A method for predicting the thickness of a solidified shell in a continuous casting argon blowing crystallizer

Abstract

The application discloses a method for predicting the thickness of a solidified shell in a continuous casting argon-blowing crystallizer, and relates to the technical field of continuous casting production process simulation, which comprises the following steps: establishing a three-dimensional geometric model according to the geometric structure parameters of a continuous casting crystallizer and a submerged nozzle thereof; extracting a calculation domain from the three-dimensional geometric model based on boundary division and Boolean operation, and performing structured grid division on the three-dimensional geometric model to obtain a grid model corresponding to the calculation domain; importing the grid model into simulation software, selecting a calculation model and a solving method, defining physical property parameters and boundary conditions, and performing iterative solving after initialization operation to obtain the distribution result of the solidified shell in the continuous casting crystallizer; and performing post-processing on the distribution result, determining the solidification front position based on a liquid phase fraction threshold, and obtaining the thickness distribution of the solidified shell in the continuous casting crystallizer at different heights and under different working conditions. The application has the advantages of accurately predicting the thickness of the solidified shell and improving reliability and engineering applicability.

Description

Technical Field

[0001] This invention relates to the field of continuous casting production process simulation technology, specifically to a method for predicting the thickness of the solidified slab shell in an argon blowing crystallizer for continuous casting slabs. Background Technology

[0002] Continuous casting, as a core process in modern steel production, directly impacts billet quality and production safety through its technological stability. Ensuring uniform growth and sufficient safe thickness of the solidified billet shell within the mold is crucial for preventing accidents such as leaks and bulging. The initial billet shell must withstand the static pressure of the high-temperature molten steel and the thermal stress of the subsequent cooling process; therefore, the uniformity and integrity of its thickness distribution have a decisive influence on the surface quality of the billet.

[0003] However, due to the high temperature, strong turbulence, and opacity of the crystallizer (forming a "black box"), the thickness of the solidified billet shell cannot be obtained through direct measurement. Current industrial practices primarily rely on empirical formulas, analysis of exposed billet shell thickness, or simplified models based on thermocouple temperature data for indirect estimation. For example, some technical solutions use temperature sensors placed on the copper plate of the crystallizer to collect data and combine this with heat flux density inversion methods to estimate the shell thickness; however, these methods have significant limitations. Empirical formulas are usually based on idealized assumptions and fail to reflect the dynamic coupling relationship between molten steel flow, argon blowing behavior, and the solidification process under actual operating conditions. Heat flux density-based inversion models rely excessively on operating condition stability, are sensitive to changes in boundary conditions, and cannot distinguish the differences in billet shell growth characteristics between narrow and wide areas of the crystallizer. Existing technologies fail to effectively integrate the comprehensive influence of key process parameters such as molten steel flow characteristics, argon blowing rate control, and casting speed variations on the solidification front, leading to discrepancies between predicted results and actual billet shell spatial distribution characteristics. Especially under argon blowing conditions, the flow field disturbance caused by the movement of argon bubbles will significantly change the heat transfer behavior. Traditional methods lack accurate simulation of the three-dimensional flow-heat transfer-solidification coupling mechanism, making it difficult to accurately characterize the evolution law of the shell thickness at different height positions and regions.

[0004] Therefore, there is an urgent need to develop a prediction method that can truly reflect the dynamic correlation of process parameters in order to improve the reliability and engineering applicability of billet shell thickness characterization. Summary of the Invention

[0005] The purpose of this invention is to provide a method for predicting the thickness of the solidified billet shell in an argon-blown crystallizer for continuous casting slabs, which has the advantages of accurately predicting the thickness of the solidified billet shell, improving reliability, and engineering applicability.

[0006] This invention provides a method for predicting the thickness of the solidified slab shell in an argon-blown crystallizer for continuous casting, comprising the following steps: S1. Based on the geometric parameters of the continuous casting mold and its submerged entry nozzle, establish a three-dimensional geometric model including the foot roll area, part of the secondary cooling zone, the continuous casting mold and the submerged entry nozzle. S2. Based on boundary partitioning and Boolean operations, the computational domain of the three-dimensional geometric model is extracted, and the extracted computational domain is divided into a structured mesh to obtain the mesh model corresponding to the computational domain; wherein, the computational domain includes the continuous casting crystallizer area, the foot roll area, and part of the secondary cooling area; S3. Import the mesh model into the simulation software, select the calculation model and solution method, define the physical property parameters and boundary conditions, perform initialization operations, and then perform iterative solution to obtain the distribution results of the solidified billet shell in the continuous casting mold. S4. Post-process the distribution results, determine the solidification front position based on the liquid phase fraction threshold, and obtain the thickness distribution of the solidified billet shell in the continuous casting mold under different heights and different working conditions.

[0007] In one optional embodiment, the geometric parameters of the continuous casting mold and its submersible nozzle in S1 include: the width, height and thickness of the mold, and the inner and outer diameters, length, inclination angle, side hole shape and nozzle insertion depth of the submersible nozzle.

[0008] In one optional implementation, the three-dimensional geometric model established in S1, which includes the foot roll area, part of the secondary cooling zone, the continuous casting crystallizer, and the submerged entry nozzle, is a 1 / 4 symmetric model.

[0009] In one optional implementation, the structured mesh in S2 is a hexahedral mesh, and the area near the wall of the computational domain is densified, with an overall mesh quality of not less than 0.6 and a maximum aspect ratio of less than 10 for a single mesh.

[0010] In one optional implementation, S3 specifically includes: S31, Using Realizable k - ε The method solves for the turbulent motion of molten steel in the continuous casting mold, uses the energy conservation equation to solve for the heat transfer behavior of molten steel in the continuous casting mold, selects the solidification and melting model to solve for the solidification and melting behavior of molten steel, and defines the billet shell movement velocity according to the casting speed; uses the DPM model to calculate and track the motion of argon bubble particles; employs the Coupled algorithm for pressure-velocity coupling, the staggered pressure algorithm for spatial discretization of pressure, the bounded central difference scheme algorithm for spatial discretization of momentum, the energy equation for discretization using the second-order upwind scheme, and the solution using the bounded second-order implicit transient formula. S32. Set the density, viscosity, specific heat capacity, thermal conductivity, solidus temperature, liquidus temperature, latent heat of molten steel, density and diameter of argon bubbles; set the submerged entry nozzle inlet as the velocity inlet boundary and discrete phase injection point, the top surface of the continuous casting mold as the adiabatic boundary, the bottom surface as the outflow boundary, and the sidewall as the no-slip wall boundary, and define the corresponding discrete phase boundary condition type and the heat transfer type of the sidewall; S33. Initialize the flow field and temperature field of the computational domain, set the solution parameters, and perform iterative solution to obtain the distribution results of the solidified billet shell in the continuous casting mold.

