DEM-CFD-VOF coupling model-based analysis method for movement of desulfurizer in ladle

The DEM-CFD-VOF coupled model accurately simulates the movement and dispersion of desulfurizing agent particles in molten iron, solving the problem of inaccurate simulation in existing technologies and providing a basis for evaluating the desulfurization effect in molten iron ladles and optimizing the process.

CN120850852APending Publication Date: 2025-10-28NORTHEASTERN UNIV CHINA
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Patent Information

Application Number
CN202510862457.1
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-06-25
Publication Date
2025-10-28

AI Technical Summary

Technical Problem

Existing computational fluid dynamics methods are insufficient to accurately simulate the movement and dispersion of desulfurizing agent particles in molten iron, and cannot effectively evaluate the desulfurization effect of the KR method.

Method used

A DEM-CFD-VOF coupled model is adopted, which combines the DEM model to describe the movement of desulfurizing agent particles and the CFD model to track the interface between molten iron and air. The DEM-CFD-VOF coupled module realizes high-precision simulation of particle-fluid interaction.

Benefits of technology

Accurate simulation of the movement and dispersion behavior of desulfurizing agent particles in molten iron provides information on microfluidic dynamics and particle dynamics, improves desulfurization effect, and provides a scientific basis for optimizing the KR method of stirred desulfurization process.

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Abstract

The invention relates to a DEM-CFD-VOF coupling model-based method for analyzing movement of a desulfurizing agent in a ladle, which belongs to the technical field of computer simulation and comprises the following steps of: 1, drawing a ladle model and a stirring paddle model by utilizing modeling software, and exporting a corresponding STL file; 2, importing the STL file into software with a DEM model, and establishing a motion control equation of desulfurizer particles; and step 3, importing the STL file into software with a CFD model, performing mesh generation on the ladle model containing the stirring paddle by using a mesh generation tool, establishing a control equation of a liquid phase (molten iron) and a gas phase (air), and tracking free interfaces of the gas phase and the liquid phase and the like by adopting a VOF model in the software with the CFD model. According to the method, the DEM-CFD-VOF coupling model is established to describe movement and dispersion behaviors of desulfurizer particles in the ladle, so that evaluation on the desulfurization effect of the ladle is realized.
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Description

Technical Field

[0001] This invention belongs to the field of computer simulation technology, and in particular relates to an analysis method for the movement of desulfurizing agent in molten iron ladle based on a DEM-CFD-VOF coupled model. Background Art

[0002] In recent years, with the rapid development of China's industry and infrastructure construction, the demand for high-quality steel has increased significantly. However, sulfur in steel significantly reduces its mechanical properties and corrosion resistance, making desulfurization essential during hot metal pretreatment. The KR method, as a preferred deep desulfurization process, uses a rotating agitator to create a vortex in the hot metal, effectively entraining the desulfurizing agent floating on the surface. The degree of dispersion of the desulfurizing agent in the hot metal is crucial to the desulfurization effect. Therefore, studying the motion characteristics of the desulfurizing agent in hot metal is of significant guiding importance for the improvement and optimization of the KR method's stirred desulfurization process.

[0003] Currently, many numerical simulations based on computational fluid dynamics (CFD) methods study the flow characteristics of molten iron in the KR stirring process, and explore measures such as changing the impeller immersion depth, increasing the impeller speed, using variable speed rotation, changing the direction of rotation, adding baffles to the molten iron ladle, and designing novel impeller structures to improve the dynamic conditions of molten iron and thus promote the dispersion of desulfurizing agent in the ladle. However, existing CFD methods often simplify or even ignore the desulfurizing agent particles, making it difficult to consider the interaction between the fluid and the moving desulfurizing agent particles, and thus unable to accurately calculate the motion, velocity, position, and forces acting on the particles. Summary of the Invention

[0004] In view of the above-mentioned shortcomings and deficiencies of the prior art, the present invention provides an analysis method for the movement of desulfurizing agent in molten iron ladle, and establishes a DEM-CFD-VOF coupled model to describe the movement characteristics of desulfurizing agent particles and the degree of dispersion in molten iron, thereby evaluating and improving the desulfurization effect.

