A method for calculating temperature distribution during the roasting process of self-baking electrodes in a DC submerged arc furnace

Abstract

The present invention provides a method for calculating the temperature distribution during the roasting process of a self-baking electrode in a DC electric arc furnace, comprising determining the structural parameters of the self-baking electrode and the operating parameters of the electric arc furnace; determining the material and physical property parameters of each component of the self-baking electrode; establishing an electric-thermal conversion relationship between each component of the self-baking electrode and the electrode paste based on the coupling principle of the electromagnetic field and the temperature field during the roasting process of the self-baking electrode, solving the energy equation and the Maxwell equations, and calculating the temperature distribution of the self-baking electrode during the roasting process. By calculating the temperature distribution of the self-baking electrode, the matching degree between the operating parameters of the electric arc furnace, the structural parameters of the self-baking electrode and the components of the electrode paste can be predicted, so that the roasting effect of the self-baking electrode is optimized. This method can significantly reduce the cost of temperature measurement, save resources, and provide a scientific basis for the roasting scheme of the self-baking electrode, thereby improving the production efficiency of the electric arc furnace, ensuring the quality of the self-baking electrode, and reducing the potential safety hazards that may occur during the roasting process of the self-baking electrode.

Description

Technical Field

[0001] The invention relates to the technical field of self-baking electrodes, and in particular to a method for calculating temperature distribution during the baking process of a self-baking electrode in a DC ore-fired furnace. Background Art

[0002] Submerged arc furnaces are industrial electric furnaces that consume significant amounts of electricity and carbon. Electrode material selection varies depending on the type of metallurgy being smelted. Graphite or carbon electrodes are typically used for pure products, but these are relatively expensive. Therefore, most submerged arc furnaces used for ferroalloy production utilize relatively inexpensive self-baking electrodes.

[0003] Self-baking electrodes are made by converting electrode paste into solid electrodes through a specific process. Anthracite, asphalt, coal tar, and coke are the primary raw materials for the electrode paste. The electrode paste is fed downward into the furnace through a cylindrical steel shell extending from a platform above the furnace. Heated by the electrode's own Joule heat, arc radiation, and convection heat transfer from the charge, the paste absorbs the heat, transforming into a fluid state and filling the remaining space in the electrode shell. As baking proceeds, the ash and volatiles in the electrode paste continuously escape, transforming the paste into a solid state, ultimately completing the baking process. Self-baking electrodes utilize the furnace's own energy to bake the electrodes, reducing additional energy consumption.

[0004] Currently, the baking of self-baking electrodes presents issues with both soft and hard fractures. Therefore, the temperature distribution of the self-baking electrodes is crucial for stable smelting in DC submerged arc furnaces. Given the high temperature environment and complex smelting conditions within the furnace, experimentally determining the temperature distribution during the baking process of self-baking electrodes faces challenges such as the high temperature resistance of the measuring instruments and high costs. Traditional calculations of the baking temperature of self-baking electrodes fail to account for the coupling between electromagnetic and temperature fields, resulting in poor accuracy. Summary of the Invention

[0005] In order to solve the above technical problems, the present invention provides a method for calculating the temperature distribution during the baking process of self-baking electrodes in a DC submerged arc furnace. By using the operating parameters of the submerged arc furnace, an electric-thermal conversion relationship between the various components of the self-baking electrode is established. Under the coupling effect of the electromagnetic field and the temperature field, heat transfer calculations are performed on each component. Without affecting the normal production of the submerged arc furnace, the baking temperature distribution of the self-baking electrode can be predicted in advance.

[0006] The present invention provides a method for calculating the temperature distribution during the roasting process of a self-baking electrode in a DC ore-fired furnace, comprising:

[0007] Step 1: Determine the structural parameters of the self-baking electrode and the operating parameters of the DC submerged arc furnace. The self-baking electrode consists of an electrode shell, copper tiles, ribs and formed electrodes.

[0008] Step 2: Determine the material and physical properties of each component of the self-baking electrode;

[0009] Step 3: Based on the coupling principle of electromagnetic field and temperature field during the baking process of the self-baking electrode, establish the electrothermal conversion relationship between each component of the self-baking electrode and the electrode paste, solve the energy equation and Maxwell equations, and calculate the temperature distribution of the self-baking electrode during the baking process.