[0011] In one optional implementation, the velocity inlet boundary in S32 is calculated based on the casting speed and the cross-sectional area of ​​the continuous casting machine's crystallizer and submerged entry nozzle, using the following formula: In the formula, This refers to the inlet velocity of the submersible nozzle. For pulling speed; This represents the cross-sectional area of ​​the outlet of the continuous casting crystallizer. This represents the cross-sectional area of ​​the immersion nozzle inlet.

[0012] In one optional implementation, the heat transfer type of the sidewall in S32 is heat flux heat transfer, and the heat flux is determined according to the Savage heat flux density equation, the formula being: In the formula, q For heat flux; A constant related to the wide or narrow face of the continuous casting mold; v c For pulling speed; d s This is the distance from the crescent moon.

[0013] In an optional implementation, S32 further includes defining the heat transfer type of the foot roller zone and the secondary cooling zone wall, wherein the heat transfer type of both the foot roller zone and the secondary cooling zone wall is convective heat transfer, and their convective heat transfer coefficient is determined according to an empirical formula, the formula being: In the formula, h s The heat transfer coefficients of the foot roller zone and the secondary cooling zone; β This is a correction factor for the heat transfer coefficients of the foot roller zone and the secondary cooling zone; w This refers to the density of the cooling water spray. T w The ambient temperature.

[0014] In one optional implementation, S4 specifically includes: Based on the liquid phase fraction distribution of molten steel in the continuous casting mold, multiple equally spaced billet pulling positions are selected along the height direction of the continuous casting mold in the post-processing software. The contour lines with a liquid phase fraction of 0.2-0.5 are used as the solidification front positions. Data of the solidification front positions at each location are extracted to establish the solidified billet shell thickness distribution of the wide and narrow faces of the continuous casting mold at different heights under different working conditions, thereby realizing a method for predicting the solidified billet shell thickness in the continuous casting mold.

[0015] As can be seen from the above, the method for predicting the thickness of the solidified billet shell in the argon blowing crystallizer provided in this application can accurately obtain the thickness distribution of the solidified billet shell by establishing a three-dimensional geometric model, performing mesh generation, simulation solution and post-processing. It solves the prediction deviation problem caused by the inability of the existing technology to integrate key parameters such as molten steel flow, argon blowing behavior and casting speed change. It has the advantages of accurately predicting the thickness of the solidified billet shell, improving reliability and engineering applicability. Attached Figure Description

[0016] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0017] Figure 1 This is a flowchart illustrating a method for predicting the thickness of a solidified billet shell in a slab continuous casting crystallizer according to an embodiment of the present invention. Figure 2 This is a schematic diagram of the three-dimensional geometric model of the computational domain in an embodiment of the present invention; Figure 3 This is a schematic diagram of the structure of the mesh model corresponding to the computational domain in an embodiment of the present invention; Figure 4 This is a schematic diagram showing the liquid phase fraction distribution and solidification front position of molten steel in a continuous casting crystallizer according to an embodiment of the present invention; Figure 5 The figure shows the distribution of the solidified billet shell thickness in the continuous casting mold as a function of the distance to the meniscus under different operating conditions according to an embodiment of the present invention; wherein, (a) is 1.0 mm / min. -1 Distribution of solidified shell thickness at different argon blowing rates under pulling speed conditions; (b) is for 5L / min. -1 Distribution of solidified shell thickness at different drawing speeds under argon blowing conditions. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] Traditional methods for predicting the thickness of solidified billet shells within continuous casting molds are difficult to measure directly in actual production processes due to the opaque nature of the mold and the high temperatures and strong turbulence inside. Current industrial practices often rely on empirical formulas, offline sectioning, or simplified models based on heat flux density for indirect estimation of shell thickness. These methods are heavily influenced by idealized assumptions, making it difficult to accurately reflect the actual distribution characteristics of the shell thickness within the mold. Furthermore, they are highly dependent on model assumptions and the stability of operating conditions, thus limiting their accuracy and stability in characterizing shell thickness.

[0020] like Figure 1 As shown, this application proposes a method for predicting the thickness of the solidified slab shell in an argon-blown crystallizer for continuous casting slabs, comprising the following steps: S1. Based on the geometric parameters of the continuous casting mold and its submerged entry nozzle, establish a three-dimensional geometric model including the foot roll area, part of the secondary cooling zone, the continuous casting mold and the submerged entry nozzle.

[0021] S2. Based on boundary decomposition and Boolean operations, the computational domain is extracted from the 3D geometric model, and the extracted computational domain is then divided into a structured mesh to obtain the mesh model corresponding to the computational domain (i.e., the mesh model of the molten steel fluid domain within the continuous casting mold). The computational domain includes the continuous casting mold area, the foot roll area, and part of the secondary cooling zone.

[0022] S3. Import the mesh model into the simulation software, select the calculation model and solution method, define the physical property parameters and boundary conditions, perform initialization operations, and then perform iterative solutions to obtain the distribution results of the solidified billet shell in the continuous casting mold.

[0023] S4. Post-process the distribution results, determine the solidification front position based on the liquid phase fraction threshold, and obtain the thickness distribution of the solidified billet shell in the continuous casting mold under different heights and working conditions.

[0024] The three-dimensional geometric model refers to a mathematical representation constructed using computer-aided design (CAD) tools that accurately describes the shape, size, and relative position of the continuous casting mold and its submerged entry nozzle in three-dimensional space. This model provides the foundation for subsequent calculations and analyses.

[0025] Boundary partitioning (B-Rep) and Boolean operations are commonly used techniques in computer graphics and geometric modeling. Boundary partitioning describes the geometry of an object by defining its surfaces (such as faces, edges, and vertices); Boolean operations allow for the combination or modification of geometry through set operations (such as union, intersection, and difference). These techniques are used to accurately define and extract complex computational regions for fluid dynamics.

[0026] Computational domain extraction refers to identifying and separating the regions that need to be numerically simulated from the complete geometric model. In continuous casting, this typically refers to the region where molten steel flows, i.e., the molten steel fluid domain. For stability calculation, the computational domain in this embodiment also includes the foot roll area and a portion of the secondary cooling zone, with an overall computational domain length of approximately 3 meters.

[0027] Structured mesh generation refers to discretizing the computational domain into a series of grid cells with regular topological structures. This type of mesh typically has high mesh quality and computational efficiency, which is beneficial for improving the accuracy and stability of numerical simulations.