[0005] To achieve the above objectives, the main technical solutions adopted by the present invention include: The analytical method for the movement of desulfurizing agent in molten iron ladle based on the DEM-CFD-VOF coupled model includes the following steps: Step 1: Use modeling software to draw the models of the molten iron ladle and stirring paddle, and export the corresponding STL files; Step 2: Import the STL file from Step 1 into software with a DEM model, use a particle size analyzer to perform industrial analysis on the particle size of the desulfurizing agent used, define different sizes of desulfurizing agent particles based on the analysis results, establish the motion control equation of the desulfurizing agent particles, and generate an initial desulfurizing agent bed above the molten iron surface. Step 3: Import the STL file from Step 1 into the software with the CFD model, set the same computational domain as the DEM software, use the meshing tool to mesh the ladle model containing the stirring paddle, establish the governing equations for molten iron and air, and use the VOF model in the software with the CFD model to track the free interface between air and molten iron. Step 4: Set the physical properties, initial conditions, and boundary conditions of the desulfurizing agent particles, molten iron, and air in software with DEM models and software with CFD models. Step 5: Setting up the coupling module for the DEM model, CFD model, and VOF model; Let ∆t be the Nth time. DEM The contact detection, collision dynamics calculation, and trajectory update of desulfurizing agent particles are completed within a certain time, where N is the time step ∆t of the DEM model calculation. DEM The time step ∆t of the CFD model computation CFD The process involves several steps: First, the key physical quantities of the desulfurization particle phase, including at least position, velocity, and particle size, are mapped to CFD grid nodes using an interpolation algorithm. Based on the desulfurizer particle position information, the particle / void volume fraction of the CFD grid cells is calculated and updated. Turbulence models are then calculated, and the flow behavior between phases (air-desulfurizer particles, molten iron-desulfurizer particles, and air-molten iron) is solved, thereby calculating the desulfurizer particle velocity and force information. This information is then fed back to the DEM model to dynamically update the desulfurizer particle motion state. The next time step of the DEM model is then calculated, and this process is repeated until the simulation ends, completing the numerical simulation of the desulfurizer motion behavior in the molten iron ladle. The calculated data is saved within the set time step. Step 6: Extract the velocity fields of air and molten iron, and evaluate the flow characteristics through data analysis and visualization; extract information on desulfurizing agent particles, including at least velocity, force, position, and particle size, and analyze and visualize them to evaluate the motion characteristics of the desulfurizing agent particles and their dispersion in the molten iron, thereby evaluating the desulfurization effect.

[0006] In step 1, a model of the molten iron ladle containing the stirring paddle is drawn using modeling software.

[0007] In step 2, the equation of motion for the desulfurizing agent particles is as follows: (1); (2); Where: m i The mass of desulfurizing agent particles i, in kg; v i The velocity of desulfurizing agent particle i is the translational velocity, in m / s; t is time, in s; w id represents the angular velocity of desulfurizing agent particle i in rad / s; d represents the derivative; k is the number of particles j in contact with particle i; F d,i It is the drag force on the desulfurizing agent particle i, N; F LS,i It is the Saffman lift force on the desulfurizer particle i, N; F LM,i It is the Magnus lift force on the desulfurizer particle i, N; F C,ij It is the contact force between desulfurizer particles i and j, in N; g is the acceleration due to gravity, in m / s². 2 ;I pi It is the moment of inertia of desulfurizing agent particle i, kg∙m 2 ; It is the tangential torque (N∙m) of desulfurizer particle j acting on desulfurizer particle i. 2 ; It is the normal torque, N∙m, exerted by desulfurizer particle j on desulfurizer particle i.

[0008] In step 3, the governing equations for molten iron and air include the continuity equation and the momentum equation.

[0009] The continuity equation for molten iron and air is as follows: (3); Where: ε f It is the local porosity of the fluid phase; ρ f It is the fluid phase density, kg / m³ 3 ;u f It is the fluid phase velocity, m / s; S mf It is the source term, kg / (m 3 ·s).

