A method for using a traveling wave linear electromagnetic stirrer for controlling square billet V-segregation

Abstract

The application provides a method for controlling V-shaped segregation of square billet by using a traveling wave linear electromagnetic stirrer, and relates to the technical field of steelmaking-continuous casting. The method sets a traveling wave linear electromagnetic stirrer at the solidification end of a square billet continuous casting machine; then a numerical simulation prediction model of the end linear electromagnetic stirring and continuous casting billet solidification growth is constructed by an electromagnetic field calculation model of the end traveling wave linear electromagnetic stirrer and a continuous casting multiphase solidification physical model; the strength of the end linear electromagnetic stirring is determined by solving the electromagnetic field calculation model; the time t0 value when the slip velocity of equiaxed crystals at the installation position of the electromagnetic stirrer at the solidification end is 0 m / s is obtained by solving the continuous casting multiphase solidification physical model, and then the distance between the center of the end electromagnetic stirrer and the meniscus is calculated, so that the installation position of the electromagnetic stirrer is determined; finally, the shell thickness of the solidification end casting billet is calculated, so as to guide the elimination of V-shaped segregation in the field production and maximize the improvement of the internal quality defects of the continuous casting billet.

Description

Technical Field

[0001] This invention relates to the field of steelmaking-continuous casting technology, and in particular to a method for using a traveling wave linear electromagnetic stirrer to control V-shaped segregation in square and round billets. Background Technology

[0002] Continuous casting, as a crucial process in modern steel manufacturing, has seen significant development in recent decades. However, the steel industry faces unprecedented pressure to reduce carbon emissions, and domestic steel companies are actively exploring and developing high-efficiency continuous casting technologies centered on homogenization and defect-free processes to further improve the quality of continuously cast billets.

[0003] With the rapid development of industrialization, the use of square and round billets has increased, and their technical requirements have become increasingly stringent. For example, the speed increase of railway trains has placed higher demands on wheels and axles; the efficiency improvement of thermal power and nuclear power units has placed higher demands on steel pipes for steam generators; the development of the petroleum industry has placed higher demands on drilling tools and oil pipelines; the machinery manufacturing industry has placed higher demands on the strength, wear resistance and homogeneity of steel products; and the rise of the wind power industry requires high-quality steel under specific service conditions.

[0004] Segregation defects have been a pressing problem in continuous casting production. The main cause is that during solidification of molten steel, the solubility of the solute differs between the solid and liquid phases, leading to selective crystallization. This causes the solute to precipitate at the solidification front, increasing the solute concentration in the molten steel. Since the solute cannot fully diffuse in the liquid phase, a high-concentration segregation layer forms at the solidification front, resulting in segregation. Based on the scale and cause of segregation, it is generally classified into microsegregation and macrosegregation. Macrosegregation is generally considered one of the main defects in continuously cast billets, reducing the mechanical properties of the product. Macrosegregation in continuously cast billets can be further classified according to its manifestation, such as center segregation and V-shaped segregation. According to its formation type, it can be classified as segregation caused by bulging, segregation caused by interdendritic enrichment, segregation caused by bridging, and segregation caused by grain group cracking under solidification shrinkage.

[0005] The current understanding is that the formation mechanism of segregation in continuous casting is related to the enrichment of solute between dendrites, the flow of molten steel, grain sedimentation, and the morphology and structure of the solidification microstructure. Several research mechanisms are identified:

[0006] (1) Theory of solute precipitation and enrichment: During the solidification of molten steel, due to the influence of selective crystallization, some solute elements (such as C, P, S, Mn, etc.) will be discharged into the liquid phase while the dendrites grow. As the solidification process continues, the discharged solute elements will be enriched in the center of the billet, and the billet will form a central segregation after complete solidification.

[0007] (2) Solidification bridging theory: Under the combined effect of columnar crystal bridging phenomenon and molten steel solidification shrinkage in the later stage of solidification, the molten steel in the core of the billet will not be replenished by molten steel, thus forming the phenomenon of "small steel ingot solidification". This phenomenon will also cause shrinkage and porosity while causing central segregation and V-shaped segregation.

