium, and the melting point of gallium is Tm = 302.91 K.

[0042] In some implementations, when the thermal property parameter includes specific heat capacity, the functional relationship between the specific heat capacity of solid gallium and temperature is as follows: Equation 3; and the functional relationship between the specific heat capacity of liquid gallium and temperature is as follows: Equation 4. +128 formula 3 Formula 4: 372 + 0.016(T - 302.91) in, This represents the specific heat capacity of solid gallium, where T represents temperature. This indicates the specific heat capacity of liquid gallium.

[0043] In some implementations, when the thermal property parameter includes thermal conductivity, the functional relationship between the thermal conductivity of solid gallium and temperature is as follows: Equation 5; and the functional relationship between the thermal conductivity of liquid gallium and temperature is as follows: Equation 6. =76.5-0.048(T-302.91) Formula 5 =33.2+0.022(T-302.91) Formula 6 in, This represents the thermal conductivity of solid-state gallium. T represents the thermal conductivity of liquid gallium, and T represents the temperature.

[0044] In some implementations, when the thermophysical property includes viscosity, solid gallium, due to its lack of flow, has a viscosity approaching infinity, and the viscosity of liquid gallium as a function of temperature is expressed by the following formula 7: = Formula 7 in, The value represents the viscosity of liquid gallium, and T represents the temperature.

[0045] In some implementations, when the thermophysical property parameter includes enthalpy, the functional relationship between the enthalpy of solid gallium and temperature is as follows: Equation 8; and the functional relationship between the enthalpy of liquid gallium and temperature is as follows: Equation 9.

[0046] = 0.3125 +128T+ Equation 8 = = +80700+372(T-302.91)+0.008 Equation 9 wherein, Tm represents the melting point temperature of gallium, represents the enthalpy of solid gallium, represents temperature, represents the specific heat capacity of solid gallium, represents the enthalpy of liquid gallium, represents the specific heat capacity of liquid gallium, and L is the latent heat of fusion of gallium.

[0047] In some embodiments, when the thermophysical property parameter includes entropy, the functional relation of entropy of solid gallium varying with temperature is shown as the following Equation 10, and the functional relation of entropy of liquid gallium varying with temperature is shown as the following Equation 11.

[0048] = Equation 10 = dT +266.4+372ln Equation 11 wherein, represents the entropy of solid gallium, represents the entropy of liquid gallium, T represents temperature, Tm represents the melting point temperature of gallium, and L is the latent heat of fusion of gallium.

[0049] In some embodiments, the functional relation of solid fraction of high-purity gallium varying with temperature is shown as the following Equation 12: Equation 12 wherein, C ps is the constant-pressure specific heat capacity of solid gallium, T m is the melting point of gallium, and L is the latent heat of fusion of gallium, wherein the latent heat of fusion of gallium is 80700 J / kg.

[0050] When T>Tm, = 0, indicating that high-purity gallium is entirely in a liquid state; when T<Tm - L / Cp s , = 1, indicating that high-purity gallium is entirely in a solid state; when Tm - L / Cp s <T<Tm, is between 0 and 1, indicating that high-purity gallium is in a solid-liquid coexistence state.

[0051] In the above formulas, T is the temperature variable, with the unit K; the unit of density is kg / m³; the unit of specific heat capacity is J / (kg·K); the unit of thermal conductivity is W / (m·K); the unit of viscosity is Pa·s; the unit of enthalpy is J / kg; and the unit of entropy is J / (kg·K).

[0052] In this embodiment, the fitted functional relationship is compiled into a callable parameter library in the form of user-defined functions (UDFs) and embedded into the preprocessing module of the ANSYS Fluent simulation software. Therefore, during subsequent transient simulation calculations, each mesh element can call the corresponding solid or liquid thermal property parameters and solid fraction values ​​in real time according to its current temperature, realizing dynamic assignment of thermal property parameters as temperature changes. This replaces the fixed constant assignment method used in traditional simulations, improving simulation accuracy.

[0053] See also Figure 1 Step 120: Construct a three-dimensional geometric model of high-purity gallium directional crystallization purification according to the structure of the actual production equipment and import it into the simulation software. The three-dimensional geometric model includes at least a crystallization tank for holding high-purity gallium, a cooling water tank for cooling high-purity gallium, and a stirring rod for stirring high-purity gallium.

[0054] In this embodiment, referring to the structural drawings of the high-purity gallium directional crystallization purification equipment at the production site, the external dimensions, structural parameters, material properties, and spatial assembly relationships of each component are determined. Specifically, the cooling water tank can be an annular jacket structure, enclosing the crystallization tank, used to circulate cooling water to cool the gallium liquid within the crystallization tank; the crystallization tank is a cylindrical open container used to hold the high-purity gallium to be purified; and the stirring rod is a cylindrical rod-shaped structure, vertically positioned inside the crystallization tank, used to stir the gallium liquid within the crystallization tank.

[0055] Using 3D modeling software (such as SolidWorks), a 3D geometric model is constructed according to the actual assembly positions at a 1:1 scale. During the modeling process, the actual internal gaps, wall structures, and cavity regions of the equipment must be fully preserved. Specifically, the actual annular gap between the stirring rod and the inner wall of the crystallization tank should be preserved, as should the thickness of the crystallization tank wall and its fit clearance with the cooling water tank, and the cavity region at the top of the crystallization tank. Although these gaps and cavity regions do not participate in the main solid-liquid phase change or flow process in macroscopic geometry, they will be used in subsequent steps to construct a complete multiphase coupled computational domain. That is, these regions are filled during mesh generation to ensure that the computational domain has complete physical spatial coverage, thereby eliminating the impact of computational blank areas on simulation stability.

[0056] After the 3D geometric model is constructed, the model file is exported to a format recognizable by the ANSYS Fluent simulation software (such as .x_t or .stp format) and imported into the simulation software. After importing, a geometric check can be performed on the model to confirm that the relative positions of each component are consistent with the actual situation, with no interference, overlap, or missing components, thus ensuring the accuracy of subsequent mesh generation and simulation calculations.

[0057] Specifically, a schematic diagram of the three-dimensional geometric model for the directional crystallization and purification of high-purity gallium can be shown as follows: Figure 2 As shown.

[0058] exist Figure 2 In the diagram, 1 represents gallium, 2 represents the crystallization tank, 3 represents the cooling tank, 4 represents the stirring rod, and 5 represents the heater.

[0059] The cooling tank 3 is an annular jacket structure, which is fitted outside the crystallization tank 2. The crystallization tank 2 is used to hold the high-purity gallium 1 to be purified. The stirring rod 4 is vertically set inside the crystallization tank 2, with its lower end extending below the liquid surface of the high-purity gallium 1. The heater 5 is set at the bottom of the crystallization tank 2 to heat the stirring rod and maintain its surface temperature constant.