[0010] In the method for calculating the temperature distribution during the roasting process of the self-baking electrode of the DC submerged arc furnace of the present invention, the structural parameters of the self-baking electrode in step 1 include: electrode diameter, total electrode height, electrode shell thickness, and rib thickness; the operating parameters of the submerged arc furnace include: voltage, current, and electrode pressing and releasing speed.

[0011] In the method for calculating the temperature distribution during the roasting process of a self-baking electrode in a DC submerged arc furnace of the present invention, the material of the electrode shell and the rib sheet is Q235 carbon structural steel; the material of the copper tile is copper; the components of the electrode paste are anthracite, coke, asphalt and coal tar; and the physical properties required for calculating the temperature distribution of the self-baking electrode during the roasting process include density, electrical conductivity, thermal conductivity and specific heat capacity.

[0012] In the method for calculating the temperature distribution during the roasting process of the self-baking electrode in the DC ore-fired furnace of the present invention, the step 3 is specifically as follows:

[0013] Step 3.1: During the baking process, the energy equation for calculating the temperature distribution of the self-baking electrode is:

[0014]

[0015] Where: t is the roasting time; c p is the specific heat capacity of the self-baking electrode; z is the unit vector along the direction of electrode release; ρ is the density of the self-baking electrode; T is the temperature of the self-baking electrode; V is the release speed of the self-baking electrode; k is the thermal conductivity of the self-baking electrode; q is the Joule heat generated by the electrothermal conversion of the self-baking electrode itself, and its calculation formula is as follows:

[0016]

[0017] Where: σ is the conductivity of the self-baking electrode; J is the current density of the self-baking electrode;

[0018] Step 3.2: According to Ohm's law, the relationship between current density and electric field is:

[0019] J=σE (3)

[0020] According to Maxwell's equations, the scalar voltage is introduced and magnetic vector potential A, and the two identities Applied to electromagnetism, the following formula is derived:

[0021]

[0022]

[0023]

[0024] Where: E is the electric field strength of the self-baking electrode; B is the magnetic flux density of the self-baking electrode; μ is the magnetic permeability of the self-baking electrode; According to the Coulomb standard The voltage equation (7) and magnetic vector potential equation (8) of the self-baking electrode are derived by simplifying and replacing equations (4)-(6):

[0025]

[0026]

[0027] The nonlinear differential equations (7) and (8) are locally linearized to solve for the scalar voltage and magnetic vector potential A, these two variables are brought into the energy equation (1) of the self-baking electrode, the Joule heat and current density are connected in sequence, the energy equation (1) is locally linearized, and the temperature distribution of the self-baking electrode is calculated. This temperature affects the conductivity / resistance of the self-baking electrode components and electrode paste, and further affects the electromagnetic field distribution.

[0028] In the method for calculating the temperature distribution during the roasting process of the self-baking electrode in a DC ore-fired furnace of the present invention, the following boundary conditions are set when calculating the temperature distribution of the self-baking electrode:

[0029] (1) Bottom of electrode

[0030] Thermal boundary: heat flux conducted by the DC arc;

[0031] Electrical boundaries: DC voltage or DC current density flux;

[0032] Magnetic field boundaries:

[0033] Where n is the unit vector of the x, y, and z coordinates of the self-baking electrode;

[0034] (2) Interface between electrode and charge

[0035] Thermal Boundary:

[0036] Electrical Boundary:

[0037] Magnetic field boundaries:

[0038] Wherein, α is the Stefan-Boltzmann constant; ε is the blackness, ε = 0.8 to 0.9; T5 is the temperature of the interface between the electrode and the charge, T5 increases in steps from 900°C to 1800°C;

[0039] (3) Interface between electrode and furnace gas

[0040] Thermal Boundary:

[0041] Electrical Boundary:

[0042] Magnetic field boundaries:

[0043] Where h4 is the convection heat transfer coefficient at the interface between the electrode and the furnace gas, h4 = 50W·m -2 ·K -1 ; T4 is the temperature of the interface between the electrode and the furnace gas, and the range of T4 is 800℃~900℃;