[0028] A mesh model is a geometric representation formed by discretizing the region of molten steel flow within a continuous casting mold, consisting of a large number of interconnected mesh cells. This model serves as input data for computational fluid dynamics (CFD) simulation analysis.

[0029] Simulation software refers to specialized software platforms used to perform numerical simulations and computational analyses, such as computational fluid dynamics (CFD) software. This software can solve complex physical equations and predict phenomena such as fluid flow, heat transfer, and solidification.

[0030] The liquid phase fraction threshold refers to the criterion for determining the solidification front when the proportion of the liquid phase in the molten steel reaches a certain value during solidification. For example, when the liquid phase fraction is below a certain preset value, the region is considered to have solidified or is in the process of solidification.

[0031] The solidification front refers to the interface between the liquid and solid phases during the solidification process of molten steel. Accurate determination of this location is crucial for analyzing shell growth and thickness distribution.

[0032] Specifically, in step S1, a three-dimensional geometric model including the foot roll area, part of the secondary cooling zone, the continuous casting mold, and the submerged entry nozzle is established. This model can be constructed using computer-aided design (CAD) software, based on design drawings or actual measurement data, by manually inputting the dimensions and shape information of each component. Alternatively, it can be quickly generated based on a preset geometric template by adjusting key dimensional parameters. Furthermore, accurate geometric representations can also be obtained by acquiring point cloud data of existing equipment through 3D scanning technology and then performing reverse engineering modeling.

[0033] In step S2, based on boundary delimitation and Boolean operations, the computational domain is extracted from the 3D geometric model, and the extracted computational domain is then meshed into a structured grid to obtain the corresponding mesh model. The extraction of the computational domain can be achieved through cutting, separating, or combining operations in geometric modeling software. For example, by defining an auxiliary body surrounding the fluid region in the geometric model and then using Boolean difference operations to remove the solid portion, the fluid domain can be obtained. Regarding mesh generation, unstructured meshes, such as tetrahedral meshes, can be used to discretize the fluid domain. Alternatively, structured meshes, such as hexahedral meshes, can be used.

[0034] In step S3, the mesh model is imported into the simulation software, and a calculation model and solution method are selected. Physical property parameters and boundary conditions are defined, and after initialization, iterative solutions are performed to obtain the distribution of the solidified billet shell within the continuous casting mold. When selecting the calculation model, only fluid flow can be considered, ignoring heat transfer and solidification processes. A steady-state solver can be used to obtain the final steady state. Physical property parameters can be defined with fixed values, such as setting the density, viscosity, specific heat capacity, and thermal conductivity of the molten steel as constants. Boundary conditions can be simplified, for example, setting all walls as fixed-temperature boundaries or adiabatic boundaries. Initialization can use a uniform initial field, for example, setting the flow velocity and temperature of the entire computational domain to a constant. Subsequently, iterative solutions are performed until the preset number of iterations is reached.

[0035] In step S4, the distribution results are post-processed to determine the solidification front position based on the liquid fraction threshold and to obtain the thickness distribution of the solidified shell in the continuous casting mold under different heights and operating conditions. Post-processing can be performed using the post-processor built into the simulation software, for example, by visual inspection or by drawing contour lines at specific cross-sections to determine the solidification front. The determination of the solidification front can also be based on a fixed-temperature isotherm, such as using the solidus temperature of the molten steel as the criterion. When obtaining the thickness distribution, sampling can be performed only at a few preset height positions within the mold, and the shell thickness data at these positions can be manually extracted.

[0036] This embodiment establishes a three-dimensional geometric model including the foot roll zone, part of the secondary cooling zone, the continuous casting mold, and the submerged entry nozzle. The computational domain is extracted and meshed. The model is then imported into simulation software for multiphysics coupled iterative solving. Finally, based on a liquid fraction threshold, the position of the solidification front is accurately determined, thus achieving continuous and accurate prediction of the solidified shell thickness within the continuous casting mold. This method overcomes the limitations of traditional empirical formulas and simplified models in terms of characterization accuracy and stability, providing a reliable theoretical basis for continuous casting process design and operation control.

[0037] In one alternative implementation, in step S1, the geometric parameters of the continuous casting mold and its submersible nozzle include: the width, height and thickness of the mold, and the inner and outer diameters, length, inclination angle, side hole shape and nozzle insertion depth of the submersible nozzle.

[0038] Specifically, the width, height, and thickness of the mold are fundamental parameters defining the geometry of the continuous casting mold. The width and thickness of the mold directly determine the cross-sectional dimensions of the produced slab, while the height of the mold affects the residence time of the molten steel within the mold and the longitudinal development of the solidification process. Accurately acquiring and inputting these parameters is crucial to ensuring that the established three-dimensional geometric model accurately reflects the actual physical dimensions and shape of the mold, thus providing precise geometric boundaries for subsequent fluid dynamics and heat transfer calculations. Meanwhile, the inner and outer diameters, length, inclination angle, side hole shape, and insertion depth of the submerged entry nozzle describe in detail the geometric characteristics of the nozzle and its spatial position within the mold. The inner and outer diameters and length of the submerged entry nozzle determine the channel size and resistance characteristics of the molten steel flow inside the nozzle; the inclination angle controls the initial direction of the molten steel when it exits from the side hole of the nozzle, and has a decisive influence on the flow field distribution of the molten steel in the mold; the shape of the side hole defines the specific geometry and size of the molten steel injection port, directly affecting the diffusion and impact mode of the molten steel jet; and the nozzle insertion depth refers to the vertical distance of the side hole of the submerged entry nozzle relative to the molten steel surface. This parameter has a significant impact on surface fluctuations, slag entrapment behavior, and the overall flow field structure within the mold. By comprehensively and accurately defining these geometric parameters, the established three-dimensional geometric model can highly reproduce the physical morphology and relative positional relationship of the actual continuous casting mold and submerged entry nozzle.

[0039] The above technical solution fully considers key geometric parameters such as the width, height, and thickness of the mold, as well as the inner and outer diameters, length, inclination angle, side hole shape, and insertion depth of the submerged entry nozzle when establishing the three-dimensional geometric model. The precise definition of these parameters allows the established three-dimensional geometric model to more realistically and accurately reflect the physical structure of the actual continuous casting mold and submerged entry nozzle. This avoids simulation deviations caused by insufficient geometric information in the model, thus providing a highly reliable geometric basis for subsequent simulation calculations of the molten steel flow field, heat transfer, and solidification process. Ultimately, this significantly improves the accuracy and reliability of predicting the thickness of the solidified billet shell within the continuous casting mold, enabling the prediction results to better guide actual production and optimize the continuous casting process.