[0010] The momentum equations for molten iron and air are as follows: (4); Where: p is static pressure, Pa; τ is stress tensor, Pa; F pf It is the interaction force between particles and fluid, N; ε f It is the local porosity of the fluid phase; ρ f It is the fluid phase density, kg / m³ 3 ;u f It is the fluid phase velocity, in m / s.

[0011] In step 3, the VOF model is as follows: Volume fraction variables a1 and a2 are introduced into the grid, and the changes in volume fraction in the grid are tracked to accurately capture the free surface between different fluid phases. To describe the evolution of the free surface, a continuity equation is used. The equation for the VOF model to track the gas-liquid interface can be expressed as: (5); (6); Where a1 and a2 are the local porosities of the molten iron fluid phase and the air fluid phase, respectively, both ranging from 0 to 1.

[0012] In each fluid cell, the properties and variables involved in the governing equations are calculated based on the volume-weighted values ​​of all constituent phases. The density and viscosity of the fluid phase in each cell can be expressed as: (7); (8); Where ρ1 is the density of molten iron, kg / m³ 3 ρ2 is the density of air, kg / m³ 3 μ1 is the kinetic viscosity of molten iron, Pa∙s; μ2 is the kinetic viscosity of air, Pa∙s; a1 = 1 indicates that the mesh is completely occupied by molten iron, and α2 = 1 indicates that the mesh is completely occupied by air; the interface between the gas phase and molten iron is captured by identifying mesh cells with a molten iron / air volume fraction of 0-1.

[0013] The beneficial effects of this invention are: a discrete element-computational fluid dynamics-volume fluid (DEM-CFD-VOF) model is established to characterize the dynamic behavior of desulfurizing agent particles in molten iron ladles, and to analyze microscopic information such as particle velocity, force, molten iron flow, velocity, and turbulent kinetic energy in molten iron ladles, providing a more valuable reference for improving the desulfurization effect in molten iron ladles.

[0014] This invention, by constructing a DEM-CFD-VOF coupled model, can accurately simulate the motion and dispersion behavior of desulfurizing agent particles in molten iron ladles, making the numerical simulation results closer to actual working conditions. It also provides detailed information on microscopic fluid dynamics and particle dynamics in the molten iron ladle, including particle velocity, forces, molten iron flow, and turbulent kinetic energy, helping to deepen the understanding of the dispersion mechanism of desulfurizing agent particles in molten iron. This provides a scientific basis for improving and optimizing the KR method of stirred desulfurization. Through the realization of the above key points and effects, this invention not only overcomes the limitations of existing technologies but also provides important technical support for the scientific research and practical application of desulfurization processes in the steel industry. Furthermore, it has significant theoretical significance, guiding role, and application value for processes involving stirring in the chemical, energy, and other fields. Attached Figure Description

[0015] Figure 1 This is a schematic diagram of the simulation analysis method for the movement of desulfurizing agent in the molten iron ladle according to the present invention; Figure 2 A schematic diagram of a ladle and agitator; Figure 3 This is a size distribution diagram of the desulfurizing agent particles; Figure 4The initial desulfurizing agent bed generated for the DEM model; Figure 5 Mesh generation diagram for the CFD model of molten iron ladle; Figure 6 The purpose was to establish a DEM-CFD-VOF model to simulate the dam-break process and compare it with previous physical experiments. Figure 7 The velocity of the desulfurizing agent particles in the molten iron ladle changes with stirring time; Figure 8 The force on the desulfurizing agent particles in the molten iron ladle changes with stirring time. DETAILED DESCRIPTION

[0016] To better explain and facilitate understanding of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0017] To more clearly analyze the movement and dispersion of desulfurizing agent particles in a molten iron ladle and the flow behavior of the molten iron, thereby providing a theoretical basis for the optimization of the KR desulfurization process and the design of the agitator, this invention provides an analysis method for the movement of desulfurizing agent in a molten iron ladle based on a DEM-CFD-VOF coupled model. Figure 1 This is a schematic diagram of the simulation process of this method, including the following steps: Step 1: Use modeling software to draw the ladle and stirring paddle models, and export the corresponding STL files; taking a flat-bottomed ladle equipped with a cross-shaped four-bladed paddle as an example, such as... Figure 2 As shown.

