A precise modeling method for a submerged arc furnace mechanism based on multi-physical field coupling
Patent Information
- Application Number
- CN202610701281.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-05-20
- Publication Date
- 2026-08-18
AI Technical Summary
[0006]本发明针对现有技术中存在的不足，提供一种基于多物理场耦合的矿热炉机理精准建模方法，该方法可适配各类供电制式及不同电极布局的矿热炉结构，通过精准确定电极底部电压边界条件，构建电磁场、温度场、流场深度耦合模型；采用自定义函数精准表征物性参数随温度的动态变化规律及电弧区源项的分布特征，进而精准模拟炉内多物理场的空间分布与动态演化规律，并依据仿真结果科学优化矿热炉操作参数，有效解决现有建模方法适配性差、仿真精度不足、实用性不强的技术问题
[0013]This invention adapts to the electrode layout characteristics of submerged arc furnaces, achieves deep coupling of multiple physical fields, effectively improves modeling accuracy and simulation practicality, and solves the problems of poor adaptability and large deviation between simulation results and actual working conditions in traditional methods. It is applicable to the simulation and optimization of ferroalloy smelting processes.
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Abstract
Description
Technical Field
[0001] This invention belongs to the field of alloy smelting technology, specifically relating to a precise modeling method for the mechanism of submerged arc furnaces based on multi-physics field coupling, which is applicable to process simulation and parameter optimization of ferroalloy smelting in submerged arc furnaces. Background Technology
[0002] Submerged arc furnaces are typical high-energy-consuming and high-efficiency industrial electric furnaces in the field of ferroalloy smelting. During the smelting process, electrical energy is transmitted to the electrodes through electrical control equipment, where plasma discharge occurs at the bottom of the electrodes to form an arc zone. Current flows through the arc and the ore to the bottom of the furnace, and then flows out from the bottom, realizing the heating, melting, and reduction reactions of the ore. Due to its advantages such as low energy consumption, stable furnace conditions, and uniform alloy quality, submerged arc furnaces are increasingly widely used in ferroalloy smelting.
[0003] However, the operating environment inside an electric arc furnace is extremely complex. The combined effects of high temperature, high current, strong magnetism, and multiple phases cause the electromagnetic field, temperature field, and flow field inside the furnace to couple and dynamically evolve, directly affecting smelting efficiency, alloy quality, and equipment lifespan. Due to the limitations of the high temperature and harsh conditions of electric arc furnace smelting, it is difficult to conduct direct experiments and tests, making it impossible to accurately obtain the distribution patterns and parameter evolution characteristics of the multi-physical fields inside the furnace. This results in a lack of scientific basis for the structural design and operating parameter optimization of electric arc furnaces, easily leading to problems such as excessive energy consumption and unstable output.
[0004] Currently, numerical simulation has become a core method for studying the smelting process of electric arc furnaces. Through multi-physics coupling solutions, accurate simulation of complex physical processes within the furnace can be achieved. However, most existing numerical modeling methods for electric arc furnaces only model single AC electrode structures, resulting in poor versatility and an inability to adapt to the electrode layout characteristics of electric arc furnaces with different arrangement forms and power supply systems. At the same time, the deep coupling effect of multi-physics fields is generally not considered in the modeling process, and the electromagnetic-fluid-thermal iteration strategy is crude, the temperature dependence of physical property parameters is simplified, and the energy source term in the arc region lacks electron enthalpy transport correction, leading to insufficient model adaptability and accuracy, and a large deviation between simulation results and actual smelting conditions.