[0008] (3) Core suction theory: At the end of the billet solidification, under the action of steel solidification shrinkage and bulging, negative pressure or even cavities are generated in the core of the billet, thereby drawing the molten steel rich in solute between dendrites into the core for solidification. The solute content in the center of the billet is too high, resulting in V-shaped segregation. Firstly, V-shaped segregation of square and round billets is a kind of quality defect in the final continuously cast billet. According to the research mechanism, V-shaped segregation is caused by the equiaxed crystals slowing down at the end of solidification and gradually accumulating at the center line of the billet. The end linear electromagnetic stirrer can generate longitudinal electromagnetic force to push the equiaxed crystals at the end of solidification to move, thereby reducing the large accumulation of equiaxed crystals at the center line of the billet, thus solving the V-shaped segregation problem. However, the current technical difficulty lies in determining the installation position of the end linear electromagnetic stirrer and the intensity of its working current.

[0009] Currently, electromagnetic stirring technology is commonly used in continuous casting machines for round and square billets. This technology can significantly improve the surface and internal quality of continuously cast billets without altering the existing equipment. The essence of electromagnetic stirring technology is to pass a low-frequency current through the coil of an electromagnetic stirrer, generating a changing magnetic field. This changing magnetic field induces a current in the molten metal. The induced current interacts with the local magnetic field, generating a Lorentz force in the molten steel. This electromagnetic force drives the molten metal within the billet to flow, thereby altering the flow, heat transfer, and mass transfer processes during solidification, thus improving the quality of the billet. Currently, to address defects such as center segregation, V-shaped segregation, center porosity, and center shrinkage cavities in continuously cast billets, a solidification-end electromagnetic stirrer is typically installed on the continuous casting machine. This is a stirring device installed at the end of the solidification process (the mushy zone) of the molten steel. Currently, there are two main types of solidification-end electromagnetic stirrers: rotary stirrers and traveling wave linear stirrers. The molten steel at the end of solidification is generally in a "slurry" state, and the solidified billet shell is relatively thick. Therefore, the process requirements for the agitator at the end of solidification are higher, such as the agitator's stirring mode, the shape of the stirring coil, the arrangement of the magnetic poles, the installation position of the agitator, and the relationship between the electromagnetic parameters and the solid fraction within the continuously cast billet. Therefore, the current electromagnetic agitation technology at the end of solidification still has the following shortcomings:

[0010] (1) Because the electromagnetic stirrer at the end of solidification must stir the equiaxed crystal region in the paste region in order to improve the quality of the billet. If the installation position of the stirrer does not match the equiaxed crystal region in the paste region, it will lead to the obstruction of solute transport and further deterioration of the quality of the continuous casting billet.

[0011] (2) The rotary electromagnetic stirrer at the solidification end can only generate electromagnetic force acting on the tangential direction of the billet. Therefore, the range of action of this electromagnetic force is limited and cannot act on the molten steel in the entire end of the billet, and it is also easy to cause the formation of "bright white band".

[0012] (3) The electromagnetic stirrer at the solidification end is arranged in parallel with the billet. The electromagnetic induction and corresponding electromagnetic force generated in the billet decays quickly. It has limited ability to act on the molten steel at the center of the billet, resulting in a central dead zone and aggravated V segregation.

[0013] Due to the complex production process and the lack of internal visibility in continuous casting, it is difficult to clearly observe the formation process of V-shaped segregation through industrial experiments or laboratory methods. Furthermore, the presence of various external interference factors during experiments significantly reduces the accuracy and stability of the results. With the rapid development of computer technology and applications, especially the emergence of large-scale and very large-scale integrated circuits and microcomputers, new technologies such as computer-aided engineering, computer-aided design, and computer-aided manufacturing have developed rapidly. Among these, computer numerical simulation technology has been widely applied in various fields such as electronics, shipbuilding, aviation, aerospace, machinery, construction, and automobiles, becoming a technological tool with the greatest production potential, demonstrating a bright future and achieving significant economic benefits. Currently, numerical simulation research on flow, heat transfer, and mass transfer in continuous casting mainly involves establishing and solving the corresponding transport equations to obtain visualized analysis results of the metal solidification process. Numerical simulation has become an effective means of speculating on the formation mechanism of macrosegregation and studying techniques to control macrosegregation. Currently, the transport model for controlling macrosegregation during the solidification process of continuously cast billets is mainly the continuous medium model.