[0018] Step 2: Import the STL file from Step 1 into software with a DEM model. Specifically, the LIGGGHTS open-source software can be used; the area contained in the geometric file is the computational domain of the DEM model. A particle size analyzer is used to perform industrial analysis of the desulfurizing agent particle size. Based on the analysis results, different sizes of desulfurizing agent particles are defined, and the motion control equations for the desulfurizing agent particles are established to generate an initial desulfurizing agent bed above the liquid phase (molten iron). The particle size analysis of the desulfurizing agent particles, such as... Figure 3 As shown. The initial desulfurizing agent bed generated by the DEM model, as... Figure 4 As shown.

[0019] In step 2, the motion equation of the desulfurizing agent particles is as follows: (1); (2); Where: m i The mass of desulfurizing agent particles i, in kg; v i The velocity of desulfurizing agent particle i is the translational velocity, in m / s; t is time, in s; w id represents the angular velocity of desulfurizing agent particle i in rad / s; d represents the derivative; k is the number of particles j in contact with particle i; F d,i It is the drag force on the desulfurizing agent particle i, N; F LS,i It is the Saffman lift force on the desulfurizer particle i, N; F LM,i It is the Magnus lift force on the desulfurizer particle i, N; F C,ij It is the contact force between desulfurizer particles i and j, in N; g is the acceleration due to gravity, in m / s². 2 ;I pi It is the moment of inertia of desulfurizing agent particle i, kg∙m 2 ; It is the tangential torque (N∙m) of desulfurizer particle j acting on desulfurizer particle i. 2 ; It is the normal torque, N∙m, exerted by desulfurizer particle j on desulfurizer particle i.

[0020] Step 3: Import the STL file from Step 1 into software with a CFD model. Specifically, you can use the Openform open-source software, setting the same computational domain as the DEM software, and using a meshing tool to mesh the ladle model containing the stirrer; establish the governing equations for the liquid phase (molten iron) and the gas phase (air), including the continuity equation and momentum equation; and use a VOF model in the software with a CFD model to trace the free interface between the gas and liquid phases. The meshing of the ladle model is shown below. Figure 5 As shown.

[0021] (3); (4); Where: ε f It is the local porosity of the fluid phase; ρ f It is the fluid phase density, kg / m³ 3 ;u f It is the fluid phase velocity, m / s; S mf It is the source term, kg / (m 3 ·s); p is static pressure, Pa; τ is stress tensor, Pa; F pf It is the interaction force between particles and fluid, N.

[0022] The equation for the VOF model to track the gas-liquid interface is as follows: (5); (6); Where a1 and a2 are the local porosities of the molten iron fluid phase and the air fluid phase, respectively, both ranging from 0 to 1.

[0023] In each fluid cell, the properties and variables involved in the governing equations are calculated based on the volume-weighted values ​​of all constituent phases. For example, the density and viscosity of the fluid phase in each cell can be expressed as: (7); (8); Where ρ1 is the density of molten iron, kg / m³ 3 ρ2 is the density of air, kg / m³ 3 μ1 is the kinetic viscosity of molten iron, Pa∙s; μ2 is the kinetic viscosity of air, Pa∙s; a1 = 1 indicates that the mesh is completely occupied by the molten iron phase, and α2 = 1 indicates that the mesh is completely occupied by air. The air-molten iron interface can be captured by identifying mesh cells with a molten iron / air volume fraction of 0-1.

[0024] Step 4: Set the physical properties, initial conditions, and boundary conditions of the desulfurizing agent particles, molten iron, and air in software with DEM models and software with CFD models. The physical properties of the desulfurizing agent particles, molten iron, and air are shown in Table 1.