[0044] (4) Copper tile bottom and copper tile side wall

[0045] Thermal Boundary:

[0046] Electrical Boundary:

[0047] Magnetic field boundaries:

[0048] Where h3 is the convection heat transfer coefficient of the bottom and side walls of the copper tile, h3 = 22W·m -2 ·K -1 ; T3 is the temperature of the bottom and side wall of the copper tile, and the range of T3 is 200℃~300℃;

[0049] (5) Copper tile top

[0050] Thermal Boundary:

[0051] Electrical Boundary:

[0052] Magnetic field boundaries:

[0053] Where h2 is the convection heat transfer coefficient at the top of the copper tile, h2 = 1000 W m -2 ·K -1 ; T2 is the temperature of the top of the copper tile, T2 range is 20℃~35℃;

[0054] (6) Electrode shell side wall

[0055] Thermal Boundary:

[0056] Electrical Boundary:

[0057] Magnetic field boundaries:

[0058] Where h1 is the convection heat transfer coefficient of the electrode shell side wall, h1 = 10W·m -2 ·K -1 ; T1 is the temperature of the side wall of the electrode shell, T1 increases in steps from 35℃ to 150℃;

[0059] (7) Electrode top

[0060] Thermal boundary: T0;

[0061] Electrical Boundary:

[0062] Magnetic field boundaries:

[0063] Wherein, T0 is the temperature of the top of the electrode, and the range of T0 is 15℃~30℃.

[0064] In the method for calculating the temperature distribution during the roasting process of the self-baking electrode in the DC ore-fired furnace of the present invention, the physical properties of the self-baking electrode parts change with temperature; the composition of the electrode paste is different, and the conductivity, thermal conductivity and specific heat capacity of the electrode paste before and after roasting are different.

[0065] In the method for calculating the temperature distribution during the roasting process of the self-baking electrode of the DC ore-fired furnace of the present invention, the self-baking electrode is pressed and released at a uniform speed during the roasting process.

[0066] In the method for calculating the temperature distribution during the roasting process of the self-baking electrode of the DC ore-fired furnace of the present invention, the self-baking electrode is roasted in a constant voltage or constant current manner.

[0067] The method for calculating the temperature distribution during the roasting process of a self-baking electrode in a DC ore-fired furnace of the present invention has the following beneficial effects:

[0068] By calculating the temperature distribution during the firing process, the method of the present invention can predict the matching degree between the submerged arc furnace operating parameters and the self-baking electrode structural parameters and electrode paste composition, thereby achieving the best firing effect for the self-baking electrode. This method can significantly reduce temperature measurement costs, conserve resources, provide a scientific basis for the firing plan of the self-baking electrode, improve the production efficiency of the submerged arc furnace, ensure the quality of the self-baking electrode, and reduce potential safety hazards that may arise during the firing process of the self-baking electrode. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 To solve the nonlinear equations of the self-baking electrode under the coupled electric-magnetic-thermal physical fields;

[0070] Figure 2a and 2b This is a schematic diagram of the self-baking electrode structure in a DC ore-fired furnace. Figure 2a is the main view, Figure 2bIt is a top view;

[0071] Figure 3 This is a schematic diagram of the boundaries of the self-baking electrode when it is working in a DC ore-fired furnace. ab is the bottom of the electrode, bc is the interface between the electrode and the charge, cd is the interface between the electrode and the furnace gas, de is the bottom of the copper tile, ef is the side wall of the copper tile, fg is the top of the copper tile, gh is the side wall of the electrode shell, and hi is the top of the electrode.

[0072] Figure 4 This is a temperature distribution cloud diagram of the cross-electrode axis section of the self-baking electrode in the embodiment of the present invention. DETAILED DESCRIPTION

[0073] This embodiment takes the silicon-manganese alloy submerged arc furnace self-baking electrode as an example and describes the present invention in detail in conjunction with the drawings, but the protection scope of the present invention is not limited to the drawings and specific embodiments.