[0060] The working principle is as follows: Heater 5 heats and maintains the stirring rod 4 at a constant temperature, continuously heating the high-purity gallium in the central region of the crystallization tank 2, keeping the gallium in the central region liquid. Cooling water is circulated in the cooling tank 3 to cool the sidewalls of the crystallization tank 2, causing the gallium near the inner wall of the crystallization tank 2 to cool and solidify first. This creates a radial temperature gradient within the crystallization tank 2, with the temperature gradually increasing from the sidewalls to the center. Under the stirring of the stirring rod 4, the gallium liquid in the crystallization tank 2 flows slowly, the solute redistributes at the solid-liquid interface, and impurities are discharged into the liquid phase region, thus achieving directional crystallization purification of high-purity gallium. After directional crystallization, high-purity solid gallium forms on the inner wall of the crystallization tank 2, while impurities are enriched in the liquid phase of the central region. Separating the liquid phase from the solid gallium in the central region yields purified high-purity gallium.

[0061] See also Figure 1 Step 130: Configure a dynamic mesh system within the computational domain. The positions of the mesh nodes in the dynamic mesh system can be adaptively adjusted or reconstructed as the stirring rod moves.

[0062] In this embodiment, the computational domain is divided into a liquid gallium phase, a cooling water phase, and an air phase. The air phase fills the gap region between the stirring rod and the crystallization tank and the cavity region above the liquid surface in the crystallization tank.

[0063] Specifically, based on the three-dimensional geometric model constructed in step 120, the spatial extent of the entire simulation computational domain is determined. This computational domain includes at least the internal space of the crystallization tank, the internal flow channel space of the cooling water tank, and the gap space and cavity region between them. In this embodiment, the above-mentioned computational domain is divided into three different phase regions.

[0064] First, the liquid gallium phase region is defined. Liquid gallium fills the molten region at the bottom of the crystallization tank, that is, the space defined by the inner wall of the crystallization tank and located below the liquid surface. This region is set as liquid gallium during simulation initialization. In subsequent simulations, as the temperature decreases, some liquid gallium will gradually transform into solid gallium. However, in this embodiment, the liquid gallium-filled space is defined at the initial moment at the computational domain partitioning level.

[0065] Secondly, the cooling water phase region is determined. Cooling water fills the internal flow channels of the cooling water tank, that is, the internal space of the annular jacket of the cooling water tank. In the computational domain partitioning, the entire internal flow channel space of the cooling water tank is set as the cooling water phase.

[0066] Finally, the air phase region is determined. The air phase fills all empty areas within the computational domain except for the liquid gallium phase and the cooling water phase. Specifically, it includes at least the following two regions: First, the gap region between the stirring rod and the inner wall of the crystallization tank. Since the diameter of the stirring rod is smaller than the inner diameter of the crystallization tank, there is an annular gap between them. Second, the cavity region above the liquid surface in the crystallization tank. This region is located between the liquid gallium surface and the top opening of the crystallization tank, and is the remaining space in the crystallization tank not occupied by liquid gallium. In traditional simulation schemes, this region is often ignored or not covered by a mesh, resulting in restricted liquid surface movement. This application fills this region with the air phase to provide gas-liquid interface support for the normal rise and fluctuation of the liquid surface.

[0067] This embodiment fills the gaps and cavities above the liquid surface within the computational domain that were originally unmesh-covered with air, thus achieving complete mesh coverage for the entire computational domain. This eliminates the "blank areas" within the computational domain and provides a complete and continuous computational domain foundation for the stable operation of the subsequent dynamic mesh system and the smooth execution of transient simulation calculations. Simultaneously, the introduction of the air phase provides physical support for the normal rise of the liquid surface through gas-liquid two-phase coupling, overcoming problems such as liquid adhering to the walls, inability to rise the liquid surface normally, and mesh distortion that occur in traditional simulations due to the lack of air phase support.

[0068] In step 130, the specific implementation method can be as follows: Figure 3 Perform the steps shown.

[0069] See Figure 3 The diagram illustrates a detailed process for configuring a dynamic mesh system within a computational domain according to an embodiment of this application, specifically including the following steps 131 to 133: Step 131: Define the movement trajectory of the stirring rod using a user-defined function.

[0070] Specifically, the axial reciprocating motion trajectory of the stirring rod can be defined by a user-defined function. In this embodiment, the stirring rod moves up and down along the central axis of the crystallization tank, that is, it moves in a periodic linear motion in the vertical direction.

[0071] See also Figure 3 Step 132: Load the dynamic mesh model in the simulation software and configure the dynamic mesh parameters through user-defined functions. The dynamic mesh parameters include the dynamic mesh relaxation factor, mesh reconstruction threshold, elastic smoothing parameter, and local reconstruction parameter.

[0072] The dynamic mesh relaxation factor controls the update magnitude of mesh node positions within each time step. This factor typically ranges from 0 to 1. A larger value results in greater displacement of mesh nodes within each time step, leading to faster mesh update response, but may cause excessively drastic mesh deformation. A smaller value results in smoother mesh node displacement changes, helping to maintain mesh quality, but with a slower response time. In this embodiment, the value of the dynamic mesh relaxation factor needs to be adjusted according to the time step size and the stirring rod's moving speed.

[0073] The mesh reconstruction threshold is used to determine whether the deformation of mesh cells exceeds the allowable range. The dynamic mesh model checks all mesh cells in the computational domain at each time step, and when the deformation of a mesh cell exceeds the threshold, the mesh cell is marked as a cell to be reconstructed.

[0074] The elastic smoothing parameter controls the stiffness distribution of the spring system in the elastic smoothing model. In the elastic smoothing method, the connections between mesh elements are equivalent to a spring system, and the displacement generated when the stirring rod moves is transmitted to the surrounding mesh nodes through the spring system.

[0075] Among them, the local reconstruction parameters are used to control the region and method of mesh reconstruction. When a mesh element is marked as a cell to be reconstructed due to excessive deformation, the dynamic mesh model needs to determine the size of the reconstruction region and the size distribution of the new mesh after reconstruction.

[0076] See also Figure 3 Step 133: The computational domain is meshed, and the meshed mesh is subjected to quality checks and dynamic mesh motion pre-performance verification in order to configure the dynamic mesh system within the computational domain.

[0077] In this embodiment, the condition for meshing the computational domain is that the mesh density of the first region within the computational domain is greater than that of the second region. The first region includes the inner wall of the crystallization tank and the solid-liquid phase transition interface of high-purity gallium. The second region includes the far-field region of the cooling water tank and the region within the computational domain that is far from the solid-liquid phase transition interface and the flow core region.