[0040] In one alternative implementation, the three-dimensional geometric model established in S1, which includes the foot roll area, part of the secondary cooling zone, the continuous casting crystallizer, and the submerged entry nozzle, is a 1 / 4 symmetric model.

[0041] A quarter-symmetric model refers to a 3D geometric model that takes into account the good symmetry of continuous casting molds and submerged entry nozzles in terms of geometry, fluid flow, heat transfer, and other physical phenomena. For example, symmetry exists along the central planes of the mold's width and thickness directions. Therefore, only one-quarter of the entire physical model can be built, and the physical behavior of the entire physical domain can be simulated by applying symmetric boundary conditions on the symmetry planes. This modeling method can significantly reduce the number of meshes and the volume of the computational domain, thereby greatly reducing the computational resources and time required for simulation calculations. In practice, the geometric modeling module of CAD software or simulation software is typically used to construct one-quarter of the geometric entity of the continuous casting mold and submerged entry nozzle according to their actual dimensions. In subsequent mesh generation and solution settings, the corresponding sections are defined as symmetry planes.

[0042] By employing the aforementioned technical solution, the three-dimensional geometric model is simplified into a quarter-symmetric model, significantly reducing the size of the computational domain. Since the flow and temperature fields in the continuous casting process exhibit good symmetry under ideal conditions, the quarter-symmetric model can accurately reflect the physical phenomena within the entire crystallizer, including the flow, heat transfer, and solidification processes of the molten steel, with relatively low computational cost. This significantly reduces the number of meshes and iteration steps required for simulation calculations, thereby greatly shortening the computation time and lowering the requirements for computing hardware. Therefore, this method can predict the thickness of the solidified billet shell with higher efficiency, and is particularly suitable for scenarios requiring extensive parameter optimization, operating condition analysis, or real-time prediction, thus improving the practicality and engineering application value of the prediction method.

[0043] In one alternative implementation, in step S2, the structured mesh is a hexahedral mesh, and the area near the walls of the computational domain is refined, with an overall mesh quality of not less than 0.6 and a maximum aspect ratio of less than 10 for a single mesh.

[0044] Specifically, the structured mesh uses a hexahedral mesh. A hexahedral mesh is a mesh composed of six-faced elements, possessing good orthogonality and isotropy. In computational fluid dynamics (CFD) simulations, it is particularly suitable for computational domains with regular geometries, effectively reducing numerical diffusion and improving computational accuracy and convergence. Using a hexahedral mesh allows for better fitting of the geometric boundaries of the computational domain, ensuring the accuracy of the simulation results.

[0045] Simultaneously, the mesh near the computational domain wall is refined. This region is a critical area where fluid flow and heat transfer behavior undergoes drastic changes; for example, boundary layer effects, shear stress, and temperature gradients are significant in this area. Refining the mesh in this region means placing more and smaller mesh cells near the wall, thereby capturing these complex physical phenomena more precisely and improving the accuracy of flow and temperature field calculations near the wall. This is crucial for accurately predicting the formation of solidified shells.

[0046] Furthermore, the overall mesh quality should be no less than 0.6. Mesh quality is an important indicator of the quality of mesh cell shape, and is usually evaluated comprehensively through parameters such as orthogonality, skewness, and aspect ratio. A mesh quality of no less than 0.6 means that the mesh cells have good shape, avoiding excessively distorted or deformed meshes, which is crucial for ensuring the stability and accuracy of numerical calculations. High-quality meshes can effectively reduce numerical errors and ensure the reliability of simulation results.

[0047] Furthermore, the maximum aspect ratio of a single mesh element is less than 10. Mesh aspect ratio refers to the ratio of the longest side to the shortest side of a mesh cell. In fluid simulations, an excessively large aspect ratio can lead to numerical diffusion and computational instability, especially when the fluid direction is inconsistent with the mesh direction. Limiting the maximum aspect ratio of a single mesh element to less than 10 helps ensure the uniformity of mesh cell shape, avoiding flat or elongated meshes in certain regions, thereby improving computational stability and accuracy, particularly when capturing anisotropic flow characteristics.

[0048] The above technical solution employs a hexahedral mesh for structured mesh generation, effectively improving mesh quality and the fit to geometric boundaries. Simultaneously, refining the mesh near the fluid domain wall allows for more precise capture of the flow field, temperature field, and complex physical phenomena during solidification in the critical region of solidified shell formation, significantly enhancing simulation accuracy. Furthermore, setting strict standards of an overall mesh quality of no less than 0.6 and a maximum aspect ratio of less than 10 for individual meshes effectively avoids numerical errors and computational instability caused by low-quality meshes, ensuring the reliability of simulation results. These measures work together to make the prediction of solidified shell thickness within the continuous casting mold more accurate and reliable, providing more dependable guidance for actual production.

[0049] In one optional implementation, step S3 specifically includes the following operations: In step S31, Realizable is adopted. k - εThe model solves for the turbulent motion of molten steel within the continuous casting mold. This model can more accurately predict turbulent fields with complex flow characteristics such as strong shear flow, separation flow, and secondary flow, and is particularly suitable for the complex flow behavior of molten steel within the continuous casting mold, providing an accurate flow field basis for subsequent heat transfer and solidification calculations. Simultaneously, the energy conservation equation is used to solve for the heat transfer behavior of molten steel within the continuous casting mold. This equation considers multiple heat transfer mechanisms such as convection, diffusion, and latent heat of phase change, accurately reflecting the energy changes of molten steel from a high-temperature liquid state to a low-temperature solid state, which is crucial for predicting the solidification process. A solidification-melting model is selected to solve for the solidification and melting behavior of molten steel. This model tracks the movement of the solidification front based on changes in the liquid phase fraction and considers the release of latent heat of phase change, thus accurately simulating the formation and growth process of the billet shell. Furthermore, the billet shell movement velocity is defined according to the casting speed, linking macroscopic continuous casting process parameters with the microscopic solidification process, simulating the dynamic growth of the billet shell, making the simulation results more consistent with actual production conditions. The DPM model was used for calculating and tracking the motion of argon bubble particles. This model can simulate the motion of discrete phases (such as argon bubbles) in the continuous phase (molten steel), thus providing a more comprehensive simulation of multiphase flow behavior within the crystallizer. For the solution algorithm, the Coupled algorithm was employed for pressure-velocity coupling. This algorithm can simultaneously solve the momentum equation and the pressure correction equation, exhibiting better convergence and stability. A staggered pressure algorithm was used for spatial discretization of pressure. This staggered arrangement effectively avoids decoupling between the pressure and velocity fields, improving the stability and accuracy of the calculation. A bounded central difference scheme was used for spatial discretization of momentum. This scheme effectively suppresses numerical oscillations while maintaining high accuracy, ensuring computational stability. The energy equation was discretized using a second-order upwind scheme. This scheme can weight the convection term based on flow direction information, thus effectively avoiding numerical diffusion while ensuring computational accuracy. A bounded second-order implicit transient formula is used for solving the problem. This formula has good stability, allows for larger time steps, and the second-order accuracy ensures the accuracy of time discretization, thus ensuring the reliability of the transient simulation.