[0005] Therefore, developing a precise modeling method for the mechanism of submerged arc furnaces based on multi-physics field coupling is of great significance for improving the smelting efficiency of submerged arc furnaces, reducing energy consumption, and extending equipment life. Summary of the Invention
[0006] This invention addresses the shortcomings of existing technologies by providing a precise modeling method for the mechanism of submerged arc furnaces based on multi-physics coupling. This method is adaptable to various power supply systems and submerged arc furnace structures with different electrode layouts. By accurately determining the voltage boundary conditions at the bottom of the electrodes, a deeply coupled model of electromagnetic field, temperature field, and flow field is constructed. A custom function is used to accurately characterize the dynamic changes of physical parameters with temperature and the distribution characteristics of source terms in the arc region. This allows for precise simulation of the spatial distribution and dynamic evolution of multi-physics fields within the furnace. Based on the simulation results, the operating parameters of the submerged arc furnace are scientifically optimized, effectively solving the technical problems of poor adaptability, insufficient simulation accuracy, and limited practicality of existing modeling methods.
[0007] The technical solution for achieving the technical objective of this invention is as follows: A precise modeling method for the mechanism of submerged arc furnaces based on multi-physics coupling includes the following steps: Step 1: Determine the structural parameters of the electric arc furnace and the physical properties of the furnace charge; these physical properties include electrical conductivity σ(T), thermal conductivity λ(T), and specific heat capacity c as a function of temperature. p ; Step 2: Construct a three-dimensional geometric model of the electric arc furnace, and on this basis, complete the three-dimensional structured mesh generation and mesh quality optimization; Step 3: Based on the coupling principle of electromagnetic field, temperature field and flow field in the smelting process of electric arc furnace, establish the control equations, realize the temperature-varying physical property parameters, special energy source terms in the electric arc region and electromagnetic field equations through linear interpolation and user-defined functions, set up multi-physics coupling model and boundary conditions; adopt the sequential coupling strategy to solve the electromagnetic field, flow field and temperature field in turn, iterate until the residuals of each field converge in each time step, update the physical property parameters and enter the next time step.
[0008] In step one, the structural parameters are set according to the actual furnace type; the physical property parameters are obtained through experimental measurement or literature retrieval, and are recorded in segments of no less than 5 data points within the temperature range of 300K to 3500K.
[0009] In step two, boundary layer meshes are densified at the electrode-arc interface, the free surface of the molten pool, and the boundary region of the furnace wall, with a maximum orthogonal mass of not less than 0.7 and an aspect ratio controlled within 1:5.
[0010] In step three, a multiphysics coupling model is constructed, including an electromagnetic field model, a temperature field model, and a flow field model. The governing equations for each model are as follows: (1) Electromagnetic field model: Following the law of conservation of charge, Ohm's law and Maxwell's equations, a magnetic vector potential is introduced to describe the magnetic field. The governing equations are as follows: ; ; ; ; In the formula: σ(T) is the conductivity, which varies with temperature, in S / m; φ is the electric potential, in V; ρ is the magnetic flux density, Wb / m 2 ; The magnetic vector potential is V·s / m; Current density, A / m 2 μ0 is the free permeability, μ0 = 4π × 10⁻⁶ -7 N / A 2 ; (2) Temperature field model: Based on the law of conservation of energy, considering arc heat, Joule heat, radiative heat and heat and mass transfer processes, the energy conservation governing equations are as follows: ; In the formula: ρ is the fluid density, kg / m³ 3 T represents the furnace temperature, in K. λ(T) is the velocity vector, m / s; λ(T) is the thermal conductivity (varying with temperature), W / (m·K); Q s c is the source term of the energy equation. p t represents specific heat capacity (as it changes with temperature), J / (kg·K); t represents time, s. The source terms of the energy equation for the ore zone are: ; Q rec Q is the heat of a chemical reaction. melt The phase change is endothermic; The source terms of the energy equation for the electric arc region are: ; ; In the formula: α is the absorption coefficient; K B This is the Boltzmann constant, with a value of 1.38 × 10⁻⁶. -23 e is the electron charge number; G is the incident radiation; ξ is the Stefan-Boltzmann constant; n is the refractive index; (3) Flow field model: The fluid flow inside the furnace is turbulent, and the standard k-ε model is adopted. The momentum conservation governing equation is as follows: ; ; ; ; In the formula: p is the pressure, Pa; μ effThe viscosity is dynamic, Pa·s; Electromagnetic force, N / m 3 ; The acceleration due to gravity is m / s². 2 μ(T) is the laminar molecular viscosity as a function of temperature. t C is the turbulent viscosity; where C μ =0.09 is a constant of the standard k-ε model. The governing equations are discretized using the finite volume method. The convergence criterion for the coupled solution is that the residual between the continuity equation and the energy equation is less than 1 × 10⁻⁹. -3 The residuals of the electromagnetic field equations are less than 1×10 -3 .