[0078] The first region includes the area between the inner wall of the crystallization tank and the solid-liquid phase transition interface of high-purity gallium. Since the crystallization process begins at the inner wall of the crystallization tank and progresses towards the center, the solid-liquid phase transition interface is always located near this region during the crystallization process. The temperature gradient and phase transition behavior are most significant in this region, requiring high computational accuracy. Therefore, a quadrilateral structured mesh with a size of 0.5 mm can be used to locally refine this region to ensure the computational accuracy of the solid-liquid phase transition interface and the flow boundary region.

[0079] The second region includes the far-field region of the cooling water tank and the region within the computational domain that is far from the solid-liquid phase transition interface and the flow core region. These regions are far from the crystallization front and the flow core region, with relatively gentle temperature and flow gradients, and therefore have lower requirements for mesh accuracy. Thus, a sparse mesh with a size of 5 mm can be used for meshing. By combining local refinement with far-field sparse meshing, the overall mesh size can be effectively controlled, reducing computational resource consumption, while ensuring the computational accuracy of the solid-liquid phase transition region and the flow boundary region.

[0080] In this embodiment, after mesh generation, the mesh quality check tool built into the simulation software is used to check the orthogonality, aspect ratio, and skewness of the generated mesh, and unqualified meshes are removed. Then, a dynamic mesh motion pre-run verification is performed, that is, monitoring changes in mesh node positions and mesh quality while only driving the stirring rod according to the motion law defined by the user-defined function. Through pre-run verification, the rationality of the dynamic mesh parameter configuration is verified, ensuring that the mesh does not exhibit negative volume or severe distortion throughout the entire stroke of the stirring rod. If the mesh quality in certain areas is found to drop below acceptable levels during the pre-run, the corresponding dynamic mesh parameters are adjusted until the pre-run verification passes. After the pre-run verification passes, the dynamic mesh system within the computational domain is configured, and its mesh node positions can adaptively adjust or reconstruct with the movement of the stirring rod during subsequent transient simulation calculations.

[0081] See also Figure 1Step 140: Set the preset conditions for the high-purity gallium directional crystallization purification process in the solver, and activate multiple preset physical models. Call the thermal property database through the solver to perform transient simulation calculations on the high-purity gallium directional crystallization purification process and obtain simulation results. The simulation results include at least one of the following: temperature distribution, flow field distribution, phase distribution, thermal property parameters, and solid fraction distribution of each grid at each transient moment. The simulation results are used to analyze the crystallization law of high-purity gallium directional crystallization purification and / or optimize process parameters.

[0082] In some implementations, the parameters in the preset conditions include at least one of the following: the initial temperature of high-purity gallium, the surface temperature of the stirring rod, the cooling water temperature, and the stirring speed.

[0083] In step 130, the preset conditions for the high-purity gallium directional crystallization purification process are first set in the solver of the simulation software. For example, the initial temperature of the high-purity gallium in the crystallization tank is set to 35℃ (i.e., 308.15K), which is higher than the melting point of high-purity gallium, 29.8℃ (i.e., 302.91K), to ensure that all the high-purity gallium in the crystallization tank is in a liquid state at the beginning. The surface temperature of the stirring rod is set to a constant 34℃, which is maintained by a heater located inside the stirring rod. The external cooling water is set to 23℃. The ambient temperature is set to 25℃. The stirring speed is set to 13 mm / s.

[0084] While setting preset conditions, multiple preset physical models are activated in the solver. In this embodiment, the multiple preset physical models may include a VOF multiphase flow model, a convection-conduction coupling model, and a solidification-melting phase transition model. The VOF multiphase flow model is used to track the interface position changes between the liquid gallium phase, cooling water phase, and air phase; the convection-conduction coupling model is used to solve for the temperature distribution within the computational domain; and the solidification-melting phase transition model is used to calculate the solid fraction distribution of high-purity gallium and the latent heat release during the phase transition process.

[0085] In this embodiment, the transient simulation calculation adopts a time-progression approach, discretizing the entire crystallization process into multiple time steps. For example, the time step can be set to 1 second, with a total calculation time of 28,800 seconds, corresponding to an 8-hour crystallization process. Within each time step, the solver sequentially solves the governing equations of each physical model, thereby obtaining the simulation results.

[0086] In the transient simulation calculation in step 140, the multiphysics control equations are iteratively solved at each time step. For the iterative solution at each time step, the convergence criterion is set as the residuals of all equations being less than 10. -4Specifically, during the iteration process at each time step, the simulation software monitors the residuals of each governing equation (including the continuity equation, momentum equations in three directions, energy equation, turbulent kinetic energy equation, turbulent dissipation rate equation, and VOF volume fraction equation) in real time. The simulation continues until the residuals of all the above equations decrease to 10. -4 If the calculation at the current time step has converged, the iteration at that time step is stopped, and the solution proceeds to the next time step. If the residual of a certain equation fails to decrease to 10 within the preset maximum number of iterations... -4 The iteration continues until the residual meets the criterion or the maximum number of iterations is reached. This convergence criterion ensures the computational accuracy at each time step, resulting in simulation results with good accuracy and reliability.

[0087] In step 140, the thermal property database is invoked through the solver to perform transient simulation calculations on the high-purity gallium directional crystallization purification process, and the specific implementation of obtaining the simulation results can be as follows: For each transient moment in the transient simulation calculation, a user-defined function calculates the position data of the stirring rod based on its movement trajectory. The dynamic mesh model updates the mesh nodes based on the stirring rod's position data. The updated flow field distribution and phase distribution of each mesh at the transient moment are obtained by solving the VOF multiphase flow model. The updated temperature distribution of each mesh at the transient moment is obtained by solving the convection-conduction coupling model. The updated solidification-melting phase change model is used to solve the solid fraction distribution and thermal property parameters of each mesh at the transient moment based on the thermal property database. The flow field distribution, phase distribution, temperature distribution, solid fraction distribution, and thermal property parameters at each transient moment are used as simulation results.

[0088] In some implementations, the multiple preset physical models also include a standard k-ε turbulence model, which is used to solve for the turbulent viscosity, and the turbulent viscosity is used to determine the input data for the convective-conductive-thermal coupling model.

[0089] The following detailed description of the collaborative workflow and data transfer relationships of various physical models during transient simulation calculations, using a specific implementation of this application, is provided below.

[0090] I. Data Preparation Before Simulation Before starting the transient simulation calculation, the following data preparations must be completed: First, the thermal property database constructed in step 110 is written into the simulation software in the form of user-defined functions (UDFs). The thermal property database can include functional relationships between the density, specific heat capacity, thermal conductivity, viscosity, enthalpy, and entropy of solid gallium and liquid gallium as a function of temperature, as well as the functional relationship between the solid fraction and temperature. These functions are compiled and loaded into the simulation software's memory before the simulation begins, remain unchanged throughout the simulation calculation process, and can be called and queried at any time.

