Multi-physics field coupling method in smelting process of ferronickel heat furnace

Abstract

The invention relates to a multi-physics field coupling method for a smelting process of a ferronickel heating furnace, and relates to the multi-physics field coupling method for the ferronickel heating furnace, the method comprises the following steps: establishing a ferronickel heating model, importing the ferronickel heating model into ICEM software for grid division, and finally importing a grid into FLUENT; according to the method, based on a Maxwell's equation and an Ohm's law, an electrothermal conversion algorithm, an electromagnetic induction algorithm and a multiphase heat transfer and mass transfer algorithm are compiled in combination with a user-defined function (UDF), so that a mathematical analysis model for mutual coupling of multiple physical fields, multiphase flows and furnace body thermal stress in smelting of the submerged arc furnace is established. The model is combined with a radiation model, a turbulence model, a multi-phase flow model and a static structure model, a heat and mass transfer mechanism among an electric arc, a molten pool and a furnace body is disclosed, an influence mechanism of a furnace body structure and a multi-physical field on furnace body temperature distribution is explored, and an action mechanism between the furnace body temperature and thermal stress is clarified, so that the deformation position and deformation amount of the furnace body are predicted.

Description

Technical Field

[0001] The present invention relates to a numerical simulation method for the smelting process of industrial nickel-iron AC submerged arc furnace, and particularly to a multi-physical field coupling method for the smelting process of nickel-iron submerged arc furnace. Background Art

[0002] The Rotary Kiln-Electric Furnace process has been widely used in the smelting of nickel-iron alloy due to its advantages such as easy control of nickel-iron grade, high productivity, and mature process technology. However, due to the complexity of the submerged arc furnace working conditions and the high-temperature smelting environment inside the furnace chamber, it is difficult to observe the smelting situation inside the submerged arc furnace through experimental means. Therefore, a method combining experimental monitoring and numerical simulation is used to predict the smelting conditions of the submerged arc furnace. With the rapid development of the Computational Fluid Dynamics (CFD) theory, researchers first studied the heating stage of the submerged arc furnace without considering the arc, and then studied the arc starting mechanism and heat transfer mode starting from the arc. However, the multi-physical field coupling in the smelting process has been limited to the research of the thermal field, and the mass transfer of multiphase flow is also limited to the theoretical research of a single substance. The thermal stress and thermal deformation of the furnace body are often separated from the real smelting environment. Although a large number of achievements have been made in the research of different modules of the submerged arc furnace, to achieve large-scale, safe, and efficient continuous production of the submerged arc furnace, the problem of furnace body thermal expansion must be solved, and the key lies in optimizing the furnace body structure of the large-scale submerged arc furnace.

[0003] There are still the following problems to be solved urgently: First, the heat and mass transfer mechanism laws among bubbles, ore materials, molten slag, alloy layer, and furnace body in the submerged arc furnace under the coupling conditions of electricity / magnetism / heat / force multi-physical fields are not clear; Second, the method for accurately predicting the thermal stress distribution of the furnace body based on the temperature of the heat preservation and condensation type furnace body is not clear, and it is necessary to deeply explore the influencing factors of the expansion stress and temperature difference stress of the furnace body structure. Summary of the Invention

[0004] The purpose of the present invention is to propose a multi-physical field coupling method for the smelting process of nickel-iron submerged arc furnace, which numerically simulates the coupling of multi-physical fields - multiphase flow - furnace body stress and strain during the smelting process in the submerged arc furnace, and comprehensively considers the coupling of multi-physical fields such as arc starting, alternating current effect, electromagnetic induction, heat and mass transfer between multiphase flows, and furnace body stress and strain on the basis of AC electro-thermal conversion.

[0005] The technical solution adopted by the present invention is as follows:

[0006] A multi-physical field coupling method for the smelting process of nickel-iron submerged arc furnace, the method comprising the following steps:

[0007] Step 1: Establish a submerged arc furnace model, import it into ICEM software for structured grid division, and finally import the meshed physical model into FLUENT;

[0008] Step 2: Use the UDF subroutine to expand the mathematical models of electrothermal conversion, electromagnetic induction, and multiphase heat transfer and mass transfer, and import them into the FLUENT software;

[0009] Step 3: Turn on the energy, turbulence, radiation, and multiphase flow models in sequence;

[0010] Step 4: Set the numerical simulation parameters, including the physical properties parameters of the electric arc, ore materials, furnace gas, alloy, slag, boundary condition parameters, phase fraction parameters, solution methods, and solution accuracies;

[0011] Step 5: Import the furnace body temperature field of the calculation result as a temperature load into the Static Structural model to add constraints and contacts, and perform numerical calculations of thermal stress and thermal deformation.

[0012] In the multi-physical field coupling method for the smelting process of a nickel-iron ore furnace, the ore furnace model described in Step 1 consists of three parts: an electric arc, a molten bath, and a furnace body. Among them, the relative displacement of the cathode spot at the top of the electric arc zone is small, and the distribution of the cathode spot current density has nothing to do with the magnitude of the electric arc current. It is assumed that the radial current density Jr satisfies the parabola law:

[0013]

[0014] In the formula, Jc is the release current density of the hot electrons on the cathode spot surface; r is the radius of the electric arc; Rc is the radius of the cathode spot, and the expression is as follows:

[0015]

[0016] In the formula, Iarc is the electric arc current.