[0014] Although the continuous medium model has been widely used in the study of solidification calculations in continuous casting and has achieved significant results, this computer numerical simulation prediction method still has the following shortcomings:

[0015] (1) The continuous medium model has a large difference from the morphology of the continuous casting billet in actual production due to its oversimplified governing equations;

[0016] (2) The continuous medium model cannot simulate the effects of dendrite morphology, molten steel solidification feeding and bulging suction on macro segregation, frame segregation and V-shaped segregation during actual production process;

[0017] (3) The continuous medium model cannot take into account the effects of equiaxed grain settling, grain migration, grain proliferation and hot melt convection on segregation and the internal quality of the billet. Summary of the Invention

[0018] The technical problem to be solved by the present invention is to address the shortcomings of the prior art by providing a method for using a traveling wave linear electromagnetic stirrer to control V-shaped segregation in round billets. By applying electromagnetic stirring technology at the solidification end of the continuous casting machine and combining it with a computer numerical simulation prediction model, the location of V-shaped segregation in the pasty area at the solidification end of the continuous casting billet is accurately captured and the intensity of electromagnetic stirring is precisely controlled. This guides the elimination of V-shaped segregation in on-site production and maximizes the improvement of the internal quality of the continuous casting billet.

[0019] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: a method for using a traveling wave linear electromagnetic stirrer to control V-shaped segregation in round billets. An electromagnetic stirrer is installed at the solidification end of the continuous casting machine; the electromagnetic stirrer at the solidification end is a traveling wave linear electromagnetic stirrer; a numerical simulation prediction model of the linear electromagnetic stirring at the solidification end and the solidification growth of the continuously cast billet is constructed, consisting of an electromagnetic field calculation model of the traveling wave linear electromagnetic stirrer and a multiphase solidification physical model of continuous casting; the intensity of the linear electromagnetic stirring at the solidification end is determined by solving the electromagnetic field calculation model using numerical simulation; the time t0 at the installation location of the electromagnetic stirrer at the solidification end is obtained by solving the multiphase solidification physical model of continuous casting; based on the obtained time t0, the distance from the center of the electromagnetic stirrer to the crescent is calculated, thereby determining the installation position of the electromagnetic stirrer at the solidification end; finally, the billet shell thickness at the solidification end is calculated from the columnar crystal growth thickness and the equiaxed crystal growth thickness during the continuous casting process, thereby guiding the elimination of V-shaped segregation in on-site production and maximizing the improvement of internal quality defects in the continuously cast billet.

[0020] The time t0 when the equiaxed crystal slip velocity at the installation location of the electromagnetic stirrer at the end of solidification is 0 m / s is obtained by the following formula; and the distance L from the center position of the electromagnetic stirrer at the end of solidification to the meniscus is calculated based on the obtained time t0.

[0021] ;

[0022] ;

[0023] In the formula, v e D represents the equiaxed crystal slip velocity at the electromagnetic stirrer installation point at the end of solidification, and t represents the solidification time of the continuously cast billet; l The diffusion coefficient of the solute in the liquid phase; , These represent the equilibrium concentrations at the solid and liquid interfaces, respectively. , T is the temperature within the cell. f ρ is the melting point of pure metallic iron, m is the slope of the liquidus line; c l R represents the concentration of molten steel. e The radius of the equiaxed spherical crystal is V. casting is the casting speed of the continuous casting machine; k is the solute redistribution coefficient;

[0024] The shell thickness S of the continuously cast billet at the end of solidification is determined by the columnar crystal growth thickness S c With equiaxed crystal growth thickness S e The result of superposition is shown in the following formula:

[0025] ;

[0026] Among them, v c The growth rate of columnar crystals is obtained by the following formula;

[0027] ;

[0028] In the formula, R f R is the radius of the main columnar crystal. c λ is the radius of the columnar crystal tip; l is a constant; e is the logarithm of the base.