[0011] The method for accurate modeling of the mechanism of submerged arc furnace based on multiphysics coupling, with boundary conditions set according to actual conditions, is as follows: Electric boundary: The temperature at the bottom of the electrode is set to 2000K, the potential is set to 150V, and the magnetic vector potential is... The electrode wall temperature is set to 1200K, and the electrode wall potential satisfies... Magnetic vector potential The potential of the molten pool wall satisfies Magnetic vector potential The thermal boundary satisfies Where h is the convective heat transfer coefficient, in W·m -2 ·K -1 h=10; the potential at the bottom of the molten pool is set to 0, and the magnetic vector potential is... The thermal boundary satisfies h=2; the surface potential of the material satisfies Magnetic vector potential The thermal boundary satisfies h=2; ensure that the boundary conditions conform to the actual smelting conditions.
[0012] The method described above is a precise modeling method for the mechanism of an electric arc furnace based on multi-physics coupling. The pressure-velocity coupling adopts an adaptive switching between a separate or coupled algorithm; the discretization method of the control equation adopts a second-order upwind scheme to ensure controllable numerical diffusion; the radiative heat transfer adopts a strong coupling solution of the DO radiation model and the energy equation; the scattering coefficient and absorption coefficient of the arc region optical parameters are dynamically corrected according to the furnace gas composition, with the initial value preferably being 0.3~0.8, the initial furnace charge temperature being 673K, and the transient simulation adopts an adaptive time step control strategy with an initial step size of 0.01~0.2s, which is dynamically adjusted according to the local thermal balance residual. The total simulation time is 30~90min until the quasi-steady-state condition is reached.
[0013] This invention adapts to the electrode layout characteristics of submerged arc furnaces, achieves deep coupling of multiple physical fields, effectively improves modeling accuracy and simulation practicality, and solves the problems of poor adaptability and large deviation between simulation results and actual working conditions in traditional methods. It is applicable to the simulation and optimization of ferroalloy smelting processes. Attached Figure Description
[0014] Figure 1 : Three-dimensional structured mesh for electric arc furnace.
[0015] Figure 2 Temperature distribution diagram inside the electric arc furnace.
[0016] Figure 3 : Current density distribution diagram inside the electric arc furnace. Detailed Implementation
[0017] The present invention will be further described in detail below with reference to specific embodiments and accompanying drawings. This embodiment takes submerged arc furnace smelting as the application scenario, and strictly follows the method described in the present invention for modeling, multiphysics coupling, and simulation to verify the feasibility and practicality of the present invention. All parameters are strictly set in accordance with the specification and claims to ensure consistency with actual smelting conditions, and the entire process of modeling, multiphysics coupling, and simulation is fully reproduced.
[0018] This embodiment addresses the actual needs of industrial-grade submerged arc furnaces by determining a voltage at the bottom of the electrode. Following the steps described in this invention, modeling, multiphysics coupling, and simulation are completed. The specific implementation process is as follows: Step 1: Determine the structural parameters of the electric arc furnace (Table 1) and the physical properties of the furnace charge (Table 2); the physical properties include electrical conductivity σ(T), thermal conductivity λ(T), and specific heat capacity c as a function of temperature. p .