[0025] Table 1. Physical properties of molten iron, air, and desulfurizing agent particles: parameter numerical values parameter numerical values density of molten iron <![CDATA[7036 kg / m 3 ]]> Desulfurizer particle density <![CDATA[3000 kg / m 3 ]]> molten iron viscosity 0.0075 Pa∙s Desulfurizer particle size 10-30 mm Inner diameter of molten iron ladle 3856 mm blade width 460 mm Ladle height 4700 mm Desulfurizer particle recovery coefficient 0.5 Initial molten iron depth 3621 mm Desulfurizer particle sliding friction coefficient 0.3 Agitator type Cross-shaped four-bladed propeller Desulfurizing agent particle rolling friction coefficient 0.01 Blade immersion depth 1833 mm Stirring speed 15 rad / s Blade height 1000 mm blade diameter 1470 mm air density <![CDATA[1.225 kg / m 3 ]]> air viscosity 0.00001 Pa∙s .

[0026] Step 5: Setting up the coupling module for the DEM model, CFD model, and VOF model: In a gas-liquid-solid three-phase flow, the distribution of the fluid phase in the CFD model affects the motion of the desulfurizing agent particles in the DEM model, and conversely, the motion of the particles in the DEM model also affects the distribution of the fluid phase in the CFD model. Therefore, a DEM-CFD bidirectional coupling module needs to be constructed to achieve high-precision analysis of the dynamic interactions between phases. Considering the time step ∆t of the DEM model calculation... DEM Typically, the time step ∆t is larger than that of the CFD operation. CFD The value is N times smaller, where N is typically between 5 and 100. The following coupling strategy is adopted. Let the Nth time ∆t... DEM The contact detection, collision dynamics calculation, and trajectory update of desulfurizing agent particles are completed within a certain time, where N is the time step ∆t of the DEM model calculation. DEM The time step ∆t of the CFD model computation CFDThe process involves several steps: First, the key physical quantities of the desulfurizing agent particles, including at least position, velocity, and particle size, are mapped to CFD grid nodes using an interpolation algorithm. Based on the particle position information, the particle / void volume fraction of the CFD grid cells is calculated and updated. Turbulence models are then calculated, and the flow behavior between phases (air-desulfurizing agent particles, molten iron-desulfurizing agent particles, and air-molten iron) is solved to calculate the desulfurizing agent particle velocity and force information. This information is then fed back to the DEM model to dynamically update the particle motion state. The next time step of the DEM model is then calculated, and this process is repeated until the simulation ends, completing the numerical simulation of the desulfurizing agent's motion behavior in the molten iron ladle. The calculated data is saved within the set time step. This invention constructs a DEM-CFD-VOF model to describe the motion behavior of desulfurizing agent particles in molten iron using the KR method.

[0027] Specifically, the calculation time step ∆t for desulfurizing agent particles DEM 5×10 -4 s, the time step ∆t of the fluid CFD 2×10 -3 s, which saves data files according to the set time step as the save interval.

[0028] Step 6: Extract the velocity fields of air and molten iron, and evaluate the flow characteristics through data analysis and visualization; extract the velocity, force, position, and particle size of the desulfurizing agent particles, and analyze and visualize them. Tecplot software can be used for visualization to evaluate the motion characteristics of the desulfurizing agent particles and their dispersion in the molten iron, thereby evaluating the desulfurization effect.

[0029] First, to verify the proposed DEM-CFD-VOF model, we compared its simulation of dam failure with previous physical experiments. Figure 6 To simulate the dam-break process using a DEM-CFD-VOF model and compare it with previous physical experiments, a water tank with dimensions of 0.2 m × 0.1 m × 0.3 m was constructed. Initially, a 0.05 m × 0.1 m × 0.1 m rectangular area of ​​water was placed within the tank, and 3883 glass spheres with a diameter of 2.7 mm were arranged at the bottom of the water body, forming a random stacking structure. When the baffle was removed, the water and particles in the tank underwent movement. The results showed that the simulation results were in good agreement with the dam-break evolution described in the literature, demonstrating the high accuracy of the proposed DEM-CFD-VOF model in simulating gas-liquid-solid three-phase flow.