[0091] Secondly, user-defined preset conditions and motion parameters of the stirring rod are set. These include the initial temperature of high-purity gallium (35℃), the constant surface temperature of the stirring rod (34℃), the cooling water temperature (23℃), the ambient temperature (25℃), and the axial reciprocating speed of the stirring rod.

[0092] Then, the dynamic mesh parameters, including the dynamic mesh relaxation factor, mesh reconstruction threshold, elastic smoothing parameter, and local reconstruction parameter, are configured through user-defined functions to control the adaptive adjustment or reconstruction behavior of the subsequent dynamic mesh system during the movement of the stirring rod.

[0093] II. Initialization at the start time At the initial moment (i.e., the zero point of the transient simulation calculation), no physical model has yet produced results. Therefore, all physical quantities required for input at the initial moment are either user-defined or retrieved from a thermal property database.

[0094] Specifically, the user set the initial temperature of high-purity gallium to 35°C. Based on this temperature, the simulation software calls the functional relationships of various thermal property parameters in the thermal property database to obtain the density, specific heat capacity, thermal conductivity, viscosity, enthalpy, and entropy values ​​at 35°C, and assigns these values ​​to the grid of all gallium liquid regions as the initial property conditions at the start time.

[0095] Meanwhile, the solidification model takes 35℃ as input and calls the function relationship between the solid fraction and temperature to obtain a solid fraction of zero, which means that at the beginning, all high-purity gallium is in the liquid state and the liquid fraction is 1.

[0096] The initial velocity field is set to zero, and the pressure field is set to ambient pressure; these are initial values ​​set by the user. The effective viscosity at the initial moment is equal to the molecular viscosity, and the turbulent viscosity is 0; the effective thermal conductivity is equal to the molecular thermal conductivity, and the turbulent thermal conductivity is 0.

[0097] III. Iterative Calculation of the First Time Step and Subsequent Time Steps Transient simulation calculations use a time-step progression method. The following uses a single time step as an example to illustrate the calculation order and data transfer relationships of each physical model.

[0098] Step 1: Calculate the new position of the stirring rod The user-defined function calculates the position coordinates of the stirring rod at the current time step based on the preset axial reciprocating motion trajectory of the stirring rod. This motion trajectory is determined by the user-preset axial movement speed and range.

[0099] Step 2: Update the grid system The dynamic mesh model performs elastic smoothing on the mesh near the stirring rod based on its new position coordinates, allowing the mesh node positions to adaptively adjust as the stirring rod moves. The dynamic mesh model monitors the deformation degree of each mesh cell in real time. When the deformation of a mesh cell exceeds a preset reconstruction threshold, that mesh cell is marked as a cell to be reconstructed. The dynamic mesh model then deletes the original mesh in that area and regenerates new mesh cells with regular shapes. After these operations, an updated mesh system is obtained.

[0100] Step 3: Calculate the velocity field and pressure field The flow solver consists of a VOF multiphase flow model, a continuity equation, and momentum equations in three directions, used to calculate the velocity and pressure fields at the current time step.

[0101] The input data for the flow solver includes: (1) the new position coordinates of the stirring rod; (2) the updated mesh system; (3) the velocity field and pressure field of the previous time step (for the initial time, the velocity field is set to zero and the pressure field is set to the ambient pressure); (4) the density and molecular viscosity of the previous time step (for the initial time, the values ​​obtained from the user-defined initial temperature); and (5) the phase distribution of the previous time step (for the initial time, the values ​​are set according to the initial filling state).

[0102] The flow solver solves the continuity equation, the momentum equation in three directions, and the VOF volume fraction equation simultaneously and iteratively, outputting the velocity field (i.e., the velocity components of each grid in the X, Y, and Z directions). This velocity field is the flow field, pressure field, and phase distribution (i.e., the volume fractions of liquid gallium, cooling water, and air in each grid).

[0103] Step 4: Calculate turbulent viscosity The standard k-ε turbulence model is used to calculate turbulent viscosity. Its input data includes the velocity field, pressure field, and effective viscosity. The effective viscosity is equal to the sum of the molecular viscosity and the turbulent viscosity. At the initial time step, the effective viscosity equals the molecular viscosity; for subsequent time steps, the effective viscosity equals the sum of the molecular viscosity and the turbulent viscosity of the previous time step.

[0104] The standard k-ε turbulence model solves for the turbulent kinetic energy equation k and the turbulent dissipation rate equation ε, and then calculates the new turbulent viscosity based on k and ε. The calculation formula is: Turbulent viscosity = density × constant × k² / ε.

[0105] Step 5: Calculate the temperature field The convection-conduction coupled model is used to calculate the temperature field at the current time step. Its input data includes: velocity field, effective thermal conductivity, phase distribution, density and specific heat capacity of the previous time step, boundary conditions, and latent heat feedback of the previous time step.

[0106] The effective thermal conductivity consists of two parts: molecular thermal conductivity and turbulent thermal conductivity. The molecular thermal conductivity is the initial value obtained from the user-defined initial temperature at the start time, and the updated thermophysical parameters from the previous time step for subsequent time steps. The turbulent thermal conductivity is calculated from the turbulent viscosity and Prandtl number output in the fourth step.

[0107] The boundary conditions include a constant surface temperature of 34°C for the stirring rod, a cooling water inlet temperature of 23°C, and an ambient temperature of 25°C. These temperatures are set by the user and remain constant throughout the simulation.

[0108] The convection-conduction coupled model substitutes the above inputs into the energy equation and solves for the temperature values ​​of each grid at the current time step, i.e., the temperature field.

[0109] Step 6: Calculate the solid fraction and liquid fraction and update the thermophysical parameters. The solidification-melting phase transition model is used to calculate the solid fraction and liquid fraction at the current time step and update the thermal property parameters of each grid.

[0110] Its input data includes: (1) the temperature field output in the fifth step; (2) the solid gallium property function library (i.e., the functional relationship of the thermal property parameters of solid gallium) and the liquid gallium property function library (i.e., the functional relationship of the thermal property parameters of liquid gallium) in the thermal property database; (3) the functional relationship of the solid fraction with temperature.

[0111] The operation consists of three steps: 1. Calculate the solid fraction and liquid fraction. For each gallium grid, using the current temperature T of that grid as input, the solid fraction as a function of temperature is used to obtain the solid fraction fs corresponding to that temperature. When the temperature is above the melting point, the solid fraction is 0; when the temperature is below the solidus temperature, the solid fraction is 1; when the temperature is between the two, the solid fraction is between 0 and 1. The liquid fraction is equal to 1 minus the solid fraction.