[0019] Table 1 Geometric Model furnace diameter 12300 Furnace height 3900 Electrode diameter 1600 Polar radius 4500 Arc height 100 Electrode insertion depth 1900
[0020] Table 2. Physical properties of furnace charge 673 971.4 0.075 2.21 1073 1004.0 0.15 3.71 1473 1078.5 15 5.53 1773 1116.4 150 7.10 2073 1345.3 150 8.85 2573 1294.7 150 12.18 3073 1353.6 150 16.00
[0021] Step 2: Construct a 3D geometric model of the submerged arc furnace, and based on this, complete the 3D structured mesh generation and mesh quality optimization. In this embodiment, ICEM is used for hexahedral dominant mesh generation. For areas with large curvature, such as the lower end of the electrode, the root of the arc column, and the free surface of the molten pool, the number of boundary layer growth layers is set to be greater than 4, with the first mesh layer thickness being 0.02m, to accurately capture the current concentration area and high temperature gradient. The overall mesh orthogonality quality is greater than 0.72, and the aspect ratio is less than 4.2. Mesh independence verification is performed: calculations are performed using 250,000, 380,000, and 500,000 elements respectively. The temperature difference at the bottom of the electrode is <2%, and the 380,000 element mesh is determined to be the optimal accuracy-efficiency balance point.
[0022] Step 3: Based on the coupling principle of electromagnetic field, temperature field and flow field in the smelting process of electric arc furnace, establish the control equations, realize the temperature-varying physical property parameters, special energy source terms in the electric arc region and electromagnetic field equations through linear interpolation and user-defined functions, and set the multi-physics coupling model and boundary conditions.
[0023] (1) Electromagnetic field model: Following the law of conservation of charge, Ohm's law and Maxwell's equations, a magnetic vector potential is introduced to describe the magnetic field. The governing equations are as follows: ; ; ; ; In the formula: σ(T) is the conductivity (which varies with temperature), S / m; φ is the electric potential, V; ρ is the magnetic flux density, Wb / m 2 ; The magnetic vector potential is V·s / m; Current density, A / m 2 μ0 is the free permeability, μ0 = 4π × 10⁻⁶ -7 N / A 2 .
[0024] (2) Temperature field model: Based on the law of conservation of energy, considering arc heat, Joule heat, radiative heat and heat and mass transfer processes, the energy conservation governing equations are as follows: ; In the formula: ρ is the fluid density, kg / m³ 3 T represents the furnace temperature, in K. λ(T) is the velocity vector, m / s; λ(T) is the thermal conductivity (varying with temperature), W / (m·K); Q s c is the source term of the energy equation. p t represents specific heat capacity (as it varies with temperature), J / (kg·K); t represents time, s.
[0025] The source terms of the energy equation for the ore zone are: ; Q rec Q is the heat of a chemical reaction. melt It is an endothermic phase change.
[0026] The source terms of the energy equation for the electric arc region are: ; ; In the formula: α is the absorption coefficient; K BThis is the Boltzmann constant, with a value of 1.38 × 10⁻⁶. -23 e is the electron charge number; G is the incident radiation; ξ is the Stefan-Boltzmann constant; n is the refractive index.
[0027] (3) Flow field model: The fluid flow inside the furnace is turbulent, and the standard k-ε model is adopted. The momentum conservation governing equation is as follows: ; ; ; ; In the formula: p is the pressure, Pa; μ eff The viscosity is dynamic, Pa·s; Electromagnetic force, N / m 3 ; The acceleration due to gravity is m / s². 2 μ(T) is the laminar molecular viscosity as a function of temperature. t C is the turbulent viscosity; where C μ =0.09 is a constant of the standard k-ε model.
[0028] Linear interpolation and user-defined functions are used to implement temperature-dependent physical property parameters and special source terms: Because there is a lack of readily available standard parameter libraries to support the changes in electrical and thermal conductivity of the furnace charge with temperature in electric arc furnaces, and because the energy equation for the arc region... Since this item is a special non-standard source item, it cannot be implemented directly using conventional methods. Therefore, a custom function is used for secondary development, and the specific implementation method is as follows: Linear interpolation methods were used to fit the electrical conductivity σ(T), thermal conductivity λ(T), and specific heat c. p The specific data is shown in Table 2. In UDF, temperature and physical properties are associated through the DEFINE_PROPERTY macro. When the temperature of a local element is between adjacent nodes in Table 2, the program automatically calls a piecewise linear function to return the real-time physical property value, avoiding numerical divergence caused by constant physical properties.