[0030] Secondly, we applied this model to an actual molten iron ladle. The computational model consisted of a flat-bottomed cylindrical ladle without baffles, filled with air (density 1.225 kg / m³). 3The viscosity is 10. -5 Pa·s), molten iron (density 7036 kg / m³) 3 (Viscosity 0.0075 Pa·s), 50,000 desulfurizer particles (density 3000 kg / m³) 3 (26 mm in diameter) and a cross-bladed impeller, the geometric model of the impeller and the tank is as follows Figure 1 As shown; the mesh generation of the impeller-equipped mixing tank model is as follows. Figure 2 As shown. Details of the simulation parameters (including the physical properties of desulfurizing agent particles, air, and molten iron) are shown in Table 1; Figure 3 The initial DEM model of the desulfurizing agent particles generated above the molten iron surface; Figure 7 The velocity of the desulfurizing agent particles in the molten iron ladle was shown as a function of stirring time. Figure 8 The changes in the force on the desulfurizing agent particles in the molten iron ladle with stirring time are shown. Analysis reveals that the proposed DEM-CFD-VOF model applied to KR stirring can effectively analyze the motion and dispersion behavior of the desulfurizing agent particles in the molten iron ladle.

[0031] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Any modifications, alterations, substitutions, and variations made by those skilled in the art to the above embodiments are within the scope of the present invention.

[0032] Furthermore, it should be noted that the gas-liquid-solid three-phase flow numerical model proposed in this invention is not only applicable to the KR process, but also applicable to stirring processes involved in chemical, metallurgical, and material preparation processes.

Claims

1. An analytical method for the movement of desulfurizing agent in a molten iron ladle based on a DEM-CFD-VOF coupled model, characterized in that, The steps include: Step 1: Use modeling software to draw the ladle and stirring paddle models, and export the corresponding STL files; Step 2: Import the STL file from Step 1 into software with a DEM model, use a particle size analyzer to perform industrial analysis on the particle size of the desulfurizing agent used, define different sizes of desulfurizing agent particles based on the analysis results, establish the motion control equation of the desulfurizing agent particles, and generate an initial desulfurizing agent bed above the molten iron surface. Step 3: Import the STL file from Step 1 into the software with the CFD model, set the same computational domain as the DEM software, use the meshing tool to mesh the ladle model containing the stirring paddle, establish the governing equations for molten iron and air, and use the VOF model in the software with the CFD model to track the free interface between air and molten iron. Step 4: Set the physical properties, initial conditions, and boundary conditions of the desulfurizing agent particles, molten iron, and air in software with DEM models and software with CFD models. Step 5: Setting up the coupling module for the DEM model, CFD model, and VOF model; Let ∆t be the Nth time. DEM The contact detection, collision dynamics calculation, and trajectory update of desulfurizing agent particles are completed within a certain time, where N is the time step ∆t of the DEM model calculation. DEM The time step ∆t of the CFD model computation CFD The process involves several steps: First, the key physical quantities of the desulfurization particulate phase, including at least position, velocity, and particle size, are mapped to CFD grid nodes using an interpolation algorithm. The particle / void volume fraction of the CFD grid cells is calculated and updated based on the desulfurizer particle position information. Turbulence models are then calculated, and the flow behavior between phases (air-desulfurizer particles, molten iron-desulfurizer particles, and air-molten iron) is solved to calculate the desulfurizer particle velocity and force information. This information is then fed back to the DEM model to dynamically update the desulfurizer particle motion state. The next time step of the DEM model is then calculated, and this process is repeated until the simulation ends, completing the numerical simulation of the desulfurizer motion behavior in the molten iron ladle and saving the calculated data within the set time step. Step 6: Extract the velocity fields of air and molten iron, and evaluate the flow characteristics through data analysis and visualization; extract information on desulfurizing agent particles, including at least velocity, force, position, and particle size, and analyze and visualize them to evaluate the motion characteristics of the desulfurizing agent particles and their dispersion in the molten iron, thereby evaluating the desulfurization effect.