[0074] The present invention provides a method for calculating temperature distribution during the roasting process of a self-baking electrode in a DC ore-fired furnace, comprising:

[0075] Step 1: Determine the structural parameters of the self-baking electrode and the operating parameters of the submerged arc furnace. First, understand the physical structure of the self-baking electrode and mathematically model it based on this physical structure. The structural parameters of the self-baking electrode that need to be determined include: electrode diameter, total electrode height, electrode shell thickness, and rib thickness. The operating parameters of the submerged arc furnace include: voltage, current, and electrode compression and release speed. The structural parameters of the self-baking electrode and the operating parameters of the submerged arc furnace in this example are shown in Table 1.

[0076] Table 1 Structural parameters and operating parameters of self-baking electrodes

[0077]

[0078] Step 2: Determine the material and physical properties of each component of the self-baking electrode, such as Figure 2a and 2b As shown, the self-baking electrode consists of an electrode shell 1, a copper tile 2, a rib 4, and a formed electrode 3. The electrode shell and ribs are made of Q235 carbon structural steel; the copper tile is made of copper; and the electrode paste is composed of anthracite, coke, asphalt, and coal tar. The physical properties required to calculate the temperature distribution of the self-baking electrode during calcination include density, electrical conductivity, thermal conductivity, and specific heat capacity. The physical properties of the self-baking electrode in this example are shown in Table 2.

[0079] Table 2 Physical properties of self-baking electrodes

[0080]

[0081]

[0082] In specific implementation, the physical properties of the self-baking electrode components change with temperature; the electrical conductivity, thermal conductivity and specific heat capacity of the electrode paste before and after baking are different due to different compositions of the electrode paste.

[0083] Step 3: Based on the coupling principle of electromagnetic field and temperature field during the baking process of the self-baking electrode, establish the electrothermal conversion relationship between each component of the self-baking electrode and the electrode paste, solve the energy equation and Maxwell equations, and calculate the temperature distribution of the self-baking electrode during the baking process. Figure 1 The relationship diagram of the nonlinear equations for solving the self-baking electrode under the coupling of electromagnetic, magnetic and thermal physical fields.

[0084] The step 3 is specifically as follows:

[0085] Step 3.1: During the baking process, the energy equation for calculating the temperature distribution of the self-baking electrode is:

[0086]

[0087] Where: t is the roasting time; c p is the specific heat capacity of the self-baking electrode; z is the unit vector along the direction of electrode release; ρ is the density of the self-baking electrode; T is the temperature of the self-baking electrode; V is the release speed of the self-baking electrode; k is the thermal conductivity of the self-baking electrode; q is the Joule heat generated by the electrothermal conversion of the self-baking electrode itself, and its calculation formula is as follows:

[0088]

[0089] Where: σ is the conductivity of the self-baking electrode; J is the current density of the self-baking electrode;

[0090] Step 3.2: According to Ohm's law, the relationship between current density and electric field is:

[0091] J=σE (3)

[0092] According to Maxwell's equations, the scalar voltage is introduced and magnetic vector potential A, and the two identities Applied to electromagnetism, the following formula is derived:

[0093]

[0094]

[0095]

[0096] Where: E is the electric field strength of the self-baking electrode; B is the magnetic flux density of the self-baking electrode; μ is the magnetic permeability of the self-baking electrode; According to the Coulomb standard The voltage equation (7) and magnetic vector potential equation (8) of the self-baking electrode are derived by simplifying and replacing equations (4)-(6):

[0097]

[0098]

[0099] The nonlinear differential equations (7) and (8) are locally linearized to solve for the scalar voltage and magnetic vector potential A, these two variables are brought into the energy equation (1) of the self-baking electrode, the Joule heat and current density are connected in sequence, the energy equation (1) is locally linearized, and the temperature distribution of the self-baking electrode is calculated. This temperature affects the conductivity / resistance of the self-baking electrode components and electrode paste, and further affects the electromagnetic field distribution.