[0017] In the multi-physical field coupling method for the smelting process of a nickel-iron ore furnace, both the electric arc and the molten bath convert electrical energy into heat energy based on Ohm's law. Under the action of the magnetic field, electrons carry heat and flow from the cathode to the surface of the molten bath. The expression of its energy equation is as follows:

[0018]

[0019] In the formula, cp is the specific heat capacity, J / (kg·K); T is the temperature; ρ is the density; is the velocity vector; keff is the thermal conductivity; SFur is the energy source term of the molten bath; S Arc is the energy source term of the electric arc, which consists of Joule heat, electron transport enthalpy, and radiation loss, and the expression is as follows:

[0020]

[0021] In the formula, Jarc is the current density flowing through the arc; σ arc is the electrical conductivity of the arc; K B is the Boltzmann constant; e is the elementary charge; S AR is the radiation loss. The P-1 radiation model is used to calculate the arc radiation, and the expression is as follows:

[0022] S AR = aL - 4an 2 ξT 4 (5)

[0023] In the formula, a is the absorption coefficient; ξ is the Stefan-Boltzman coefficient; n is the refractive coefficient; L is the incident radiation, and its transport equation expression is as follows:

[0024]

[0025] In the formula, C is the linear anisotropic phase function coefficient, ξ s is the scattering coefficient.

[0026] The energy source term S of the molten pool Fur is composed of Joule heat, latent heat of melting, the source term for explaining the melting process, and endothermic heat of phase change. Its expression is as follows:

[0027]

[0028] In the formula, J Fur is the current density flowing through the molten pool; σFur is the electrical conductivity of the molten pool; ρFur is the density of the molten pool; H is the enthalpy of the molten nickel-iron ore; S R is the endothermic heat of melting phase change, and its expression is as follows:

[0029]

[0030] In the formula, q is the heat absorbed by the phase change; Δc is the change in the phase change mass fraction; M is the equivalent molar mass of the material; Δt is the time step of the simulation.

[0031] For the multi-physical field coupling method in the nickel-iron ore smelting process in the blast furnace, the electrothermal conversion in step two is based on the potential boundary conditions. The current continuity equation is established by using the user-defined scalar (UDS) and Ohm's law, and the expression is as follows:

[0032]

[0033] In the formula, is the electric potential; σ is the electrical conductivity; E is the electric field; J is the current density, and its expression is as follows:

[0034]

[0035] In the formula, J x is the magnitude of the current in the x direction; J y is the magnitude of the current in the y direction; J z is the magnitude of the current in the z direction; A x is the magnetic vector in the x direction; A y is the magnetic vector in the y direction; A z is the magnetic vector in the z direction.

[0036] For the multi - physical - field coupling method in the nickel - iron ore smelting process, the electromagnetic induction described in step two is based on the magnetic potential boundary condition. Using the user - defined scalar (UDS) and Maxwell's equations, the Poisson equation of the magnetic vector is established, and at the same time, the electromagnetic field is solved using the Coulomb gauge. The expressions are as follows:

[0037]

[0038] Using the Coulomb gauge: An equation is established to solve the electric potential and the magnetic vector, and the relationship is as follows:

[0039]

[0040] The magnetic induction intensity formula can be obtained:

[0041]

[0042] In the formula, ρ is the density; is the electric field; is the velocity vector; μ is the true magnetic permeability; is the magnetic induction intensity.

[0043] For the multi - physical - field coupling method in the nickel - iron ore smelting process, the ore materials described in step four are composed of laterite ore pellets, quicklime, and anthracite coal, and have the characteristics of porous media. Therefore, the porous - medium resistance source term is added to the momentum equation. In addition, the influence of the electromagnetic force on the multiphase flow is also loaded into the momentum equation through the source term. The expressions are as follows:

[0044]

[0045] In the formula, ρ is the density; p is the pressure; is the velocity vector; g is the gravitational acceleration; is the thermal buoyancy; is the surface tension of the phase interface; is the electromagnetic force; Si is the porous - medium resistance source term, and the expression is as follows:

[0046]

[0047] In the formula, the viscous drag coefficient λ is expressed as:

[0048]

[0049] In the formula, the inertial drag coefficient C2 is expressed as:

[0050]

[0051] The electromagnetic force mentioned above The expression is as follows:

[0052]

[0053] For the multi-physical field coupling method in the smelting process of a nickel-iron ore furnace, in step two, the mass transfer of the multiphase flow is processed using the VOF model to handle the distribution and conversion among the furnace gas, furnace slag, materials, and nickel-iron alloy phases. The mass fraction transport equation is established using the user-defined scalar (UDS), and the volume fraction of each phase is solved in combination with the VOF module. The expression is as follows:

[0054]

[0055] α1 = 1 - α2 - α3 - α4 (34)

[0056] m slag = W × M slag (35)

[0057] m alloy = W × M alloy (36)

[0058] m gas = W × M gas (37)

[0059] In the formula, m is the mass, i = 1 represents the ore material phase, i = 2 represents the furnace slag phase, i = 3 represents the nickel-iron alloy phase, i = 4 represents the furnace gas phase, α is the volume fraction, where ρ is the density, where is the fluid velocity. mslag is the mass of the material generating furnace slag; malloy is the mass of the material generating nickel-iron alloy; mgas is the mass of the material generating furnace gas; W is the phase change conversion rate; M is the molar mass.

[0060] Among them, the changes in the mass fractions of the ore material and solid carbon are expressed as follows:

[0061]

[0062] S1 = -W × M1(40)

[0063] S C = -W × MC (41)

[0064] w1 is the mass fraction of the material; w c is the mass fraction of solid carbon; S c is the oxidation amount of C, Γ is the diffusion coefficient, and the phase transformation rate W of the phase transformation rate constant K is expressed as follows:

[0065]

[0066] In the formula, A is the pre-exponential factor; Ea is the activation energy; R is the molar gas constant;

[0067] The Static Structural model in Step 2 constructs geometric equations, physical equations, equilibrium equations, and compatibility equations based on Hooke's law. Among them, the constitutive equation uses the furnace body thermal field gradient to solve the thermal strain components in different axial directions; the equilibrium equation solves the thermal stress components in different axial directions based on the thermal strain components; the kinematic equation also solves the displacement components and shear stress components in different directions based on the thermal strain components, and the expressions are as follows:

[0068] Equilibrium equation of Hooke's law:

[0069]

[0070] Among them, σ x , σy, σ z are the thermal stress components parallel to the x, y, and z axes, and τ xy , τy z , τ xz are the shear stress components parallel to the x, y, and z axes.