[0050] In step S32, the density, viscosity, specific heat capacity, thermal conductivity, solidus temperature, liquidus temperature, latent heat of the molten steel, and the density and diameter of argon bubbles are set. These physical properties directly determine the flow, heat transfer, and solidification behavior of the molten steel, as well as the motion characteristics of argon bubbles in the molten steel, and are the basis for accurate numerical simulation. The submerged entry nozzle is set as the velocity inlet boundary and discrete phase injection point to simulate the initial state of molten steel and argon bubbles entering the mold from the nozzle. The top surface of the continuous casting mold is set as an adiabatic boundary, reflecting the heat transfer characteristics at the contact point between the liquid surface and air. The bottom surface is set as the outflow boundary, simulating the conditions under which the billet leaves the mold. The sidewalls are set as no-slip wall boundaries, conforming to the physical characteristics of fluids on solid walls. At the same time, the corresponding discrete phase boundary condition types and sidewall heat transfer types are defined to ensure that the simulation model is highly consistent with the physical boundary conditions of the actual continuous casting process.

[0051] In step S33, the flow field and temperature field of the computational domain are initialized to provide an initial guess value for the iterative calculation. After setting the solution parameters, iterative solution is performed. Through repeated calculations and corrections, each physical quantity reaches a convergent state, and finally the distribution result of the solidified billet shell in the continuous casting mold is obtained.

[0052] Through the above technical solution, the complex physical behavior of molten steel can be simulated more comprehensively and accurately during the prediction of the solidified shell thickness in the continuous casting mold. Specifically, Realizable... k - ε The model accurately captures the turbulence of molten steel, combining the energy conservation equation and the solidification-melting model to accurately describe the heat transfer and phase transformation processes, while also considering the dynamic growth of the billet shell. The DPM model's tracking of argon bubble movement allows the influence of multiphase flow to be reflected. In terms of the solution algorithm, the coupled Coupled algorithm and a series of high-precision discretization schemes and transient formulas are employed to ensure the stability and accuracy of the numerical calculations. By precisely setting physical property parameters and meticulously defining various boundary conditions, the simulation model highly replicates the actual continuous casting physical environment. These detailed and precise model selections, parameter settings, and solution methods significantly improve the accuracy and reliability of predicting the thickness of the solidified billet shell within the continuous casting mold, effectively solving the problem that general simulation steps alone are insufficient to accurately capture complex physical phenomena, and providing a solid data foundation for optimizing continuous casting process parameters.

[0053] In one alternative implementation, the velocity inlet boundary in step S32 is calculated based on the casting speed and the cross-sectional area of ​​the continuous casting machine crystallizer and submerged entry nozzle.

[0054] Specifically, when performing simulation calculations of the molten steel fluid domain within the continuous casting mold, the velocity boundary conditions at the submerged entry nozzle inlet need to be precisely set. In this application, the determination of this velocity inlet boundary is not based on empirical or assumed values, but rather on the actual operating parameters of the continuous casting process—the casting speed. and the cross-sectional area of ​​the continuous casting crystallizer outlet. and the cross-sectional area of ​​the submersible inlet The calculations are performed using geometric parameters. This method ensures a close correlation between the simulation model and the actual physical process, providing a clear physical basis and accuracy for setting the inlet velocity. Specifically, the calculation is based on the principle of mass conservation, which states that in a stable continuous casting process, the flow rate of molten steel entering the crystallizer should be equal to the flow rate of molten steel leaving the crystallizer.

[0055] Submersible inlet velocity The calculation formula is: In the formula, This refers to the inlet velocity of the submersible nozzle. For pulling speed; This represents the cross-sectional area of ​​the outlet of the continuous casting crystallizer. This represents the cross-sectional area of ​​the immersion nozzle inlet.

[0056] Specifically, This represents the average flow velocity at the inlet of the submersible nozzle, which is the velocity inlet boundary value that needs to be set in the simulation software. The casting speed, representing the continuous casting machine, is a key process parameter in the production process; This represents the cross-sectional area at the outlet of the continuous casting mold, and is usually the width of the slab multiplied by its thickness. This represents the cross-sectional area at the inlet of the submerged entry nozzle, typically determined by the nozzle's inner diameter. The formula is derived by calculating the volumetric flow rate (casting speed) at the outlet of the continuous casting mold. Multiply by the cross-sectional area of ​​the crystallizer outlet ) and the volumetric flow rate (inlet velocity of the submersible nozzle) at the inlet. Multiply by the cross-sectional area of ​​the submerged water inlet By performing equivalent calculations, the inlet velocity of the submersible nozzle can be derived. This method ensures the mass balance of the entire fluid system, providing accurate initial conditions for subsequent flow field, heat transfer, and solidification calculations.

[0057] The above technical solution will reduce the actual casting speed during the continuous casting process. The cross-sectional area of ​​the continuous casting crystallizer outlet and the cross-sectional area of ​​the submersible inlet. By combining geometric parameters, the inlet velocity of the submersible nozzle can be accurately calculated using physical formulas. This calculation method, based on the principle of mass conservation, avoids the empirical or hypothetical settings that may exist in traditional methods, thus ensuring the accuracy and physical rationality of the velocity inlet boundary conditions in the simulation model. This is crucial for the subsequent iterative solutions of the flow field, temperature field, and solidification behavior, significantly improving the prediction accuracy of the solidified billet shell distribution results in the continuous casting mold. This allows the simulation results to more realistically reflect actual production conditions, providing a reliable theoretical basis for optimizing continuous casting process parameters and improving billet quality.

[0058] In an optional implementation, in step S32, the heat transfer type of the sidewall is set to heat flux heat transfer, and the heat flux is determined according to the Savage heat flux density equation, the formula of which is: In the formula, q For heat flux; A constant related to the wide or narrow face of the continuous casting mold; v c For pulling speed; d s This is the distance from the crescent moon.