[0029] The governing equations of the electromagnetic field calculation model are as follows:

[0030] (1);

[0031] (2);

[0032] (3);

[0033] (4);

[0034] In the formula, B is the magnetic induction intensity; E is the electric field intensity; J is the current density vector; H is the magnetic field intensity of electromagnetic stirring; and D is the electric flux density. is the partial derivative with respect to time; q is the charge volume density;

[0035] Neglecting the effect of molten steel flow on the electromagnetic field, Ohm's law is simplified to:

[0036] (5);

[0037] In the formula, σ e Electrical conductivity;

[0038] The constitutive equation of equation (2) above is:

[0039] (6);

[0040] (7);

[0041] In the formula, μ is the magnetic permeability; ε is the dielectric constant;

[0042] In the numerical simulation of linear electromagnetic stirring at the end of solidification and the solidification growth of continuously cast billets, since the electromagnetic force is a vector, the real part of its complex vector, i.e., the average electromagnetic force F, is used. j Coupled with the physical model of multiphase solidification in continuous casting, the time-averaged electromagnetic stirring force F is calculated. j It can be obtained through the following formula:

[0043] (8);

[0044] (9);

[0045] In the formula, Re represents the real part of the complex number; is the real part of the current density vector;

[0046] The continuous casting multiphase solidification physical model consists of a columnar crystal growth model, an equiaxed crystal growth model, mass conservation, momentum conservation, solute conservation, energy conservation, and a V-shaped segregation back-diffusion mechanism.

[0047] In the columnar crystal growth model, the columnar crystal is defined as a cylinder growing perpendicular to the cooling wall and having a cone-like tip; firstly, the columnar crystal is restricted to a radius of R. f Grown within a cylindrical volume, R f It is derived from the geometric arrangement of crystals and the spacing of primary dendrites. If the crystals are arranged in an orderly manner, then... If the crystals are arranged in an alternating pattern, then Furthermore, considering that the cylinder exists independently, its internal mass and solute must be conserved, as shown in the following formula:

[0048] (10);

[0049] (11);

[0050] In the formula, ρ l ρ s ρ c The density of the liquid phase, solid phase, and columnar crystalline phase; f l f s f c c represents the volume fractions of the liquid phase, solid phase, and columnar crystalline phase. c This refers to the concentration of the solute in columnar crystals.

[0051] Furthermore, the mass of solute discharged into the molten steel during columnar crystal growth is equal to the change in the mass of solute in the molten steel, as shown in the following formula:

[0052] (12);

[0053] Therefore, the growth rate of columnar crystals is:

[0054] (13);

[0055] In the formula, W represents the growth rate of columnar crystals. c The cross-sectional area of ​​the columnar crystal; l l,c The initial length of the columnar crystals in the numerical simulation model is given; in the equiaxed crystal growth model, the equiaxed crystals are defined as movable spherical particles; therefore, the growth diameter of the equiaxed crystal spheres is determined by... The nucleation process of equiaxed crystals is obtained using a three-parameter homogeneous nucleation model, the specific expression of which is:

[0056] (14);

[0057] In the formula, N e d represents the equiaxed crystal nucleation rate; e f is the growth diameter of the equiaxed sphere; e n is the integral number of the equiaxed crystal; n is the grain density of the equiaxed crystal; n max ΔT represents the maximum nucleation density of equiaxed grains; ΔT is the undercooling degree of the molten steel; ΔT N ΔT represents the average nucleation undercooling. σ This represents the standard deviation of the grain distribution.

[0058] The mass conservation equations for the liquid phase, columnar phase, and equiaxed phase are as follows:

[0059] (15);

[0060] (16);

[0061] (17);

[0062] In the formula, u l u c u e These represent the migration velocities of molten steel, columnar crystalline phase, and equiaxed crystalline phase, respectively; M le M is the average interphase mass transport rate between the liquid phase and the equiaxed crystalline phase. lc M is the average interphase mass transport rate between the liquid phase and the columnar crystalline phase. ec The average mass transport rate between equiaxed and columnar crystals;

[0063] The momentum conservation equations for the liquid phase and the equiaxed crystalline phase are:

[0064] (18);

[0065] (19);

[0066] In the formula, ρ l ρ e ρ represents the density of the molten steel and the equiaxed phase, respectively; P represents the hydrostatic pressure of the molten steel. , These are the stress-strain tensors for the liquid phase and the equiaxed crystalline phase, respectively.