[0112] 2. Calculate the actual mixing properties of the current grid. For each gallium grid, using the current temperature T of the grid as input, call the solid-state gallium function library and the liquid gallium function library respectively to obtain the solid density ρ at that temperature. s (T), Solid specific heat Cp s (T), solid thermal conductivity k s (T), solid viscosity μ s (T), Solid enthalpy H s(T), Solid-state entropy S s (T), and liquid density ρ l (T), specific heat of liquid Cp l (T), liquid thermal conductivity k l (T), Liquid viscosity μ l (T), Liquid enthalpy H l (T), Liquid entropy S l (T). Then, using the solid fraction fs of the grid, the solid and liquid properties are weighted and averaged to obtain the current actual mixture properties of the grid, specifically as shown in formulas 13 to 18 below: Actual density ρ = fs × ρ s (T) + (1-fs) × ρ l (T) Formula 13 Actual specific heat Cp = fs × Cp s (T) + (1-fs) × Cp l (T) Formula 14 Actual thermal conductivity k = fs × k s (T) + (1-fs) × k l (T) Formula 15 Actual molecular viscosity μ = fs × μ s (T) + (1-fs) × μ l (T) Formula 16 Actual enthalpy H = fs × H s (T) + (1-fs) × H l (T) Formula 17 Actual entropy S = fs × S s (T) + (1-fs) × S l (T) Formula 18 3. Calculate the latent heat of solidification. The latent heat of solidification is equal to the change in solid fraction multiplied by the latent heat of fusion, where the change in solid fraction is the solid fraction of the current time step minus the solid fraction of the previous time step, and the latent heat of fusion is the material constant of gallium.

[0113] The output data of the solidification-melting phase transition model includes: (1) solid fraction field and liquid fraction field, which are used for post-processing to observe the crystallization progress and for the flow solver to calculate the flow resistance of the mushy region; (2) updated actual thermophysical parameters, including new density, new specific heat capacity, new thermal conductivity, new molecular viscosity, new enthalpy and new entropy for each grid, which are passed to the flow solver and the convection-conduction coupled model for the next time step; (3) latent heat of solidification, which is passed to the convection-conduction coupled model for the next time step.

[0114] IV. Time Step Loop Repeat steps one through six until the preset total computation time is reached (e.g., 28,800 seconds, corresponding to an 8-hour crystallization process). The calculation at each time step depends on the output data of the previous time step, including the velocity field, pressure field, temperature field, phase distribution, and updated thermophysical parameters, thereby realizing the full transient evolution simulation of the high-purity gallium directional crystallization purification process from the fully liquid state to the completion of crystallization.

[0115] V. Output of Simulation Results After the transient simulation calculation is completed, the simulation results, such as temperature distribution, flow field distribution, phase distribution, thermophysical parameters and solid fraction distribution at each transient moment, are output. These results are used to analyze the crystallization law of high-purity gallium directional crystallization purification and to optimize process parameters.

[0116] In some embodiments of this application, the following steps may also be performed: adjusting at least one parameter in the preset conditions, and / or adjusting at least one model parameter in a plurality of preset physical models, and / or adding a preset physical model, and repeatedly performing transient simulation calculations to obtain multiple sets of simulation results; the parameters in the preset conditions include at least one of the following: the initial temperature of high-purity gallium, the surface temperature of the stirring rod, the cooling water temperature, and the stirring speed.

[0117] The following detailed explanation, in conjunction with specific embodiments, details the process of adjusting the above parameters and comparing and analyzing multiple sets of simulation results.

[0118] Example 1 (Baseline Parameter Set) In this embodiment, transient simulation calculations are performed using baseline process parameters according to the methods described in steps 110 to 140. Specific parameter settings are as follows: the initial temperature of high-purity gallium is 35°C, the surface temperature of the stirring rod is 34°C, the external cooling water temperature is 23°C, the ambient temperature is 25°C, and the axial movement speed of the stirring rod is 13 mm / s. The initial temperature of gallium in the crystallization tank is 35°C (higher than the melting point of 29.8°C) to ensure that all high-purity gallium is in a liquid state at the initial stage.

[0119] Under the above parameters, the total duration of the transient simulation calculation is 28800 s (corresponding to an 8-hour crystallization process), with a time step set to 1 s. After the simulation calculation is completed, temperature field distribution cloud maps at different transient times (e.g., 0.5h, 1h, 2h, 4h, 6h, 8h) are output (e.g., the temperature distribution cloud map at 8h is shown below). Figure 4 As shown, the vector diagrams are taken from a longitudinal section passing through the central axis of the crystallization tank, and the flow field velocity vector diagram (e.g., the flow field distribution diagram for 8 hours). Figure 5 As shown, this is a longitudinal section taken from the central axis of the crystallization tank. Figure 4In the crystallization process, after 8 hours of crystallization, the temperature distribution exhibits a temperature gradient that gradually increases from the inner wall of the crystallization tank towards the center, with the lowest temperature on the outer wall and the highest temperature in the central region, forming a radial temperature distribution of "cold outside and hot inside". Figure 5 In the vector diagram, the flow velocity vector shows that the gallium liquid near the stirring rod flows upward under the stirring action of the stirring rod, and after reaching the liquid surface, it flows towards the inner wall of the crystallization tank. Near the wall, it flows downward, forming a large-scale circulation in the crystallization tank. This circulation promotes the homogenization of the temperature field and the redistribution of impurities in the crystallization tank.

[0120] Based on the solidification-melting phase transition model, the solid fraction distribution data for each grid was calculated. By statistically analyzing the solid fraction data at each transient moment, quantitative results of the crystallization rate and the crystallization interface advancement rate can be obtained. Under the conditions of external cooling water at 23℃, stirring rod at 34℃, and stirring speed at 13mm / s, the final crystallization rate exceeded 80% after 8 hours of crystallization, and the crystallization interface advanced in a dendritic pattern from the inner wall of the crystallization tank towards the center. Based on the above simulation results, this set of process parameters was recorded in the process parameter optimization database as basic reference data for the baseline operating conditions, for subsequent comparative analysis with other operating conditions.

[0121] Example 2 (Adjusting cooling water temperature and stirring speed) The difference between this embodiment and Embodiment 1 is that the cooling water temperature and stirring speed in the preset conditions are adjusted, while other conditions remain the same as in Embodiment 1. Specifically, the external cooling water temperature is set to 25°C (2°C higher than in Embodiment 1), the axial movement speed of the stirring rod is set to 14 mm / s (1 mm / s higher than in Embodiment 1), and the surface temperature of the stirring rod is kept constant at 34°C.

[0122] After the transient simulation calculation was completed, the temperature field and flow field distribution at different times were output. The results show that under the above parameter combination conditions, the crystallization driving force weakens due to the cooling water temperature increasing by 2℃ compared to Example 1; at the same time, the stirring speed increases by 1mm / s, enhancing the convective heat transfer effect of the melt, resulting in a significant slowdown in the crystallization interface propagation speed in the later stage of crystallization (4-8h). This result indicates that a higher cooling water temperature is not conducive to efficient propagation in the later stage of crystallization.