[0059] Specifically, when simulating the heat transfer behavior of molten steel within a continuous casting mold, the mold sidewalls are considered as heat flux boundary conditions. Heat flux transfer refers to directly specifying the rate of heat transfer per unit area, which differs from indirectly calculating heat transfer through temperature differences and heat transfer coefficients. By directly setting the heat flux, the heat carried away by the cooling water in the mold can be reflected more accurately, especially suitable for scenarios where the heat flow distribution is known or predictable. The Savage heat flux density equation is an empirical formula used to describe the heat flux density distribution along the height direction within a continuous casting mold. This equation considers the casting speed. v c Distance from the crescent moon d s Key factors, such as the constant ∅ related to the wide or narrow face of the crystallizer, can effectively reflect the non-uniformity of heat flux density within the crystallizer. In simulation software, the Savage equation can be used as a user-defined function or input as an expression into the definition of the heat flux boundary conditions. Based on the actual continuous casting process parameters and geometric parameters, the heat flux of each grid cell on the wall surface can be calculated. q And apply it as a boundary condition. Where, constant The value is usually obtained through experimental measurement or empirical values, and may differ for the wide and narrow faces, as well as the distance from the meniscus. d s It is a coordinate along the height of the crystallizer, usually measured downwards with the meniscus as the zero point.

[0060] By setting the heat transfer type of the continuous casting mold sidewall as heat flux heat transfer and accurately calculating the heat flux based on the Savage heat flux density equation, this application can more realistically reflect the actual heat transfer process between the molten steel and the mold wall in the continuous casting mold. The Savage equation considers key factors such as casting speed, differences in the width of the mold surface, and distance along the height direction, making the simulation of heat flux density distribution more refined and accurate. This precise setting of thermal boundary conditions effectively avoids the problem of inaccurate determination of the heat transfer coefficient in traditional convective heat transfer models, thereby significantly improving the accuracy and reliability of predicting the solidified billet shell thickness in the continuous casting mold. This provides a more solid data foundation for subsequent determination of the solidification front position and analysis of billet shell thickness distribution, thus enhancing the engineering application value of the entire prediction method.

[0061] In an optional implementation, step S32 further includes defining the heat exchange type of the foot roller zone and the secondary cooling zone wall.

[0062] Specifically, the heat transfer type of the walls in the foot roll zone and the secondary cooling zone is set as convective heat transfer. Convective heat transfer refers to the process of heat transfer between a fluid and a solid wall through fluid flow, which is consistent with the physical mechanism of cooling water spraying onto the surface of the billet in the secondary cooling zone. To accurately quantify this convective heat transfer, its convective heat transfer coefficient is determined according to an empirical formula. This empirical formula is: in, h s The heat transfer coefficient of the foot roller zone and the secondary cooling zone directly reflects the intensity and efficiency of the secondary cooling. β is the correction factor for the heat transfer coefficient of the foot roller zone and the secondary cooling zone. This correction factor allows the heat transfer coefficient to be adjusted according to actual production conditions, equipment characteristics, or through experimental calibration, so as to improve the applicability and accuracy of the model; w is the cooling water spray density, which is an important process parameter of the secondary cooling zone and directly affects the cooling effect. T w The ambient temperature usually refers to the temperature of the cooling water or the ambient temperature of the secondary cooling zone. Using this empirical formula, the heat transfer coefficient can be dynamically calculated based on actual process parameters (such as spray density and ambient temperature), thus more realistically simulating the heat transfer process in the secondary cooling zone.

[0063] The above technical solution, when predicting the thickness of the solidified billet shell in the continuous casting mold, considers not only the heat transfer inside the mold but also the heat transfer mechanisms in the foot roll zone and secondary cooling zone. By defining the heat transfer type of the walls in the foot roll zone and secondary cooling zone as convective heat transfer and using empirical formulas based on actual process parameters to determine the convective heat transfer coefficient, the simulation model can more comprehensively and accurately reflect the thermal state and solidification behavior of the billet throughout the cooling process. This significantly improves the accuracy of the solidified billet shell thickness prediction, especially the thickness evolution after the billet leaves the mold and enters the foot roll zone and secondary cooling zone. More accurate prediction results help optimize continuous casting process parameters, such as the secondary cooling water flow distribution, thereby effectively controlling the solidification process of the billet, reducing the generation of internal defects, and improving billet quality and production efficiency.

[0064] In an optional implementation, this application proposes a more specific and precise post-processing method, wherein S4 specifically includes: Based on the liquid phase fraction distribution of molten steel in the continuous casting mold, multiple equally spaced billet pulling positions are selected along the height direction of the continuous casting mold in the post-processing software. The contour lines with a liquid phase fraction of 0.2-0.5 are used as the solidification front positions. Data of the solidification front positions at each location are extracted to establish the solidified billet shell thickness distribution of the wide and narrow faces of the continuous casting mold at different heights under different working conditions, thereby realizing a method for predicting the solidified billet shell thickness in the continuous casting mold.

[0065] Specifically, after simulating the flow field, temperature field, and solidification behavior of molten steel within the continuous casting mold, professional post-processing software (such as ANSYS Fluent Post, Tecplot 360, ParaView, etc.) is used to visualize and analyze the simulation results. These software programs can display the distribution of physical quantities at various points within the computational domain, including the liquid phase fraction distribution of the molten steel. The liquid phase fraction is a key parameter characterizing the solidification state of a material, with values ​​ranging from 0 (completely solid) to 1 (completely liquid). To systematically analyze the variation of the solidified billet shell along the height of the mold, a series of equally spaced sections or positions need to be selected along the height of the mold. These "drawing positions" represent the cross-sections of the billet shell at different solidification stages. At each selected drawing position, contour lines with liquid phase fractions of 0.2-0.5 are used as the boundaries of the solidification front. Based on this, data from the solidification front positions are extracted to establish the solidified billet shell thickness distribution of the wide and narrow faces at different heights of the continuous casting mold under different operating conditions, thereby realizing a method for predicting the solidified billet shell thickness within the continuous casting mold. Specifically: At each determined billet-drawing position (i.e., an equally spaced section along the height of the crystallizer), a contour line with a liquid phase fraction of 0.2–0.5 is used as the solidification front boundary. Using the data export function of the post-processing software, several feature points are selected along this contour line on both the wide and narrow faces. The spatial coordinates of these feature points are extracted, with the radial coordinate distance relative to the inner wall of the crystallizer serving as candidate data for the billet shell thickness. Simultaneously, the height coordinates of the corresponding billet-drawing positions are recorded, forming the original dataset of "height—position—billet shell thickness".

[0066] For different continuous casting process conditions, the above simulation calculation and data extraction process is repeated. The solidification front position data under each condition are classified and stored according to the condition label to form a billet shell thickness database with multiple conditions, heights, and locations.