[0029] The energy source term Q in the ore zone and the arc zone is determined by a custom source term definition method (DEFINE_SOURCE). s By using region identification technology to distinguish different regions, a special source term containing electron enthalpy transport terms is loaded in the arc region to correct the thermodynamic contribution of high-energy particles in the plasma.
[0030] The magnetic vector potential in the electromagnetic field equations is realized through a combination of custom scalars and custom functions. The components of the electric potential φ and the magnetic vector A are defined as different custom scalars, and their flux characteristics are determined by a custom flux definition method. The coupled solution adopts a segregated solver architecture. After each physical step (electromagnetism → flow field → energy), the maximum temperature change rate and the mass conservation residual are checked. If the convergence threshold is not reached, the solution returns to the electromagnetic field to recalculate J and B, forming a closed-loop feedback.
[0031] (4) Boundary conditions are set as follows (Table 3): Table 3 Boundary Conditions
[0032] Where h is the convective heat transfer coefficient, W·m -2 ·K -1 The convective heat transfer coefficient of the sidewall of the molten pool is 10, and that of the top and bottom of the molten pool is 2.
[0033] like Figure 2 The figure shows the temperature distribution inside the electric arc furnace of the present invention. The figure includes a high-temperature crucible area below the electric arc, with a maximum temperature of 5587K. The temperature in the electric arc area transfers heat into the furnace through heat conduction and radiation.
[0034] like Figure 3 As shown, the current mainly flows from the bottom of the electrode to the furnace bottom, with the main path being from the electrode out, through the furnace charge, and then to the furnace bottom. The region of maximum current density highly overlaps with the high-temperature crucible region, verifying the correctness of the electromagnetic-thermal coupling mechanism.
[0035] The embodiments described above can be further combined or replaced, and these embodiments are merely descriptions of preferred embodiments of the present invention, not limitations on the concept and scope of the present invention. Various changes and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the inventive concept are all within the protection scope of the present invention. The protection scope of the present invention is given by the appended claims and any equivalents.
Claims
1. A method for accurate modeling of the mechanism of a submerged arc furnace based on multiphysics coupling, characterized in that, Includes the following steps: Step 1: Determine the structural parameters of the electric arc furnace and the physical properties of the furnace charge; these physical properties include electrical conductivity σ(T), thermal conductivity λ(T), and specific heat capacity c as a function of temperature. p ; Step 2: Construct a three-dimensional geometric model of the electric arc furnace, and on this basis, complete the three-dimensional structured mesh generation and mesh quality optimization; Step 3: Based on the coupling principle of electromagnetic field, temperature field and flow field in the smelting process of electric arc furnace, establish the control equations, realize the temperature-varying physical property parameters, special energy source terms in the electric arc region and electromagnetic field equations through linear interpolation and user-defined functions, set up multi-physics coupling model and boundary conditions; adopt the sequential coupling strategy to solve the electromagnetic field, flow field and temperature field in turn, iterate until the residuals of each field converge in each time step, update the physical property parameters and enter the next time step.
2. The method for accurate modeling of the mechanism of a submerged arc furnace based on multiphysics coupling according to claim 1, characterized in that, In step one, the structural parameters are set according to the actual furnace type; the physical property parameters are obtained through experimental measurement or literature retrieval, and are recorded in segments of no less than 5 data points within the temperature range of 300K to 3500K.
3. The method for accurate modeling of the mechanism of a submerged arc furnace based on multiphysics coupling according to claim 1, characterized in that, In step two, boundary layer meshes are densified at the electrode-arc interface, the free surface of the molten pool, and the boundary region of the furnace wall, with a maximum orthogonal mass of not less than 0.7 and an aspect ratio controlled within 1:
5.