[0067] The solute conservation equations for the liquid phase, equiaxed crystalline phase, and columnar crystalline phase are as follows:

[0068] (20);

[0069] (twenty one);

[0070] (twenty two);

[0071] In the formula, c l c e c c These represent the solute concentrations in the liquid phase, equiaxed crystalline phase, and columnar crystalline phase, respectively; C le C is the average interphase solute transport rate between the liquid phase and the equiaxed crystalline phase. lc C represents the average interphase solute transport rate between the liquid phase and the columnar crystalline phase. ec The average solute transport rate between equiaxed and columnar crystals;

[0072] The energy conservation equations for the liquid phase, columnar crystalline phase, and equiaxed crystalline phase are as follows:

[0073] (twenty three);

[0074] (twenty four);

[0075] (25);

[0076] In the formula, h l h e h c These represent the enthalpy values ​​of the liquid phase, equiaxed crystalline phase, and columnar crystalline phase, respectively; k l k e k c T represents the thermal conductivity of the liquid phase, equiaxed crystalline phase, and columnar crystalline phase, respectively; l T e T c The temperature of the liquid phase, equiaxed crystalline phase, and columnar crystalline phase; Q le Q is the average interphase energy transfer rate between the liquid phase and the equiaxed crystalline phase. lc Q is the average interphase energy transfer rate between the liquid phase and the columnar crystalline phase. ecThe average energy transfer rate between the equiaxed and columnar crystal phases;

[0077] Calculating V-shaped segregation requires considering the back diffusion phenomenon between the solid and liquid phases. The back diffusion equation supplements the diffusion mechanism between the lever rule and the Scherrer rule, as shown in the following formula:

[0078] (26);

[0079] (27);

[0080] (28);

[0081] (29);

[0082] (30);

[0083] In the formula, γ is the diffusion coefficient between 0 and 1; α m To correct the Fourier number; α f λ is the Fourier number calculated at the local solidification time; λ2 is the distance of the secondary dendrite shoulder, t f Local solidification time; α c To enhance the anti-diffusion coefficient, the value is 0.1; D s T is the diffusion coefficient of the solute in the solid phase; m M is the local solidification temperature. l M is the average mass transfer rate between the liquid and solid phases. l =M le +M lc M S M is the average mass transfer rate between the solid and liquid phases. S =-M l .

[0084] The beneficial effects of adopting the above technical solution are as follows: The method of using a traveling wave linear electromagnetic stirrer to control V-shaped segregation in square and round billets provided by this invention addresses the issue that, due to the high viscosity, large flow resistance, and poor solidification feeding capacity of the molten steel at the solidification end region, defects such as center segregation, V-shaped segregation, and center shrinkage cavities are easily formed. Through a computer numerical simulation prediction model, the location of V-shaped segregation in the pasty region at the solidification end of the continuously cast billet is accurately captured, and the electromagnetic stirring intensity is precisely controlled. This guides the elimination of V-shaped segregation in on-site production, enabling better use of the end linear electromagnetic stirrer and maximizing the improvement of the internal quality of the continuously cast billet. Attached Figure Description

[0085] Figure 1 This is a schematic diagram showing the position of the electromagnetic stirrer at the solidification end installed on the round billet continuous casting machine provided in this embodiment;

[0086] Figure 2 This is a schematic diagram showing the position of the electromagnetic stirrer at the solidification end installed on the billet continuous casting machine provided in this embodiment;

[0087] Figure 3 This is a schematic diagram illustrating the elimination of V-shaped segregation using a double-sided stirring mode with a traveling wave linear electromagnetic stirring pattern at the solidification end, as provided in this embodiment.

[0088] Figure 4 This is a schematic diagram illustrating the elimination of V-shaped segregation using a single-sided stirring mode with a traveling wave linear electromagnetic stirring pattern at the solidification end, as provided in this embodiment.