[0067] For each working condition and each billet pulling height, the billet shell thickness values ​​at each characteristic point on both the wide and narrow faces are statistically analyzed. Through interpolation or fitting methods, thickness distribution curves are constructed along the transverse direction of the wide face (from one narrow face to the other) and along the longitudinal direction of the narrow face (from corner to corner). Furthermore, the distribution curves for all heights are combined to obtain thickness distribution cloud maps of the wide and narrow faces along the entire height of the crystallizer. These distribution maps can visually display the uniformity of billet shell growth and whether there are excessively thin or thick corner regions.

[0068] Based on the aforementioned distribution data, a predictive model is established using regression analysis, machine learning, or empirical formula calibration. This model takes process parameters (casting speed, superheat, cooling intensity, etc.) as input and outputs the shell thickness at different heights and positions. This model can be embedded into the continuous casting process control system: when a new combination of process parameters is input, the system can quickly output the predicted shell thickness at any height on the wide and narrow faces within the crystallizer. By comparing and verifying the model with thermocouple temperature or leakage prediction data from actual production, the model is continuously refined, ultimately forming a reliable dynamic prediction method for the solidified shell thickness within the continuous casting crystallizer.

[0069] The above technical solution will be explained in more detail below through a more specific example: Step 1: Based on the geometric parameters of the slab continuous casting mold and its supporting submerged entry nozzle at a steel plant, and considering the structural symmetry of both the mold and the nozzle, a 1 / 4 symmetrical 3D geometric model of the continuous casting mold and nozzle was constructed using Discovery 3D modeling software, as shown below. Figure 2 As shown, save it as a .scdoc file. The geometric parameters of the foot roll zone, part of the secondary cooling zone, the continuous casting mold, and the submerged entry nozzle are shown in Table 1.

[0070] Table 1

[0071] Step 2: Using Discovery 3D modeling software, the computational domain for solving the molten steel flow within the continuous casting mold and submerged entry nozzle is extracted based on boundary refactoring (B-Rep) and Boolean operations. The extracted computational domain is then imported into Meshing mesh generation software. First, each boundary surface is defined and named. Then, the association of vertices, edges, and faces, as well as the generation of logical blocks, are performed. The overall mesh quality is higher than 0.6, the maximum aspect ratio of each individual mesh is less than 10, and the total number of meshes is approximately 600,000. The mesh is exported as a .msh format file. Figure 3 As shown.

[0072] Step 3: Import the exported .msh format crystallizer mesh file into ANSYS Fluent and configure the solution settings: Based on the specific flow conditions of the molten steel in the continuous casting mold, select Realizable in the ANSYS Fluent simulation software. k - ε A turbulence model is used to solve the turbulent motion of molten steel within the continuous casting mold. The energy conservation equation is used to solve for the heat transfer behavior of the molten steel. A solidification and melting model is selected to solve for the solidification and melting behavior of the molten steel. A coupled algorithm is used for pressure-velocity coupling, and a staggered pressure algorithm (PRESTO! algorithm) is used for spatial discretization of pressure. A bounded central difference scheme algorithm is used for spatial discretization of momentum, and a second-order upwind discretization is used for the energy equation. Furthermore, a bounded second-order implicit transient formula is used to ensure computational stability.

[0073] Among them, Realizable k - ε Turbulence models are commonly used in engineering numerical simulations to accurately solve the complex turbulent motion of molten steel in continuous casting molds. By redefining the turbulent viscosity formula and introducing flow curl constraints, this model can better adapt to complex flow field scenarios such as jet impact, backflow separation, and multiphase disturbances, improving the accuracy of turbulence characteristic calculations. The PRESTO! algorithm (PREssure STaggering Option, PRESTO!) is a staggered pressure algorithm used to discretize the pressure term so that the pressure better satisfies both the momentum equation and the continuity equation simultaneously. The PRESTO! algorithm is an option in the Fluent software.

[0074] The physical property parameters of the continuous phase molten steel and the discrete phase argon gas were set in the ANSYS Fluent software, as shown in Table 2.

[0075] Table 2

[0076] In ANSYS Fluent software, boundary conditions were set. The immersion nozzle inlet was set as a velocity inlet boundary condition. The inlet velocity was set according to the three pulling speeds used in this embodiment, as shown in Table 3, where 1.0 / 1.2 / 1.5 mm / min. -1 The corresponding actual entry velocities are 0.0167 / 0.02 / 0.025 ms. -1 .

[0077] Table 3

[0078] Using the Surface Injection function in the DPM model of ANSYS Fluent software, the inlet of the immersion nozzle was used as the injection point for argon bubbles, with argon flow rates of 0 / 1 / 2 / 3 L / min selected. -1 Four operating conditions are shown in Table 3. Based on the actual casting process, the diameter of the argon bubble is 1.2 mm, and the inlet velocity of the argon bubble is consistent with that of the molten steel. Based on the actual casting temperature, the inlet molten steel temperature is 1816.15 K. The discrete phase boundary condition type at the inlet is set to Reflect. The top surface of the crystallizer is set to adiabatic boundary condition, and the discrete phase boundary condition type is set to Escape. The bottom surface of the crystallizer is set to fluid outflow boundary condition, and the discrete phase boundary condition type is set to Escape. The side wall of the crystallizer is set to no-slip wall boundary condition, and the discrete phase boundary condition type is set to Reflect. The heat transfer type is heat flux heat transfer, and the heat flux is determined according to the heat flux density equation proposed by Savage, as shown in the following formula: In the formula, q For heat flux, MW m -2 . The constants related to the wide or narrow face of the continuous casting mold are 0.23 and 0.25, respectively; v c For pulling speed, ms -1 ; d s The distance from the meniscus is in meters (m).

[0079] The heat transfer type on the walls of the foot roller zone and the secondary cooling zone is convective heat transfer. The convective heat transfer coefficient is determined according to an empirical formula, as follows: In the formula, h s The heat transfer coefficients of the foot roller zone and the secondary cooling zone are given by W (m). 2 ·K) -1 ; β This is a correction factor for the heat transfer coefficients of the foot roller zone and the secondary cooling zone; w The density of the cooling water spray, L (m 2 ·s) -1 ; T w The ambient temperature is in K.

[0080] After initializing the flow and temperature fields of the computational domain, the solution parameters were set. The initial velocity of the computational domain was set to 0, and the initial temperature was set to 1816.15 K. The billet's velocity was initialized using a patch, with values ​​of 1.0 / 1.2 / 1.5 m / min. -1 The corresponding billet moving speeds for the casting speeds are 0.0167 / 0.02 / 0.025 ms. -1 The solution time step is set to 1×10. -3 The calculation is performed iteratively for 20 steps within each time step, and the results are saved every 0.1s interval, exporting .cas and .dat format files.