4. The method for accurate modeling of the mechanism of a submerged arc furnace based on multiphysics coupling as described in claim 1, characterized in that, In step three, a multiphysics coupling model is constructed, including an electromagnetic field model, a temperature field model, and a flow field model. The governing equations for each model are as follows: (1) Electromagnetic field model: Following the law of conservation of charge, Ohm's law and Maxwell's equations, a magnetic vector potential is introduced to describe the magnetic field. The governing equations are as follows: ； ； ； ； In the formula: σ(T) is the conductivity, which varies with temperature, in S / m; φ is the electric potential, in V; ρ is the magnetic flux density, Wb / m 2 ; The magnetic vector potential is V·s / m; Current density, A / m 2 ; μ0 is the free permeability, μ0 = 4π × 10⁻⁶ -7 N / A 2 ; (2) Temperature field model: Based on the law of conservation of energy, considering arc heat, Joule heat, radiative heat and heat and mass transfer processes, the energy conservation governing equations are as follows: ； In the formula: ρ is the fluid density, kg / m³ 3 T represents the furnace temperature, in K. λ(T) is the velocity vector, m / s; λ(T) is the thermal conductivity (varying with temperature), W / (m·K); Q s c is the source term of the energy equation. p t represents specific heat capacity (as it changes with temperature), J / (kg·K); t represents time, s. The source terms of the energy equation for the ore zone are: ； Q rec Q is the heat of a chemical reaction. melt The phase change is endothermic; The source terms of the energy equation for the electric arc region are: ； ； In the formula: α is the absorption coefficient; K B This is the Boltzmann constant, with a value of 1.38 × 10⁻⁶. -23 e is the electron charge number; G is the incident radiation; ξ is the Stefan-Boltzmann constant; n is the refractive index; (3) Flow field model: The fluid flow inside the furnace is turbulent, and the standard k-ε model is adopted. The momentum conservation governing equation is as follows: ； ； ； ； In the formula: p is the pressure, Pa; μ eff The viscosity is dynamic, Pa·s; Electromagnetic force, N / m 3 ; The acceleration due to gravity is m / s². 2 μ(T) is the laminar molecular viscosity as a function of temperature. t C is the turbulent viscosity; where C μ =0.09 is a constant of the standard k-ε model. The governing equations are discretized using the finite volume method. The convergence criterion for the coupled solution is that the residual between the continuity equation and the energy equation is less than 1 × 10⁻⁹. -3 The residuals of the electromagnetic field equations are less than 1×10 -3 .
5. The method for accurate modeling of the mechanism of a submerged arc furnace based on multiphysics coupling according to claim 1, characterized in that, Based on the actual situation, the boundary conditions are set as follows: Electric boundary: The temperature at the bottom of the electrode is set to 2000K, the potential is set to 150V, and the magnetic vector potential is... The electrode wall temperature is set to 1200K, and the electrode wall potential satisfies... Magnetic vector potential The potential of the molten pool wall satisfies Magnetic vector potential The thermal boundary satisfies Where h is the convective heat transfer coefficient, in W·m -2 ·K -1 h=10; the potential at the bottom of the molten pool is set to 0, and the magnetic vector potential is... The thermal boundary satisfies h=2; the surface potential of the material satisfies Magnetic vector potential The thermal boundary satisfies h=2; ensure that the boundary conditions conform to the actual smelting conditions.
6. The method for accurate modeling of the mechanism of a submerged arc furnace based on multiphysics coupling according to claim 1, characterized in that, The pressure-velocity coupling algorithm is adaptively switched between a separate and a coupled approach; the discretization method of the control equation adopts a second-order upwind scheme to ensure controllable numerical diffusion; the radiative heat transfer is solved by strongly coupling the DO radiation model with the energy equation; the scattering coefficient and absorption coefficient of the arc region optical parameters are dynamically corrected according to the furnace gas composition, with the initial value preferably being 0.3~0.8, the initial furnace charge temperature being 673K, and the transient simulation adopts an adaptive time step control strategy with an initial step size of 0.01~0.2s, which is dynamically adjusted according to the local thermal balance residual. The total simulation time is 30~90min until the quasi-steady-state condition is reached.