[0123] Example 3 (Adjusting the surface temperature of the stirring rod) The difference between this embodiment and Embodiment 1 is that the surface temperature of the stirring rod in the preset conditions is adjusted. Specifically, while maintaining a relatively low cooling water temperature of 23°C, the surface temperature of the stirring rod is set to 35°C (1°C higher than in Embodiment 1), and the axial movement speed of the stirring rod is set to 14 mm / s.

[0124] Under the above parameter conditions, the lower cooling water temperature provides sufficient crystallization driving force, while the 1°C increase in the stirring rod temperature compared to Example 1 delays premature solidification of the melt near the stirring rod, which helps maintain the fluidity of the area near the stirring rod and makes the crystallization process more stable. Simulation results show that moderately increasing the stirring rod temperature under lower cooling water temperature conditions can ensure the crystallization driving force while avoiding stirring failure caused by premature "freezing" of the stirring area, which is a better combination of process parameters.

[0125] Example 4 (Adding a preset physical model) The difference between this embodiment and Embodiment 1 is that the construction method of the computational domain and the preset physical model have been adjusted.

[0126] In this embodiment, in addition to filling the gap region between the stirring rod and the crystallization tank and the cavity region above the liquid surface in the crystallization tank with air phase, a mixed computational domain of solid phase (insulation material) and air phase is also constructed simultaneously in the insulation layer region between the cooling water tank and the external environment. The air in the tiny pores inside the insulation layer is treated as an independent phase and coupled using a porous media model. The air phase filling employs an adaptive mesh initialization method: based on the volume of each region in the geometric model, it automatically determines whether filling is necessary and the filling priority, prioritizing filling the space above the liquid surface, then filling narrow gap regions, and finally filling far-field cavities, ensuring a reasonable order of air phase filling.

[0127] In the VOF multiphase flow model setup, this embodiment enables the Open Channel Flow mode and sets the air phase as a compressible ideal gas to account for the pressure changes caused by the compression of the air volume above during liquid level rise, thereby more realistically simulating the dynamic behavior of the liquid surface within the closed crystallization tank. The primary phase is set as air, and the secondary phases are set as liquid gallium and cooling water.

[0128] Regarding the preset physical model, this embodiment, in addition to the VOF multiphase flow model, convection-conduction coupling model, solidification-melting phase change model and standard k-ε turbulence model activated in Embodiment 1, also additionally enables the Discrete Coordinate Radiation Model (DO model) to calculate the radiative heat transfer between the melt surface and the crystallization tank wall; at the same time, the Boussinesq assumption is enabled to simulate the natural convection effect driven by the temperature difference between cooling water and air, and the buoyancy term is added to the momentum equation in the form of a source term.

[0129] Comparative analysis of multiple sets of simulation results By executing at least two of the above embodiments 1 to 4, multiple sets of simulation results were obtained. Each set of simulation results includes the temperature distribution, flow field distribution, phase distribution, thermophysical parameter distribution, and solid fraction distribution at each transient moment under the corresponding parameter conditions. By comparing and analyzing multiple sets of simulation results, the influence of different process parameters (such as cooling water temperature, stirring speed, and stirring rod temperature) on the crystallization rate, crystallization ratio, and crystallization interface morphology can be revealed, thereby determining the optimal combination of process parameters for the directional crystallization purification of high-purity gallium.

[0130] For example, by comparing the simulation results of Example 1 and Example 2, the influence of cooling water temperature on the propagation speed in the later stage of crystallization can be analyzed; by comparing the simulation results of Example 1 and Example 3, the influence of stirring rod temperature on the fluidity of the stirring zone can be analyzed; by comparing the simulation results of Example 1 and Example 4, the influence of turbulence model, radiation model and natural convection model on simulation accuracy can be analyzed.

[0131] The comparative analysis of the above simulation results provides quantitative data support for adjusting process parameters in actual production, which can effectively reduce the number of physical experiments and lower process development costs.

[0132] In some embodiments of this application, during the simulation of the high-purity gallium directional crystallization purification process, firstly, a thermal property database is constructed and embedded into the preprocessing module of the simulation software. The thermal property database includes functional relationships between different thermal property parameters of high-purity gallium and temperature, as well as a functional relationship between the solid fraction of high-purity gallium and temperature. Secondly, according to the structure of the actual production equipment, a three-dimensional geometric model of high-purity gallium directional crystallization purification is constructed and imported into the simulation software. The three-dimensional geometric model includes at least a crystallization tank for holding high-purity gallium, a cooling water tank for cooling high-purity gallium, and a stirring rod for stirring high-purity gallium. Secondly, a dynamic mesh system is configured within the computational domain, whose mesh node positions can adaptively adjust or reconstruct as the stirring rod moves. Finally, preset conditions for the high-purity gallium directional crystallization purification process are set in the solver, and multiple preset physical models are activated. The solver calls the thermophysical property database to perform transient simulation calculations on the high-purity gallium directional crystallization purification process, obtaining simulation results. The simulation results include at least one of the following: temperature distribution, flow field distribution, phase distribution, thermophysical property parameters, and solid fraction distribution at each transient moment. The simulation results are used to analyze the crystallization law of high-purity gallium directional crystallization purification and / or optimize process parameters.

[0133] Based on the technical solution of this application, at least the following beneficial effects can be achieved: 1. By constructing a thermal property database containing functional relationships between different thermal properties of high-purity gallium and temperature, and embedding it into the preprocessing module of simulation software, each mesh cell can dynamically assign thermal property parameters based on its current temperature during the simulation process. Compared with the fixed constant assignment method used in existing technologies, this application can accurately reflect the actual changes in thermal properties such as specific heat capacity, density, thermal conductivity, and viscosity of high-purity gallium with temperature, eliminating simulation deviations caused by inaccurate property parameters and significantly improving simulation accuracy.

[0134] 2. By activating multiple preset physical models in the solver and performing transient simulation calculations, the temperature distribution, flow field distribution, phase distribution, and solid fraction distribution of each grid at each transient moment during the crystallization process can be obtained, realizing dynamic simulation of the entire process from the fully liquid state to the completion of crystallization. Compared with the steady-state calculations of existing technologies, this application can track the migration path of the crystallization interface and the evolution of the solid fraction over time, providing complete transient information support for the optimization of process parameters.

[0135] 3. By configuring a dynamic mesh system within the computational domain, the mesh node positions can be adaptively adjusted or reconstructed as the stirring rod moves, avoiding mesh distortion and negative volume problems caused by the movement of the stirring rod, ensuring the stability and accuracy of the simulation calculation, and making the simulation boundary conditions highly consistent with the actual working conditions.

[0136] In summary, the simulation method for high-purity gallium directional crystallization purification process provided in this application can provide high-precision simulation results covering the entire process for optimizing process parameters, thereby effectively reducing the trial-and-error costs in process development.