[0071] Kinematic equation:

[0072]

[0073] Among them, ε x , εy, ε z are the thermal strain components parallel to the x, y, and z axes; u, v, and w are the displacement components in three directions; γ xy , γ yz , γ zx are the shear strain components.

[0074] Constitutive equation:

[0075]

[0076] In the formula, E is the elastic modulus; μ is the Poisson's ratio; G is the shear modulus.

[0077] For the multi-physical field coupling method in the smelting process of a nickel-iron ore thermal furnace, the electric potential boundary condition in step four is crucial for the formation of the physical field. The distribution of the current density is solved based on Ampere's law and the electric potential boundary condition, where the conductivity of the materials and the arc directly affects the accuracy of the multi-physical field distribution. Due to the strong conductivity of the self-baking electrode, the influence of the electrode partial voltage is ignored to simplify the model, and the secondary voltage is directly applied as an input condition on the upper surface of the arc (the bottom of the electrode). The bottom of the molten bath is set to zero electric potential, and the side walls of the molten bath are insulated.

[0078] The setting of the magnetic potential boundary condition in step four is also crucial for the formation of the physical field. Electromagnetic induction is used to establish the magnetohydrodynamic equation through UDF, and the electric and magnetic fields are established with an equal relationship using Coulomb's gauge. The magnetic permeability of both the arc sub-model and the molten bath model is 1, the magnetic potential of the side walls of the molten bath is 0, and the internal surfaces are all coupled. The other walls of the molten bath are insulated.

[0079] The model in step four considers the smelting situation in the furnace. To ensure the rationality and accuracy of the multi-physical field coupling, the following assumptions are made for this model:

[0080] (1) The arc plasma is in a state of local thermodynamic equilibrium. Therefore, it is assumed that the complex physical processes in the regions near the cathode and anode are not considered, and the models of the regions near the cathode and anode are simplified during simulation.

[0081] (2) Considering that the velocity of the arc jet is relatively large, the impact force on the molten bath will form an arc cavity, and gas ionization occurs in the cavity.

[0082] (3) Since the smelting environment of the ore thermal furnace is a closed space, the metal vapor generated during the smelting process is ignored, and it is assumed that the gas in the cavity is high-temperature air.

[0083] (4) The pellet ore flows into the furnace through the feed bin. It is assumed that the ore thermal furnace is initially filled with ore. The ore thermal furnace remains in a conducting state, and the current forms a loop in the furnace.

[0084] (5) The three electrodes in the AC ore thermal furnace are inserted into the ore to the same depth. Three arcs will be generated by the three electrodes during the smelting process, and it is assumed that the shape of the arc cavity is approximately cylindrical.

[0085] (6) Since this method mainly studies the multi-physical field coupling in the AC ore thermal furnace, the inductive voltage of the AC ore thermal furnace during the smelting process is ignored.

[0086] (7) In the multiphase flow, the furnace gas is subject to the gravity of the ore, the pressure of the ore, the self-gravity of the furnace gas, and the buoyancy of the furnace gas.

[0087] The described method for coupling multiple physical fields in the smelting process of a nickel-iron ore furnace uses a custom scalar equation and an added source term to simultaneously solve electrothermal conversion, electromagnetic induction, reduction reactions, and multiphase heat and mass transfer. The k-epsilon turbulence model is used to study the behavior of nickel-iron alloy droplets; the P-1 method is used to solve radiative heat transfer, with the absorption coefficient and scattering coefficient of arc radiation both being 0.6, and the distribution of the temperature field is analyzed by combining with the energy equation; in order to meet the convergence criterion, transient simulation is carried out with a time step of 0.0001 s; the widely used SIMPLE algorithm is adopted to handle the pressure-velocity coupling problem; the method uses a second-order upwind discretization. When discretizing in time, the Courant number is less than 1.0. The beneficial effects of the present invention are:

[0088] 1. The method for coupling multiple physical fields in the smelting process of a submerged-arc furnace proposed by the present invention, on the basis of electrothermal conversion, uses Maxwell's equations to solve electromagnetic induction, studies the heat transfer mechanism from the arc to the molten bath by using thermal radiation, thermal convection and heat conduction, solves multiphase heat and mass transfer based on VOF, and processes the pressure-velocity coupling problem through the SIMPLE algorithm, obtaining the coupling of multiple physical fields (electricity-thermal-magnetic-flow-mass fraction), multiphase flow (furnace gas-ore charge-furnace slag-nickel-iron alloy) and the thermal stress and thermal deformation of the furnace body.

[0089] 2. The present invention numerically studies the coupling of multiple physical fields in the smelting process of a submerged-arc furnace based on the RKEF nickel-iron smelting process, and develops a method for coupling electrothermal conversion, electromagnetic induction, multiphase heat and mass transfer, and the thermal stress and thermal deformation of the furnace body in a numerically simulated submerged-arc furnace based on UDF compilation. First, current is introduced through the electrodes, and electrothermal conversion is carried out in the arc region, and then heat is provided to the molten bath in three ways: heat conduction, convective heat transfer and thermal radiation. During the electrothermal conversion process, a magnetic field is formed, and the magnetic field reacts on the plasma to form an electron jet. The electron jet can not only carry the heat on the cathode surface to the anode surface of the material, but its movement will also generate a skin effect and a proximity effect in the arc region. During the process of the material heating up and melting, the material is transformed, and the generated furnace gas, furnace slag, and alloy melt need to use VOF to solve the heat and mass transfer between multiphase flows, and the temperature distribution of the furnace body also needs to be analyzed by static structural analysis to ensure the safe and efficient production of the nickel-iron ore furnace. Description of the Drawings