2. The method for analyzing the movement of desulfurizing agent in a molten iron ladle based on a DEM-CFD-VOF coupled model according to claim 1, characterized in that: In step 1, a model of a ladle containing a stirring paddle is drawn using modeling software.

3. The method for analyzing the movement of desulfurizing agent in a molten iron ladle based on a DEM-CFD-VOF coupled model according to claim 1, characterized in that: In step 2, the motion equation of the desulfurizing agent particles is as follows: (1); (2); Where: m i The mass of desulfurizing agent particles i, in kg; v i The velocity of desulfurizing agent particle i is the translational velocity, in m / s; t is time, in s; w i d represents the angular velocity of desulfurizing agent particle i in rad / s; d represents the derivative; k is the number of particles j in contact with particle i; F d,i It is the drag force on the desulfurizing agent particle i, N; F LS,i It is the Saffman lift force on the desulfurizer particle i, N; F LM,i It is the Magnus lift force on the desulfurizer particle i, N; F C,ij It is the contact force between desulfurizer particles i and j, in N; g is the acceleration due to gravity, in m / s². 2 ;I i It is the moment of inertia of desulfurizing agent particle i, kg∙m 2 ; It is the tangential torque (N∙m) of desulfurizer particle j acting on desulfurizer particle i. 2 ; It is the normal torque, N∙m, exerted by desulfurizer particle j on desulfurizer particle i.

4. The analysis method for the movement of desulfurizing agent in molten iron ladle based on the DEM-CFD-VOF coupled model according to claim 1, characterized in that: In step 3, the governing equations for molten iron and air include the continuity equation and the momentum equation.

5. The method for analyzing the movement of desulfurizing agent in a molten iron ladle based on a DEM-CFD-VOF coupled model according to claim 4, characterized in that: The continuity equation for molten iron and air is as follows: (3); Where: ε f It is the local porosity of the fluid phase; ρ f It is the fluid phase density, kg / m³ 3 ;u f It is the fluid phase velocity, m / s; S mf It is the source term, kg / (m 3 ·s).

6. The analysis method for the movement of desulfurizing agent in molten iron ladle based on the DEM-CFD-VOF coupled model according to claim 4, characterized in that: The momentum equations for molten iron and air are as follows: (4); Where: p is static pressure, Pa; τ is stress tensor, Pa; F pf It is the interaction force between particles and fluid, N; ε f It is the local porosity of the fluid phase; ρ f It is the fluid phase density, kg / m³ 3 ;u f It is the fluid phase velocity, in m / s.

7. The method for analyzing the movement of desulfurizing agent in a molten iron ladle based on a DEM-CFD-VOF coupled model according to claim 1, characterized in that: In step 3, the VOF model is as follows: Volume fraction variables a1 and a2 are introduced into the grid, and the changes in volume fraction in the grid are tracked to accurately capture the free surfaces between different fluid phases. To describe the evolution of the free surfaces, a continuity equation is used. The equation for the VOF model to track the gas-liquid interface can be expressed as: (5); (6); Where: a1 and a2 are the local porosity of the molten iron fluid phase and the air fluid phase, respectively, both ranging from 0 to 1; In each fluid cell, the properties and variables involved in the governing equations are calculated based on the volume-weighted values ​​of all constituent phases. The density and viscosity of the fluid phase in each cell can be expressed as: (7); (8); Where: ρ1 is the density of molten iron, kg / m³ 3 ρ2 is the density of air, kg / m³ 3 μ1 is the kinetic viscosity of molten iron, Pa∙s; μ2 is the kinetic viscosity of air, Pa∙s; a1 = 1 indicates that the mesh is completely occupied by molten iron, and α2 = 1 indicates that the mesh is completely occupied by air; the interface between the gas phase and molten iron is captured by identifying mesh cells with a molten iron / air volume fraction of 0-1.

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