[0089] In the diagram: 1. Submersible nozzle; 2. Crystallizer; 3. Traveling wave linear electromagnetic stirrer; 4. Round billet continuous casting machine; 5. Square billet continuous casting machine. Detailed Implementation

[0090] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0091] In this embodiment, a method for controlling V-shaped segregation in round billets using a traveling-wave linear electromagnetic stirrer is described. An electromagnetic stirrer is installed at the solidification end of the continuous casting machine. This electromagnetic stirrer at the solidification end is a traveling-wave linear electromagnetic stirrer. A numerical simulation prediction model of the solidification end linear electromagnetic stirring and the solidification growth of the continuously cast billet is constructed, consisting of an electromagnetic field calculation model of the traveling-wave linear electromagnetic stirrer and a multiphase solidification physical model of continuous casting. By solving the numerical simulation prediction model of the solidification end linear electromagnetic stirring and the solidification growth of the continuously cast billet, the location of V-shaped segregation in the pasty region at the solidification end of the continuously cast billet can be captured, and the intensity of the electromagnetic stirring can be precisely controlled. This guides on-site production to eliminate V-shaped segregation and maximize its effectiveness. To improve the internal quality of continuously cast billets, the following methods are employed: First, the intensity of linear electromagnetic stirring at the solidification end is determined by solving an electromagnetic field calculation model using numerical simulation. Then, the time t0 at the installation location of the electromagnetic stirrer at the solidification end is obtained by solving a multiphase solidification physical model of continuous casting. Based on this time t0, the distance between the center of the electromagnetic stirrer and the crescent moon is calculated, thus determining the installation position of the electromagnetic stirrer. Finally, the billet shell thickness at the solidification end is calculated from the columnar crystal growth thickness and the equiaxed crystal growth thickness during the continuous casting process. This guides the elimination of V-shaped segregation in on-site production, maximizing the improvement of internal quality defects in continuously cast billets.

[0092] The moment t0 when the equiaxed crystal slip velocity at the electromagnetic stirrer installation point at the end of solidification is 0 m / s (t0 is the equiaxed crystal slip velocity v) eThe time value corresponding to 0 m / s is obtained by the following formula; and the distance L from the center of the electromagnetic stirrer at the end of solidification to the meniscus is calculated based on the obtained time t0.

[0093] ;

[0094] ;

[0095] In the formula, v e D represents the equiaxed crystal slip velocity at the electromagnetic stirrer installation point at the end of solidification, and t represents the solidification time of the continuously cast billet; l The diffusion coefficient of the solute in the liquid phase; , These represent the equilibrium concentrations at the solid and liquid interfaces, respectively. , T is the temperature within the cell. f ρ is the melting point of pure metallic iron, m is the slope of the liquidus line; c l R represents the concentration of molten steel. e The radius of the equiaxed spherical crystal is V. casting is the casting speed of the continuous casting machine; k is the solute redistribution coefficient;

[0096] The shell thickness S of the continuously cast billet at the end of solidification is determined by the columnar crystal growth thickness S c With equiaxed crystal growth thickness S e The result of superposition is shown in the following formula:

[0097] ;

[0098] Among them, v c The growth rate of columnar crystals is obtained by the following formula;

[0099] ;

[0100] In the formula, R f R is the radius of the main columnar crystal. c λ is the radius of the columnar crystal tip; l is a constant; e is the logarithm of the base.

[0101] In this embodiment, the maximum value of the central magnetic induction intensity of the electromagnetic stirrer at the end of solidification is set to be no less than 0.08T when it is running under no-load; the working current of the electromagnetic stirrer at the end of solidification is 0~800A and the frequency is 0~10Hz; the maximum penetration depth of the electromagnetic force generated by the electromagnetic stirrer at the end of solidification is no less than 200mm.

[0102] The governing equations of the electromagnetic field calculation model are as follows:

[0103] (1);

[0104] (2);

[0105] (3);

[0106] (4);

[0107] In the formula, B is the magnetic induction intensity; E is the electric field intensity; J is the current density vector; H is the magnetic field intensity of electromagnetic stirring; and D is the electric flux density. is the partial derivative with respect to time; q is the charge volume density;

[0108] Neglecting the effect of molten steel flow on the electromagnetic field, Ohm's law is simplified to:

[0109] (5);

[0110] In the formula, σ e Electrical conductivity;

[0111] The constitutive equation of equation (2) above is:

[0112] (6);

[0113] (7);

[0114] In the formula, μ is the magnetic permeability; ε is the dielectric constant;

[0115] In the numerical simulation of linear electromagnetic stirring at the end of solidification and the solidification growth of continuously cast billets, since the electromagnetic force is a vector, the real part of its complex vector, i.e., the average electromagnetic force F, is used. j Coupled with the physical model of multiphase solidification in continuous casting, calculations are performed. Therefore, for time-harmonic electromagnetic fields, it is necessary to study the solidification and segregation process of molten steel under different electromagnetic stirring parameters, and the time-averaged electromagnetic stirring force F. j It can be obtained through the following formula:

[0116] (8);

[0117] (9);

[0118] In the formula, Re represents the real part of the complex number; is the real part of the current density vector;

[0119] The continuous casting multiphase solidification physical model consists of a columnar crystal growth model, an equiaxed crystal growth model, mass conservation, momentum conservation, solute conservation, energy conservation, and a V-shaped segregation back-diffusion mechanism.