[0137] Based on the same inventive concept, embodiments of the present invention provide a simulation device for a high-purity gallium directional crystallization purification process, which can be used to execute the simulation method for the high-purity gallium directional crystallization purification process described in the above embodiments of this application. For details not disclosed in the embodiments of this application, please refer to the embodiments of the simulation method for the high-purity gallium directional crystallization purification process described in the above embodiments of this application.

[0138] See Figure 6 The diagram shows a block diagram of a simulation apparatus for a high-purity gallium directional crystallization purification process according to an embodiment of this application.

[0139] like Figure 6 As shown, a simulation device 600 for a high-purity gallium directional crystallization purification process according to an embodiment of this application includes: a first building unit 601, a second building unit 602, a configuration unit 603, and a solution unit 604.

[0140] The first construction unit 601 is used to construct a thermal property database and embed it into the preprocessing module of the simulation software. The thermal property database includes functional relationships between different thermal property parameters of high-purity gallium and temperature, as well as a functional relationship between the solid fraction of high-purity gallium and temperature. The second construction unit 602 is used to construct a three-dimensional geometric model of high-purity gallium directional crystallization purification according to the structure of actual production equipment and import it into the simulation software. The three-dimensional geometric model includes at least a crystallization tank for holding high-purity gallium, a cooling water tank for cooling high-purity gallium, and a stirring rod for stirring high-purity gallium. The configuration unit 603 is used to configure the high-purity gallium within the computational domain. A dynamic mesh system is included, whose mesh node positions can be adaptively adjusted or reconstructed as the stirring rod moves. A solver unit 604 is used to set preset conditions for the high-purity gallium directional crystallization purification process in the solver and activate multiple preset physical models. The solver calls a thermophysical property database to perform transient simulation calculations on the high-purity gallium directional crystallization purification process, obtaining simulation results. The simulation results include at least one of the following: temperature distribution, flow field distribution, phase distribution, thermophysical property parameters, and solid fraction distribution for each mesh at each transient moment. The simulation results are used to analyze the crystallization law of high-purity gallium directional crystallization purification and / or optimize process parameters.

[0141] In some embodiments of this application, based on the aforementioned scheme, the computational domain is divided into a liquid gallium phase, a cooling water phase, and an air phase, with the air phase filling the gap region between the stirring rod and the crystallization tank and the cavity region above the liquid surface in the crystallization tank.

[0142] In some embodiments of this application, based on the foregoing scheme, the functional relationship between the solid fraction of high-purity gallium and temperature is as follows:

[0143] Among them, C ps For the constant-voltage specific heat capacity of solid-state gallium, T m is the melting point of gallium, and L is the latent heat of fusion of gallium.

[0144] In some embodiments of this application, based on the foregoing scheme, the configuration unit 603 is further configured to: define the movement trajectory of the stirring rod through a user-defined function; load the dynamic mesh model in the simulation software and configure the dynamic mesh parameters through a user-defined function, the dynamic mesh parameters including the dynamic mesh relaxation factor, mesh reconstruction threshold, elastic smoothing parameter and local reconstruction parameter; perform meshing on the computational domain, and perform quality checks and dynamic mesh motion pre-performance verification on the mesh after partitioning, so as to configure the dynamic mesh system in the computational domain.

[0145] In some embodiments of this application, based on the aforementioned scheme, the grid density of the first region in the computational domain is greater than that of the second region. The first region includes the inner wall of the crystallization tank and the solid-liquid phase transition interface of high-purity gallium. The second region includes the far-field region of the cooling water tank and the region in the computational domain that is far from the solid-liquid phase transition interface and the flow core region.

[0146] In some embodiments of this application, based on the aforementioned scheme, multiple preset physical models include: VOF multiphase flow model, convection-thermal coupling model and solidification-melting phase change model.

[0147] In some embodiments of this application, based on the foregoing scheme, the solver 604 is further configured to: for each transient moment of the transient simulation calculation, use a user-defined function to calculate the position data of the stirring rod at that transient moment based on the moving trajectory of the stirring rod; update the mesh nodes of the dynamic mesh model based on the position data of the stirring rod at that transient moment; obtain the updated flow field distribution and phase distribution of each mesh at that transient moment by solving the VOF multiphase flow model; obtain the updated temperature distribution of each mesh at that transient moment by solving the convection-conduction coupling model; obtain the updated solid fraction distribution and thermal property parameters of each mesh at that transient moment by solving the solidification-melting phase change model based on the thermal property database; and use the flow field distribution, phase distribution, temperature distribution, solid fraction distribution, and thermal property parameters at each transient moment as simulation results.

[0148] In some embodiments of this application, based on the aforementioned scheme, multiple preset physical models also include a standard k-ε turbulence model, which is used to solve for turbulent viscosity, and the turbulent viscosity is used to determine the input data of the convection-conduction coupling model.

[0149] In some embodiments of this application, based on the foregoing scheme, the solving unit 604 is further configured to: adjust at least one parameter in the preset conditions, and / or adjust at least one model parameter in a plurality of preset physical models, and / or add a preset physical model, and repeatedly perform transient simulation calculations to obtain multiple sets of simulation results; the parameters in the preset conditions include at least one of the initial temperature of high-purity gallium, the surface temperature of the stirring rod, the cooling water temperature, and the stirring speed.

[0150] Based on the same inventive concept, embodiments of this application provide a computer-readable storage medium storing at least one computer program instruction, which is loaded and executed by a processor to perform the operations described above.

[0151] Based on the same inventive concept, embodiments of this application also provide an electronic device.

[0152] See Figure 7The diagram illustrates the structure of an electronic device according to an embodiment of the present application. The electronic device includes one or more memories 704, one or more processors 702, and at least one computer program (computer program instructions) stored in the memory 704 and executable on the processor 702. When the processor 702 executes the computer program, it implements the method described above.

[0153] Among them, Figure 7 In this document, a bus architecture (represented by bus 700) is used. Bus 700 may include any number of interconnected buses and bridges, linking various circuits including one or more processors represented by processor 702 and memory represented by memory 704. Bus 700 may also link various other circuits such as peripheral devices, voltage regulators, and power management circuits, which are well known in the art and therefore will not be described further herein. Bus interface 705 provides an interface between bus 700 and receiver 701 and transmitter 703. Receiver 701 and transmitter 703 may be the same element, i.e., a transceiver, providing a unit for communicating with various other devices over a transmission medium. Processor 702 is responsible for managing bus 700 and general processing, while memory 704 can be used to store data used by processor 702 during operation.

[0154] The functions described herein may be implemented in hardware, software executed by a processor, firmware, or any combination thereof. If implemented in software executed by a processor, the functions may be stored as one or more instructions or codes on or transmitted via a computer-readable medium. Other examples and embodiments are within the scope and spirit of this application and the appended claims. For example, due to the nature of software, the functions described above may be implemented using software executed by a processor, hardware, firmware, hardwired, or any combination thereof. Furthermore, the functional units may be integrated into a single processing unit, or each unit may exist physically separately, or two or more units may be integrated into a single unit.