[0090] Figure 1 Schematic diagram of the method for coupling multiple physical fields - multiphase flow - thermal stress and thermal deformation in the smelting process of a submerged-arc furnace numerically simulated by the present invention;

[0091] Figure 2 Flow block diagram of the method for coupling multiple physical fields - multiphase flow - thermal stress and thermal deformation in the smelting process of a submerged-arc furnace numerically simulated by the present invention;

[0092] Figure 3This is the UDF subroutine flowchart of the method for coupling multi-physical fields, multi-phase flow, and thermal stress and thermal deformation in the numerical simulation of the smelting process of submerged arc furnaces in the present invention. Specific implementation manners

[0093] To make the objectives, technical solutions, and advantages of the present technical solution clearer, the present technical solution will be further specifically described below in conjunction with specific implementation manners:

[0094] The method for coupling multi-physical fields of electro-thermal conversion, electromagnetic induction, heat and mass transfer of multi-phase flow, and stress and strain of the furnace body in the numerical simulation of submerged arc furnaces includes the following steps:

[0095] Step 1: Establish a physical model of the submerged arc furnace smelting, then import it into ICEM software for structured grid division, and finally import the meshed physical model into FLUENT;

[0096] Step 2: Use the UDF subroutine to expand the mathematical models of electro-thermal conversion, electromagnetic induction, heat and mass transfer of multi-phase flow, and stress and strain of the furnace body, and import them into FLUENT software;

[0097] Step 3: Turn on the energy, turbulence, radiation, and multi-phase flow models in sequence;

[0098] Step 4: Set the numerical simulation parameters, including arc physical property parameters, furnace gas physical property parameters, alloy physical property parameters, slag physical property parameters, material physical property parameters, boundary condition parameters, phase ratio parameters, solution methods, and solution accuracies.

[0099] Step 5: Import the temperature field result of the calculation result as the temperature load into the static structure (Static Structural) model for numerical calculation of thermal stress and thermal deformation.

[0100] Step 6: Add constraints, add contacts, apply loads, solve, and display the results in sequence.

[0101] Preferably, in Step 1, the submerged arc furnace model is divided into an arc sub-model and a molten bath sub-model, which is determined by the different electro-thermal conversion methods of the arc and the molten bath. Among them, the cathode spot temperature is specified by the DEFINRE_PROFILE macro and determined by the Richardson-Dushman theoretical formula. The expression is as follows:

[0102]

[0103] In the formula, J c is the emission current density of thermoelectrons on the surface of the cathode spot, with a value of 4.4×107; r is the arc radius; T cis the cathode spot temperature. The thermoelectron current density of the cathode spot is specified by DEFINRE_UDS_FLUX, and the radial current density satisfies the parabolic law. The expression is as follows:

[0104]

[0105] r is the arc radius; Rc is the cathode spot radius. Use the macros begin_f_loop and end_f_loop to traverse the upper surface of the arc to determine the cathode spot area size, current distribution, and temperature value. The relationship between it and the thermoelectron current density can be expressed by the following formula:

[0106]

[0107] In the formula, I is the arc current.

[0108] Preferably, although the electrothermal conversion of the arc and the molten pool is to convert electrical energy into heat energy based on Ohm's law, there are complex physical phenomena and arc starting mechanisms in the arc and electrode contact area (near the cathode region). Therefore, the submerged arc furnace model is divided into an arc sub-model and a molten pool sub-model, and the energy equation source term is modified using the macro DEFINRE_SOURCE to achieve the difference in electrothermal conversion. The energy equation expression is as follows:

[0109]

[0110] In the formula, SArc is the energy source term of the arc sub-model, and the expression is as follows:

[0111]

[0112] In the formula, J arc is the current density flowing through the arc; σ arc is the electrical conductivity of the arc, specified using the macro DEFINRE_DIFFUSIVITY; k B is the Boltzmann constant; e is the elementary charge; is the velocity vector. The three terms on the right side of the equal sign are Joule heat, electron transport enthalpy, and radiation loss S AR , the P-1 radiation model is used to calculate the arc radiation, and the radiation weighting factor is specified using the macro DEFINEEMISSIVITY WEIGHTING FACTOR. The expression is as follows:

[0113] S AR = aL-4αn 2 ξT 4 (6)

[0114] where a is the absorption coefficient; ξ is the Stefan - Boltzman coefficient; n is the refractive index of the medium; L is the incident radiation, and its transport equation is expressed as follows:

[0115]

[0116] where C is the coefficient of the linear anisotropic phase function, ξ s is the scattering coefficient.

[0117] For the molten pool, the source term SFur of its energy equation is expressed as follows:

[0118]

[0119] where J Fur is the current density flowing through the molten pool; σ Fur is the conductivity of the molten pool, specified by the macro DEFINRE_DIFFUSIVITY; ρ melt is the density of the molten pool; H is the enthalpy of the molten nickel - iron ore. The four terms on the right - hand side of the equal sign are the joule heat, the latent heat of melting, the source term for explaining the melting process, and the phase - change endothermic heat S R , where the phase - change endothermic heat is loaded into the energy source term using the macro DEFINRE_SOURCE, and its expression is as follows:

[0120]

[0121] where q is the heat absorbed during the phase change; Δc is the change in the phase - change mass fraction; M is the equivalent molar mass of the material; Δt is the time step of the simulation.

[0122] Preferably, the heat transfer mechanism from the arc sub - model to the molten - pool sub - model mainly consists of four parts: convective heat transfer, radiative heat transfer, the Thompson effect, and the condensation of electrons, and the expression is as follows:

[0123]

[0124] where Q c is the convective heat transfer of the arc plasma to the furnace charge; the quantity with subscript w is the value at the molten - pool surface; the quantity with subscript b is the value at the arc boundary layer; h is the enthalpy.