[0100] The temperature distribution calculation of self-baking electrodes is to solve the coupled Maxwell equations and energy equations, and certain boundary conditions must be met to ensure the uniqueness of the solution. Figure 3 This is a boundary diagram of a self-baking electrode in a DC ore-fired furnace. ab is the bottom of the electrode, bc is the interface between the electrode and the charge, cd is the interface between the electrode and the furnace gas, de is the bottom of the copper tile, ef is the side wall of the copper tile, fg is the top of the copper tile, gh is the side wall of the electrode shell, and hi is the top of the electrode. When calculating the temperature distribution of the self-baking electrode, the following boundary conditions are set:

[0101] (1) Bottom of electrode

[0102] Thermal boundary: q = 9127 W / m 2 ;

[0103] Electrical boundary: J = 94222.29 A / m 2 ;

[0104] Magnetic field boundaries:

[0105] Where n is the unit vector of the x, y, and z coordinates of the self-baking electrode;

[0106] (2) Interface between electrode and charge

[0107] Thermal Boundary: T5=900℃~1800℃ step-by-step increase, ε=0.8~0.9, α=5.67×10 -8 ;

[0108] Electrical Boundary:

[0109] Magnetic field boundaries:

[0110] (3) Interface between electrode and furnace gas

[0111] Thermal Boundary: T4=900℃,h4=50W·m -2 ·K -1 ;

[0112] Electrical Boundary:

[0113] Magnetic field boundaries:

[0114] (4) Copper tile bottom and copper tile side wall

[0115] Thermal Boundary: T3=227℃,h3=22W·m -2 ·K -1 ;

[0116] Electrical Boundary:

[0117] Magnetic field boundaries:

[0118] (5) Copper tile top

[0119] Thermal Boundary: T2=35℃,h2=1000W·m -2 ·K -1 ;

[0120] Electrical Boundary:

[0121] Magnetic field boundaries:

[0122] (6) Electrode shell side wall

[0123] Thermal Boundary: T1=35℃~150℃ stepwise increase, h1=10W·m -2 ·K -1 ;

[0124] Electrical Boundary:

[0125] Magnetic field boundaries:

[0126] (7) Electrode top

[0127] Thermal boundary: T0 = 30°C;

[0128] Electrical Boundary:

[0129] Magnetic field boundaries:

[0130] In a specific implementation, the self-baking electrode is pressed and released at a uniform speed during the baking process and baked in a constant voltage or constant current manner.

[0131] Figure 4 This is a temperature distribution cloud diagram of a self-baking electrode, taken along its axis, in an embodiment of the present invention. The calculated results show a parabolic temperature distribution. The temperature of each isotherm is plotted and its position on the electrode is indicated. As the electrode is pressed and fired, the temperature of the self-baking electrode eventually stabilizes, and the two processes reach equilibrium.

[0132] The above description is only a preferred embodiment of the present invention and is not intended to limit the concept of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for calculating the temperature distribution during the roasting process of a self-baking electrode in a DC ore-fired furnace, characterized in that: include: Step 1: Determine the structural parameters of the self-baking electrode and the operating parameters of the DC submerged arc furnace. The self-baking electrode consists of an electrode shell, copper tiles, ribs and formed electrodes. Step 2: Determine the material and physical properties of each component of the self-baking electrode; Step 3: Based on the coupling principle of electromagnetic field and temperature field during the baking process of the self-baking electrode, the electric-thermal conversion relationship between each component of the self-baking electrode and the electrode paste is established, the energy equation and Maxwell equations are solved, and the temperature distribution of the self-baking electrode during the baking process is calculated; The structural parameters of the self-baking electrode in step 1 include: electrode diameter, electrode total height, electrode shell thickness, and rib thickness; the operating parameters of the submerged arc furnace include: voltage, current, and electrode pressing and releasing speed; The step 3 is specifically as follows: Step 3.1: During the baking process, the energy equation for calculating the temperature distribution of the self-baking electrode is: Where: t is the roasting time; c p is the specific heat capacity of the self-baking electrode; z is the unit vector along the direction of electrode release; ρ is the density of the self-baking electrode; T is the temperature of the self-baking electrode; V is the release speed of the self-baking electrode; k is the thermal conductivity of the self-baking electrode; q is the Joule heat generated by the electrothermal conversion of the self-baking electrode itself, and its calculation formula is as follows: Where: σ is the conductivity of the self-baking electrode; J is the current density of the self-baking electrode; Step 3.2: According to Ohm's law, the relationship between current density and electric field is: J=σE (3) According to Maxwell's equations, the scalar voltage is introduced and magnetic vector potential A, and the two identities Applied to electromagnetism, the following formula is derived: Where: E is the electric field strength of the self-baking electrode; B is the magnetic flux density of the self-baking electrode; μ is the magnetic permeability of the self-baking electrode; According to the Coulomb standard The voltage equation (7) and magnetic vector potential equation (8) of the self-baking electrode are derived by simplifying and replacing equations (4)-(6): The nonlinear differential equations (7) and (8) are locally linearized to solve for the scalar voltage and magnetic vector potential A, these two variables are brought into the energy equation (1) of the self-baking electrode, the Joule heat and current density are connected in sequence, the energy equation (1) is locally linearized, and the temperature distribution of the self-baking electrode is calculated. This temperature affects the conductivity / resistance of the self-baking electrode components and electrode paste, and further affects the electromagnetic field distribution.