[0155] In the several embodiments provided in this application, it should be understood that the disclosed technical content can be implemented in other ways. The device embodiments described above are merely illustrative; for example, the division of units can be a logical functional division, and in actual implementation, there may be other division methods. For instance, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the displayed or discussed mutual coupling, direct coupling, or communication connection may be through some interfaces; the indirect coupling or communication connection between units or modules may be electrical or other forms.

[0156] The units described as separate components may or may not be physically separate. Similarly, the components of the control device may or may not be physical units; they may be located in one place or distributed across multiple units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0157] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing computer program instructions, such as USB flash drives, read-only memory (ROM), random access memory (RAM), portable hard drives, magnetic disks, or optical disks.

[0158] The above description is merely an embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A simulation method for the high-purity gallium directional crystallization purification process, characterized in that, The simulation method includes: A thermal property database is constructed and embedded in the preprocessing module of the simulation software. The thermal property database includes functional relationships of different thermal property parameters of high-purity gallium as a function of temperature, and functional relationships of the solid fraction of high-purity gallium as a function of temperature. Based on the structure of the actual production equipment, a three-dimensional geometric model for the directional crystallization and purification of high-purity gallium is constructed and imported into the simulation software. The three-dimensional geometric model includes at least a crystallization tank for holding high-purity gallium, a cooling water tank for cooling high-purity gallium, and a stirring rod for stirring high-purity gallium. A dynamic mesh system is configured within the computational domain, wherein the positions of the mesh nodes in the dynamic mesh system can be adaptively adjusted or reconstructed as the stirring rod moves; The solver sets preset conditions for the high-purity gallium directional crystallization purification process and activates multiple preset physical models. The solver then calls the thermophysical property database to perform transient simulation calculations on the high-purity gallium directional crystallization purification process, obtaining simulation results. The simulation results include at least one of the following: temperature distribution, flow field distribution, phase distribution, thermophysical property parameters, and solid fraction distribution at each transient moment. The simulation results are used to analyze the crystallization law of high-purity gallium directional crystallization purification and / or optimize process parameters.

2. The simulation method according to claim 1, characterized in that, The computational domain is divided into a liquid gallium phase, a cooling water phase, and an air phase. The air phase fills the gap region between the stirring rod and the crystallization tank and the cavity region above the liquid surface in the crystallization tank.

3. The simulation method according to claim 1, characterized in that, The functional relationship between the solid fraction of the high-purity gallium and temperature is as follows: Where Cps is the specific heat capacity of solid gallium at constant pressure, Tm is the melting point of gallium, and L is the latent heat of fusion of gallium.

4. The simulation method according to claim 1, characterized in that, The configuration of the dynamic mesh system within the computational domain includes: The movement trajectory of the stirring rod is defined by a user-defined function; A dynamic mesh model is loaded into the simulation software, and the dynamic mesh parameters are configured through the user-defined function. The dynamic mesh parameters include a dynamic mesh relaxation factor, a mesh reconstruction threshold, an elastic smoothing parameter, and a local reconstruction parameter. The computational domain is divided into grids, and the divided grids are subjected to quality checks and dynamic mesh motion pre-simulation verification in order to configure a dynamic mesh system within the computational domain.

5. The simulation method according to claim 4, characterized in that, The grid density of the first region within the computational domain is greater than that of the second region. The first region includes the inner wall of the crystallization tank and the solid-liquid phase transition interface of high-purity gallium. The second region includes the far-field region of the cooling water tank and the region within the computational domain that is far from the solid-liquid phase transition interface and the flow core region.

6. The simulation method according to claim 4, characterized in that, The plurality of preset physical models include: VOF multiphase flow model, convection-conduction-thermal coupling model and solidification-melting phase change model.

7. The simulation method according to claim 6, characterized in that, The process involves calling the thermophysical property database through the solver to perform transient simulation calculations on the high-purity gallium directional crystallization purification process, obtaining simulation results including: For each transient moment in the transient simulation calculation, a user-defined function calculates the position data of the stirring rod at that transient moment based on the moving trajectory of the stirring rod; The dynamic mesh model updates the mesh nodes based on the position data of the stirring rod at this transient moment; The updated flow field distribution and phase distribution of each grid at this transient moment are obtained by solving the VOF multiphase flow model. The updated temperature distribution of each grid at this transient moment is obtained by solving the aforementioned convection-conduction coupling model. Based on the thermal property database, the solidification-melting phase transition model is used to solve for the updated solid fraction distribution and thermal property parameters of each grid at the transient moment. The flow field distribution, phase distribution, temperature distribution, solid fraction distribution, and thermal property parameters at each transient moment are used as simulation results.

8. The simulation method according to claim 6, characterized in that, The multiple preset physical models also include a standard k-ε turbulence model, which is used to solve for the turbulent viscosity, and the turbulent viscosity is used to determine the input data of the convection-conduction coupling model.

9. The simulation method according to claim 1, characterized in that, The simulation method further includes: Adjust at least one parameter in the preset conditions, and / or adjust at least one model parameter in the plurality of preset physical models, and / or add a preset physical model, and repeatedly execute the transient simulation calculation to obtain multiple sets of simulation results; the parameters in the preset conditions include at least one of the following: the initial temperature of high-purity gallium, the surface temperature of the stirring rod, the cooling water temperature, and the stirring speed.

10. A simulation device for the high-purity gallium directional crystallization purification process, characterized in that, The simulation device includes: The first building unit is used to build a thermal property database and embed it into the preprocessing module of the simulation software. The thermal property database includes functional relationships of different thermal property parameters of high-purity gallium as a function of temperature, and functional relationships of the solid fraction of high-purity gallium as a function of temperature. The second construction unit is used to construct a three-dimensional geometric model of high-purity gallium directional crystallization purification according to the structure of the actual production equipment and import it into the simulation software. The three-dimensional geometric model includes at least a crystallization tank for holding high-purity gallium, a cooling water tank for cooling high-purity gallium, and a stirring rod for stirring high-purity gallium. A configuration unit is used to configure a dynamic mesh system within the computing domain, wherein the mesh node positions of the dynamic mesh system can be adaptively adjusted or reconfigured as the stirring rod moves; The solver unit is used to set preset conditions for the high-purity gallium directional crystallization purification process in the solver and activate multiple preset physical models. The solver calls the thermophysical property database to perform transient simulation calculations on the high-purity gallium directional crystallization purification process and obtain simulation results. The simulation results include at least one of the following: temperature distribution, flow field distribution, phase distribution, thermophysical property parameters, and solid fraction distribution of each grid at each transient moment. The simulation results are used to analyze the crystallization law of high-purity gallium directional crystallization purification and / or optimize process parameters.

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