[0125]

[0126] where Q r is the radiative heat from the arc to the molten pool, described by the radiation - heat - transfer factor; k is the Stefan - Boltzmann constant; ε is the radiation coefficient; T top is the highest temperature in the furnace, T amb is the ambient temperature in the furnace.

[0127]

[0128] In the formula, Q e is the heat carried by electrons flowing from the cathode to the molten pool; J melt is the current density of the molten pool; T g is the temperature value at a distance of 0.1 mm from the molten pool; T w is the temperature of the molten pool; K B is the Boltzmann constant.

[0129] Q a = J arc (V a + q a )(14)

[0130] In the formula, Q a is the condensation heat generated when electrons enter the molten pool; qa represents the work function (the voltage drop required to remove a unit electron charge from the surface of the molten pool); V a and q a are respectively assumed to be 4V.

[0131] Preferably, the electrothermal conversion is based on the potential boundary condition. The current continuity equation is established by using the user-defined scalar (UDS) and Ohm's law, and then the Joule heat is loaded into the energy equation by the macro DEFINRE_SOURCE to solve the temperature field. The expression is as follows:

[0132]

[0133] It can be obtained that:

[0134]

[0135] In the formula, is the electric potential; σ is the conductivity; E is the electric field; J i is the current density in the i direction; A x is the magnetic vector in the x direction; A y is the magnetic vector in the y direction; A z is the magnetic vector in the z direction.

[0136] Preferably, the electromagnetic induction is based on the magnetic potential boundary condition. The Poisson equation of the magnetic vector is established by using the user-defined scalar (UDS) and Maxwell's equations, and the electromagnetic field is solved by using the Coulomb gauge. Among them, the current is loaded into the source term of the magnetic vector equation by the macro DEFINRE_SOURCE. The expression is as follows:

[0137]

[0138]

[0139] Using the Coulomb gauge: The electric potential is equated with the magnetic vector for solution, and the relational expression is as follows:

[0140]

[0141] The magnetic induction intensity formula can be obtained:

[0142]

[0143] In the formula, ρ is the density; is the velocity vector; μ is the magnetic permeability, taking the magnetic permeability of vacuum as 4.0×10-7; is the magnetic induction intensity.

[0144] Preferably, a changing electric field generates a magnetic field, the electromagnetic force will affect the distribution of the fluid, and the flow of the magnetofluid will in turn affect the temperature field and the flow field. During the multi-physical field coupling process, the molten pool is not only affected by gravity, thermal buoyancy and the surface tension of the phase interface, but also by the perturbation of the electromagnetic force on the alloy. Its momentum equation of the nickel-iron ore smelting furnace is solved by loading with the macro DEFINRE_SOURCE, and the expression is as follows:

[0145]

[0146] In the formula, p is the pressure; g is the acceleration of gravity; is the thermal buoyancy; is the surface tension of the phase interface; S i is the resistance source term of the porous medium; is the electromagnetic force, and the expression is as follows:

[0147]

[0148] Preferably, the roasted ore material is composed of laterite ore pellets, quicklime and anthracite, and has the characteristics of a porous medium. The porosity change with temperature is specified through the macro DEFINRE_PROFILE. Therefore, the resistance source term of the porous medium is added to the momentum equation of the ore material area, and the expression is as follows:

[0149]

[0150] In the formula, the viscous resistance coefficient λ is expressed as:

[0151]

[0152] In the formula, the inertial resistance coefficient C2 is expressed as:

[0153]

[0154] Preferably, in step two, the VOF model is used to process the distribution and conversion among the furnace gas, slag, materials, and nickel-iron alloy phases in the multiphase mass transfer. The volume fraction equation is established using the user-defined scalar (UDS), and the multiphase heat and mass transfer are solved in combination with the VOF module. The expression is as follows:

[0155]

[0156] α1 = 1 - α2 - α3 - α4 (40)

[0157] m slag = W × M slag (41)

[0158] m alloy = W × M alloy (42)

[0159] m gas = W × M gas (43)

[0160] In the formula, i represents the serial number of each phase. i = 1 is the ore material phase, i = 2 represents the slag phase, i = 3 represents the nickel-iron alloy phase, i = 4 represents the furnace gas phase, α is the volume fraction, where ρ is the density, where is the fluid velocity. m slag is the mass of the material generating slag; m alloy is the mass of the material generating nickel-iron alloy; m gas is the mass of the material generating furnace gas; where the changes in the mass fractions of the ore material and solid carbon are expressed as follows:

[0161]

[0162] S1 = -W × M1(46)

[0163] S C = -W × M C (47)

[0164] w1 is the mass fraction of the material; w c is the mass fraction of solid carbon; S c is the oxidation amount of C, Γ is the diffusion coefficient, and the phase transformation rate W of the phase change rate constant K is expressed as follows:

[0165]

[0166] In the formula, A z is the pre-exponential factor; E a is the activation energy; R is the molar gas constant.

[0167] Example

[0168] As shown Figures 1 to 3 in the figure, it is a method for mutual coupling of multiple physical fields, multiphase flow, and thermal stress and thermal deformation during the smelting process of a submerged arc furnace by numerical simulation, including the following:

[0169] As shown Figure 1 in the figure, the submerged arc furnace model includes: arc region, material region, slag layer, alloy layer, electrode, furnace shell, furnace body, etc. The current is introduced through the electrode, and most of the current undergoes electrothermal conversion in the arc region, while a small part flows into the ore materials and is converted into Joule heat; the arc region mainly provides heat to the molten pool through three heat transfer mechanisms: thermal radiation, thermal convection, and thermal conduction, providing a high-temperature environment for the melting and phase change of the ore materials, and the furnace body also undergoes deformation and stress concentration under the action of the thermal field.