[0081] S4. Import the .cas and .dat format files exported from S3 into the post-processing software ANSYS CFD-post for post-processing. Select 33 billet-drawing positions spaced 0.01m apart along the height of the continuous casting mold, covering a range of 0.17~0.50m along the height of the mold. At each billet-drawing position, extract the liquid phase fraction distribution of the molten steel at a cross-section 1 / 4 of the distance from the centerline of the narrow and wide faces, and determine the location of the solidification front using contour lines with a liquid phase fraction of 0.3. In the horizontal height direction corresponding to each billet-drawing position, take a sampling point at the solidification front, such as... Figure 4 As shown.

[0082] The location data of sampling points at each billet pulling position were extracted to obtain the solidified billet shell thickness at quasi-steady state after 300s. The results were exported in .csv format and processed and plotted using Origin 2024 plotting and analysis software. The solidified billet shell thickness distribution of different heights and widths of the crystallizer under different working conditions is shown below. Figure 4 As shown, where Figure 5 (a) is 1.0 m min -1 Distribution of solidified shell thickness under different argon blowing rates at different pulling speeds. Figure 5 (b) is 5L min -1 Distribution of solidified shell thickness at different drawing speeds under argon blowing conditions.

[0083] Although embodiments of the invention have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the invention, and such modifications and variations all fall within the scope defined by the appended claims.

Claims

1. A method for predicting the thickness of the solidified slab shell in an argon-blown crystallizer for continuous casting slabs, characterized in that, Includes the following steps: S1. Based on the geometric parameters of the continuous casting mold and its submerged entry nozzle, establish a three-dimensional geometric model including the foot roll area, part of the secondary cooling zone, the continuous casting mold and the submerged entry nozzle. S2. Based on boundary partitioning and Boolean operations, the computational domain of the three-dimensional geometric model is extracted, and the extracted computational domain is divided into a structured mesh to obtain the mesh model corresponding to the computational domain; wherein, the computational domain includes the continuous casting crystallizer area, the foot roll area, and part of the secondary cooling area; S3. Import the mesh model into the simulation software, select the calculation model and solution method, define the physical property parameters and boundary conditions, perform initialization operations and then perform iterative solution to obtain the distribution results of the solidified billet shell in the continuous casting crystallizer. S3 specifically includes: S31, Using Realizable k - ε The method solves for the turbulent motion of molten steel in the continuous casting mold, uses the energy conservation equation to solve for the heat transfer behavior of molten steel in the continuous casting mold, selects the solidification and melting model to solve for the solidification and melting behavior of molten steel, and defines the billet shell movement velocity according to the casting speed; uses the DPM model to calculate and track the motion of argon bubble particles; employs the Coupled algorithm for pressure-velocity coupling, the staggered pressure algorithm for spatial discretization of pressure, the bounded central difference scheme algorithm for spatial discretization of momentum, the energy equation for discretization using the second-order upwind scheme, and the solution using the bounded second-order implicit transient formula. S32. Set the density, viscosity, specific heat capacity, thermal conductivity, solidus temperature, liquidus temperature, latent heat of molten steel, density and diameter of argon bubbles; set the submerged entry nozzle inlet as the velocity inlet boundary and discrete phase injection point, the top surface of the continuous casting mold as the adiabatic boundary, the bottom surface as the outflow boundary, and the sidewall as the no-slip wall boundary, and define the corresponding discrete phase boundary condition type and the heat transfer type of the sidewall; S33. Initialize the flow field and temperature field of the computational domain, set the solution parameters, and then perform iterative solution to obtain the distribution results of the solidified billet shell in the continuous casting mold. S4. Post-process the distribution results, determine the solidification front position based on the liquid phase fraction threshold, and obtain the thickness distribution of the solidified billet shell in the continuous casting mold under different heights and different working conditions.

2. The method according to claim 1, characterized in that, The geometric parameters of the continuous casting mold and its submerged entry nozzle in S1 include: the width, height and thickness of the mold, as well as the inner and outer diameters, length, inclination angle, side hole shape and nozzle insertion depth of the submerged entry nozzle.

3. The method according to claim 1, characterized in that, The three-dimensional geometric model established in S1, which includes the foot roll area, part of the secondary cooling zone, the continuous casting crystallizer, and the submerged entry nozzle, is a 1 / 4 symmetrical model.

4. The method according to claim 1, characterized in that, The structured mesh in S2 is a hexahedral mesh, and the area near the wall of the computational domain is densified. The overall mesh quality is not less than 0.6, and the maximum aspect ratio of a single mesh is less than 10.

5. The method according to claim 1, characterized in that, The velocity inlet boundary in S32 is calculated based on the casting speed and the cross-sectional area of ​​the continuous casting machine's crystallizer and submerged entry nozzle. The calculation formula is as follows: In the formula, This refers to the inlet velocity of the submersible nozzle. For pulling speed; This represents the cross-sectional area of ​​the outlet of the continuous casting crystallizer. This represents the cross-sectional area of ​​the immersion nozzle inlet.

6. The method according to claim 1, characterized in that, The heat transfer type of the sidewall in S32 is heat flux heat transfer, and the heat flux is determined according to the Savage heat flux density equation, the formula is: In the formula, q For heat flux; A constant related to the wide or narrow face of the continuous casting mold; v c For pulling speed; d s This is the distance from the crescent moon.

7. The method according to claim 1, characterized in that, S32 further includes defining the heat transfer type of the foot roller zone and the secondary cooling zone wall surface. The heat transfer type of both the foot roller zone and the secondary cooling zone wall surface is convective heat transfer, and their convective heat transfer coefficient is determined according to an empirical formula, which is: In the formula, h s The heat transfer coefficients of the foot roller zone and the secondary cooling zone; β This is a correction factor for the heat transfer coefficients of the foot roller area and the secondary cooling area; w This refers to the density of the cooling water spray. T w The ambient temperature.

8. The method according to claim 1, characterized in that, S4 specifically includes: Based on the liquid phase fraction distribution of molten steel in the continuous casting mold, multiple equally spaced billet pulling positions are selected along the height direction of the continuous casting mold in the post-processing software. The contour lines with a liquid phase fraction of 0.2-0.5 are used as the solidification front positions. Data of the solidification front positions at each location are extracted to establish the solidified billet shell thickness distribution of the wide and narrow faces of the continuous casting mold at different heights under different working conditions, thereby realizing a method for predicting the solidified billet shell thickness in the continuous casting mold.

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