2. The method for calculating the temperature distribution during the roasting process of the self-baking electrode of the DC ore-fired furnace according to claim 1, characterized in that: The electrode shell and ribs are made of Q235 carbon structural steel; the copper tiles are made of copper; the electrode paste is composed of anthracite, coke, asphalt and coal tar; the physical properties required to calculate the temperature distribution of the self-baking electrode during the baking process include density, electrical conductivity, thermal conductivity and specific heat capacity.

3. The method for calculating temperature distribution during the roasting process of the self-baking electrode of the DC ore-fired furnace according to claim 1, characterized in that: When calculating the temperature distribution of the self-baking electrode, the following boundary conditions are set: (1) Bottom of electrode Thermal boundary: heat flux conducted by the DC arc; Electrical boundaries: DC voltage or DC current density flux; Magnetic field boundaries: Where n is the unit vector of the x, y, and z coordinates of the self-baking electrode; (2) Interface between electrode and charge Thermal Boundary: Electrical Boundary: Magnetic field boundaries: Wherein, α is the Stefan-Boltzmann constant; ε is the blackness, ε = 0.8 to 0.9; T5 is the temperature of the interface between the electrode and the charge, T5 increases in steps from 900°C to 1800°C; (3) Interface between electrode and furnace gas Thermal Boundary: Electrical Boundary: Magnetic field boundaries: Where h4 is the convection heat transfer coefficient at the interface between the electrode and the furnace gas, h4 = 50W·m -2 ·K -1 ; T4 is the temperature of the interface between the electrode and the furnace gas, and the range of T4 is 800℃~900℃; (4) Copper tile bottom and copper tile side wall Thermal Boundary: Electrical Boundary: Magnetic field boundaries: Where h3 is the convection heat transfer coefficient of the bottom and side walls of the copper tile, h3 = 22W·m -2 ·K -1 ; T3 is the temperature of the bottom and side wall of the copper tile, and the range of T3 is 200℃~300℃; (5) Copper tile top Thermal Boundary: Electrical Boundary: Magnetic field boundaries: Where h2 is the convection heat transfer coefficient at the top of the copper tile, h2 = 1000 W m -2 ·K -1 ; T2 is the temperature of the top of the copper tile, T2 range is 20℃~35℃; (6) Electrode shell side wall Thermal Boundary: Electrical Boundary: Magnetic field boundaries: Where h1 is the convection heat transfer coefficient of the electrode shell side wall, h1 = 10W·m -2 ·K -1 ; T1 is the temperature of the side wall of the electrode shell, T1 increases in steps from 35℃ to 150℃; (7) Electrode top Thermal boundary: T0; Electrical Boundary: Magnetic field boundaries: Wherein, T0 is the temperature of the top of the electrode, and the range of T0 is 15℃~30℃.

4. The method for calculating temperature distribution during the roasting process of a DC ore-fired furnace self-baking electrode according to claim 1, characterized in that: The physical properties of self-baking electrode components change with temperature; the electrical conductivity, thermal conductivity and specific heat capacity of the electrode paste before and after baking are different due to different compositions of the electrode paste.

5. The method for calculating temperature distribution during the roasting process of a self-baking electrode in a DC ore-fired furnace according to claim 1, characterized in that: During the baking process, the self-baking electrode is pressed and released at a uniform speed.

6. The method for calculating temperature distribution during the roasting process of a DC ore-fired furnace self-baking electrode according to claim 1, characterized in that: The self-baking electrode is baked in a constant voltage or constant current mode.

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