[0170] As shown Figure 2 in the figure, in this embodiment, a submerged arc furnace model is established and imported into ICEM software for structured grid division, and then the grid is imported into FLUENT software; the mathematical models of electrothermal conversion, electromagnetic induction, multiphase flow heat and mass transfer, and furnace body stress and strain are extended using UDF subroutines and imported into FLUENT software, and the solved furnace body temperature field is imported as a load into the static structural analysis to solve the thermal stress and thermal strain of the furnace body structure.

[0171] The model enables the energy model; enables the multiphase flow model and uses the VOF model; enables the turbulence model and uses the standard k-epsilon model, adds the number of user-defined scalars (UDS), and compiles and loads codes (UDF) such as energy source terms, momentum source terms, mass source terms, magnetic vector equation source terms, and physical property parameters.

[0172] Set the numerical simulation parameters, including arc physical property parameters, furnace gas physical property parameters, alloy physical property parameters, slag physical property parameters, ore material physical property parameters, boundary condition parameters, phase ratio parameters, solution methods, and solution accuracy, and use the SIMPLE algorithm to handle pressure-velocity coupling to solve multiple physical fields.

[0173] Import the furnace body temperature field solved by FLUENT as a load into Static Structure analysis, and solve the thermal stress and thermal deformation of the furnace body by adding constraints, adding contacts, and applying loads.

[0174] As shown Figure 3 in the figure, the UDF subroutine of the method for mutual coupling of multiple physical fields, multiphase flow, and stress and strain during the smelting process of a submerged arc furnace by numerical simulation is compiled according to the process flow diagram, and the specific content of the UDF subroutine is as follows:

[0175] First, the UDF subroutine for electrothermal conversion is written. Based on Ohm's law and the user-defined scalar equation, the electric potential and magnetic vector are introduced to solve the current density distribution, and the expression is as follows:

[0176]

[0177] It can be obtained that:

[0178]

[0179] In the formula, is the electric potential; σ is the conductivity; E is the electric field; J i is the current density in the i direction; A x is the magnetic vector in the x direction; A y is the magnetic vector in the y direction; A z is the magnetic vector in the z direction. Then, through Maxwell's equations and magnetic vector equations, the current is stored using the C_UDMI macro, and then the magnetic vector source term is written by calling the DEFINE_SOURCE macro in the UDF subroutine. The expression is as follows:

[0180]

[0181] The magnetic induction intensity formula can be obtained:

[0182]

[0183] Using the programming language of Fluent, the electromagnetic force, electron transport enthalpy, and Joule heat are used as source terms, and the corresponding memory cells are allocated respectively, and then written into the program code for calculation. The Joule heat is loaded into the energy equation source term using the DEFINE_SOURCE macro to accurately simulate the electrothermal conversion process. The expression is as follows:

[0184]

[0185] In the formula, SArc is the energy source term of the arc submodel, and the expression is as follows:

[0186]

[0187] In the formula, J arc is the current density flowing through the arc; σarc is the conductivity of the arc, specified using the macro DEFINRE_DIFFUSIVITY; k B is the Boltzmann constant; e is the elementary charge; is the velocity vector. The three terms on the right side of the equal sign are Joule heat, electron transport enthalpy, and radiation loss S AR , and the P-1 radiation model is used to calculate the arc radiation, and the radiation weighting factor is specified using the macro DEFINE_EMISSIVITY_WEIGHTING_FACTOR. The expression is as follows:

[0188] S AR= aL - 4αn 2 ξT 4 (14)

[0189] where a is the absorption coefficient; ξ is the Stefan - Boltzman coefficient; n is the refractive index of the medium; L is the incident radiation, and the expression of its transport equation is as follows:

[0190]

[0191] where C is the coefficient of the linear anisotropic phase function, ξ s is the scattering coefficient.

[0192] For the molten pool, the source term SFur of its energy equation is expressed as follows:

[0193]

[0194] where J Fur is the current density flowing through the molten pool; σ Fur is the conductivity of the molten pool, specified by the macro DEFINRE_DIFFUSIVITY; ρ Fur is the density of the molten pool; H is the enthalpy of the molten nickel - iron ore. The four terms on the right - hand side of the equal sign are the Joule heat, the latent heat of melting, the source term for explaining the melting process, and the heat absorption for phase change S R , where the heat absorption for phase change is loaded into the energy source term using the macro DEFINRE_SOURCE, and its expression is as follows:

[0195]

[0196] where q is the heat absorbed by the phase change; Δc is the change in the mass fraction of the phase change; M is the equivalent molar mass of the material; Δt is the time step of the simulation.

[0197] Finally, the volume - fraction transport equation of the multiphase flow is written using the UDF subroutine. The reduction reaction mechanism of the ore is determined through the thermodynamics and kinetics of the reduction reaction, and the generation and loss of each phase are realized by studying the relationship between temperature and reaction rate. The expression is as follows:

[0198]

[0199] α1 = 1 - α2 - α3 - α4(20)

[0200] m slag = W×M slag (21)

[0201] m alloy = W×M alloy (22)

[0202] mgas = W × M gas (23)

[0203] In the formula, i represents the serial number of each phase. i = 1 is the ore phase, i = 2 represents the slag phase, i = 3 represents the nickel-iron alloy phase, i = 4 represents the furnace gas phase, α is the volume fraction, where ρ is the density, where is the fluid velocity. m slag is the mass of the material generating slag; m alloy is the mass of the material generating nickel-iron alloy; m gas is the mass of the material generating furnace gas; where the changes in the mass fractions of the ore and solid carbon are expressed by the following expressions:

[0204]

[0205] S1 = -W × M1(26)

[0206] S C = -W × M C (27)

[0207] w1 is the mass fraction of the material; w c is the mass fraction of solid carbon; S c is the oxidation amount of C, Γ is the diffusion coefficient, and from the phase transformation rate W of the phase transformation rate constant K, the expression is as follows:

[0208]

[0209] In the formula, A z is the pre-exponential factor; E a is the activation energy; R is the molar gas constant.

[0210] The above content is only the preferred embodiment of the present invention. For those of ordinary skill in the art, many changes can be made in the specific implementation manners and application scopes according to the idea of the present technical content. As long as these changes do not depart from the concept of the present invention, they all fall within the protection scope of this patent.

Claims

1. A multi-physical field coupling method for the smelting process of a nickel-iron electric arc furnace, characterized in that The method includes the following steps: Step 1: Establish a submerged arc furnace model, import it into ICEM software for structured mesh generation, and finally import the meshed physical model into FLUENT; Step 2: Use the UDF subroutine to expand the mathematical models of electrothermal conversion, electromagnetic induction, and multiphase heat and mass transfer, and import them into the FLUENT software; Step 3: Turn on the energy, turbulence, radiation, and multiphase flow models in sequence; Step 4: Set the numerical simulation parameters, including the physical properties of the arc, the physical properties of the ore, the physical properties of the furnace gas, the physical properties of the alloy, the physical properties of the slag, the boundary condition parameters, the proportion parameters of each phase, the solution method, and the solution accuracy; Step 5: Import the furnace body temperature field of the calculation result as a temperature load into the Static Structural model to add constraints and contacts, and perform numerical calculations of thermal stress and thermal deformation.

2. A multi-physical field coupling method for the smelting process of a nickel-iron ore thermal furnace according to claim 1, characterized in that The submerged-arc furnace model described in Step 1 consists of three parts: an electric arc, a molten bath, and a furnace body. Among them, the relative displacement of the cathode spots at the top of the electric arc zone is small, and the distribution of the cathode spot current density has nothing to do with the magnitude of the electric arc current. It is assumed that the radial current density J r satisfies the parabola law: Where, J c is the release current density of thermoelectrons on the surface of the cathode spot; r is the arc radius; R c is the cathode spot radius, and the expression is as follows: Where I arc is the arc current.

3. A multi-physical field coupling method for the smelting process of a nickel-iron ore electric furnace according to claim 2, characterized in that, Both the arc and the molten pool convert electrical energy into heat energy based on Ohm's law. Under the action of the magnetic field, electrons carry heat and flow from the cathode to the surface of the molten pool. The expression of its energy equation is as follows: where c p is the specific heat capacity, J / (kg·K); T is the temperature; ρ is the density; is the velocity vector; k eff is the thermal conductivity; S Fur is the energy source term of the molten pool; S Arc is the energy source term of the arc, which consists of Joule heat, electron transport enthalpy and radiation loss, and the expression is as follows: where J arc is the current density flowing through the arc; σ arc is the electrical conductivity of the arc; K B is the Boltzmann constant; e is the elementary charge; S AR is the radiation loss. The P-1 radiation model is used to calculate the arc radiation, and the expression is as follows: S AR = aL - 4an 2 ξT 4 (5) In the formula, a is the absorption coefficient; ξ is the Stefan-Boltzman coefficient; n is the refraction coefficient; L is the incident radiation, and the expression of its transport equation is as follows: where C is the coefficient of the linear anisotropic phase function, and ξ s is the scattering coefficient; The energy source term S of the molten pool Fur , consists of Joule heat, latent heat of melting, the source term for explaining the melting process, and heat absorption during phase change. Its expression is as follows: Where, J Fur is the current density flowing through the molten pool; σ Fur is the conductivity of the molten pool; ρ Fur is the density of the molten pool; H is the enthalpy of the molten nickel-iron ore; S R is the endothermic heat of melting phase change, and its expression is as follows: In the formula, q is the heat absorbed by the phase change; Δc is the change in the mass fraction of the phase change; M is the equivalent molar mass of the material; Δt is the simulation time step.

4. A multi-physical field coupling method for the smelting process of a nickel-iron ore thermal furnace according to claim 1, characterized in that The electrothermal conversion described in Step 2 is based on the electric potential boundary condition, and the current continuity equation is established by using the user-defined scalar (UDS) and Ohm's law. The expression is as follows: In the formula, is the electric potential; σ is the conductivity; E is the electric field; J is the current density, and its expression is as follows: where J x is the magnitude of the current in the x - direction; J y is the magnitude of the current in the y - direction; J z is the magnitude of the current in the z - direction; A x is the magnetic vector in the x - direction; A y is the magnetic vector in the y - direction; A z is the magnetic vector in the z - direction.

5. A multi-physical field coupling method for the smelting process of a nickel-iron ore electric furnace according to claim 1, characterized in that, The electromagnetic induction described in Step 2 is based on the magnetic potential boundary condition, and the Poisson equation of the magnetic vector is established by using the user-defined scalar (UDS) and Maxwell's equations. At the same time, the electromagnetic field is solved using the Coulomb gauge. The expression is as follows: Using the Coulomb gauge: An equation is established by equating the electric potential and the magnetic vector for solving, and the relationship is as follows: The magnetic induction intensity formula can be obtained: where ρ is the density; is the electric field; is the velocity vector; μ is the true magnetic permeability; is the magnetic induction intensity.

6. A multi-physical field coupling method for the smelting process of a nickel-iron electric arc furnace according to claim 1, characterized in that The ore described in Step 4 is composed of laterite ore pellets, quicklime, and anthracite, and has the characteristics of a porous medium; therefore, the porous medium resistance source term is added to the momentum equation; in addition, the influence of the electromagnetic force on the multiphase flow is also loaded into the momentum equation through the source term. The expression is as follows: where ρ is the density; p is the pressure; is the velocity vector; g is the acceleration due to gravity; is the thermal buoyancy; is the surface tension of the phase interface; is the electromagnetic force; S i is the resistance source term of the porous medium, and the expression is as follows: In the formula, the viscous resistance coefficient λ is expressed as: In the formula, the inertial resistance coefficient C2 is expressed as: The electromagnetic force mentioned above The expression is as follows:

7. A multi-physical field coupling method for the smelting process of a nickel-iron electric arc furnace according to claim 1, characterized in that, The multiphase mass transfer described in Step 2 uses the VOF model to handle the distribution and conversion between the furnace gas, slag, material, and nickel-iron alloy phases, and uses the user-defined scalar (UDS) to establish the mass fraction transport equation, and combines the VOF module to solve the volume fraction of each phase. The expression is as follows: α1＝1-α2-α3-α4 (34) m slag = W × M slag (35) m alloy = W × M alloy (36) m gas = W × M gas (37) In the formula, m is the mass, i = 1 represents the ore phase, i = 2 represents the slag phase, i = 3 represents the nickel-iron alloy phase, i = 4 represents the furnace gas phase, α is the volume fraction, where ρ is the density, where is the fluid velocity; m slag is the mass of the material forming slag; m alloy is the mass of the material forming nickel-iron alloy; m gas is the mass of the material forming furnace gas; W is the phase change conversion rate; M is the molar mass; Among them, the changes in the mass fractions of the ore and solid carbon are expressed as follows: S1 = -W × M1 (40) S C = -W × M C (41) $w_1$ is the mass fraction of the material; $w$ c is the mass fraction of solid carbon; $S$ c is the oxidation amount of $C$, $\Gamma$ is the diffusion coefficient, and the phase transformation rate $W$ of the phase transformation rate constant $K$ is expressed as follows: In the formula, A is the pre-exponential factor; E a is the activation energy; R is the molar gas constant; The Static Structural model in Step 2 constructs geometric equations, physical equations, equilibrium equations, and compatibility equations based on Hooke's law in general. Among them, the constitutive equation uses the furnace body thermal field gradient to solve the thermal strain components in different axial directions; The equilibrium equation solves the thermal stress components in different axial directions based on the thermal strain components; the kinematic equation also solves the displacement components and shear stress components in different directions based on the thermal strain components. The expression is as follows: Equilibrium equations of the generalized Hooke's law: Among them, σ x , σ y , σ z are the thermal stress components parallel to the x, y, and z axes, and τ xy , τ yz , τ xz are the shear stress components parallel to the x, y, and z axes; Kinematics equations: where ε x , ε y , ε z are the thermal strain components parallel to the x, y, and z axes; u, v, and w are the displacement components in three directions; γ xy , γ yz , γ zx are the shear strain components; Constitutive equations: Where E is the elastic modulus; μ is the Poisson's ratio; G is the shear modulus.

8. A multi-physical field coupling method for the smelting process of a nickel-iron ore electric furnace according to claim 1, characterized in that In step 4, the electric potential boundary conditions are crucial for the formation of the physical field. The distribution of the current density is solved based on Ampere's law and the electric potential boundary conditions. The conductivity of the material and the arc directly affects the accuracy of the multi-physical field distribution. Due to the strong conductivity of the self-baking electrode, the influence of the electrode partial voltage is ignored to simplify the model, and the secondary voltage is directly applied as an input condition on the upper surface of the arc (the bottom of the electrode). The bottom of the molten pool is set to zero electric potential; the side walls of the molten pool are insulated. In step 4, the setting of the magnetic potential boundary conditions is also crucial for the formation of the physical field. Electromagnetic induction is used to establish the magnetohydrodynamic equation through UDF, and the electric field and magnetic field are established with an equal relationship using the Coulomb gauge. The magnetic permeability of the arc sub-model and the molten pool model is 1. The magnetic potential of the side walls of the molten pool is 0, and the internal surfaces are all coupled. The other walls of the molten pool are insulated. In step 4, the model considers the situation of smelting in the furnace. To ensure the rationality and accuracy of the multi-physical field coupling, the following assumptions are made for this model: (1) The arc plasma is in a state of local thermodynamic equilibrium. Therefore, it is assumed that the complex physical processes in the regions near the cathode and anode are not considered, and the regions near the cathode and anode are simplified in the simulation. (2) Considering that the velocity of the arc jet is relatively large, the impact force on the molten pool will form an arc cavity, and gas ionization occurs in the cavity. (3) Since the smelting environment of the submerged arc furnace is a closed space, the metal vapor generated during the smelting process is ignored, and the gas in the cavity is assumed to be high-temperature air. (4) The pellet ore flows into the furnace through the feed bin. It is assumed that the submerged arc furnace is initially filled with ore; the submerged arc furnace remains in a conducting state, and the current forms a loop in the furnace. (5) The depths of the three electrodes inserted into the ore in the AC submerged arc furnace are the same; three arcs will be generated by the three electrodes during the smelting process, and it is assumed that the shape of the arc cavity is approximately cylindrical. (6) Since this method mainly studies the multi-physical field coupling in the AC submerged arc furnace, the inductance voltage of the AC submerged arc furnace during the smelting process is ignored. (7) In the multiphase flow, the furnace gas is subject to the gravity of the ore, the pressure of the ore, the self-gravity of the furnace gas, and the buoyancy of the furnace gas.

9. A multi-physical field coupling method for the smelting process of a nickel-iron ore electric furnace, characterized in that, This method uses a user-defined scalar equation and an added source term to simultaneously solve electrothermal conversion, electromagnetic induction, reduction reactions, and multi-phase heat and mass transfer; the k-epsilon turbulence model is used to study the behavior of nickel-iron alloy droplets; the P-1 method is used to solve the radiative heat transfer. The absorption coefficient and scattering coefficient of the arc radiation are both 0.6, and the distribution of the temperature field is analyzed by combining the energy equation. To meet the convergence criterion, a transient simulation is carried out with a time step of 0.0001 s; the widely used SIMPLE algorithm is used to handle the pressure-velocity coupling problem; the method uses a second-order upwind discretization; when discretizing in time, the Courant number is less than 1.0.

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