[0120] In the columnar crystal growth model, the columnar crystal is defined as a cylinder growing perpendicular to the cooling wall and having a cone-like tip; firstly, the columnar crystal is restricted to a radius of R. f Grown within a cylindrical volume, R f It is derived from the geometric arrangement of crystals and the spacing of primary dendrites. If the crystals are arranged in an orderly manner, then... If the crystals are arranged in an alternating pattern, then Furthermore, considering that the cylinder exists independently, its internal mass and solute must be conserved, as shown in the following formula:

[0121] (10);

[0122] (11);

[0123] In the formula, ρ l ρ s ρ c The density of the liquid phase, solid phase, and columnar crystalline phase; f l f s f c c represents the volume fractions of the liquid phase, solid phase, and columnar crystalline phase. c This refers to the concentration of the solute in columnar crystals.

[0124] Furthermore, the mass of solute discharged into the molten steel during columnar crystal growth is equal to the change in the mass of solute in the molten steel, as shown in the following formula:

[0125] (12);

[0126] Therefore, the growth rate of columnar crystals is:

[0127] (13);

[0128] In the formula, W represents the growth rate of columnar crystals. c The cross-sectional area of ​​the columnar crystal; l l,c The initial length of the columnar crystals in the numerical simulation model is given; in the equiaxed crystal growth model, the equiaxed crystals are defined as movable spherical particles; therefore, the growth diameter of the equiaxed crystal spheres is determined by... The nucleation process of equiaxed crystals is obtained using a three-parameter homogeneous nucleation model, the specific expression of which is:

[0129] (14);

[0130] In the formula, N e d represents the equiaxed crystal nucleation rate; e f is the growth diameter of the equiaxed sphere; e n is the integral number of the equiaxed crystal; n is the grain density of the equiaxed crystal; n maxΔT represents the maximum nucleation density of equiaxed grains; ΔT is the undercooling degree of the molten steel; ΔT N ΔT represents the average nucleation undercooling. σ This represents the standard deviation of the grain distribution.

[0131] The mass conservation equations for the liquid phase, columnar phase, and equiaxed phase are as follows:

[0132] (15);

[0133] (16);

[0134] (17);

[0135] In the formula, u l u c u e These represent the migration velocities of molten steel, columnar crystalline phase, and equiaxed crystalline phase, respectively; M le M is the average interphase mass transport rate between the liquid phase and the equiaxed crystalline phase. lc M is the average interphase mass transport rate between the liquid phase and the columnar crystalline phase. ec The average mass transport rate between equiaxed and columnar crystals;

[0136] The momentum conservation equations for the liquid phase and the equiaxed crystalline phase are:

[0137] (18);

[0138] (19);

[0139] In the formula, ρ l ρ e ρ represents the density of the molten steel and the equiaxed phase, respectively; P represents the hydrostatic pressure of the molten steel. , These are the stress-strain tensors for the liquid phase and the equiaxed crystalline phase, respectively.

[0140] The solute conservation equations for the liquid phase, equiaxed crystalline phase, and columnar crystalline phase are as follows:

[0141] (20);

[0142] (twenty one);

[0143] (twenty two);

[0144] In the formula, c l c e c c These represent the solute concentrations in the liquid phase, equiaxed crystalline phase, and columnar crystalline phase, respectively; Cle C lc C ec Both represent the average solute transport rate between phases; C le C is the average interphase solute transport rate between the liquid phase and the equiaxed crystalline phase. lc C represents the average interphase solute transport rate between the liquid phase and the columnar crystalline phase. ec The average solute transport rate between equiaxed and columnar crystals;

[0145] The energy conservation equations for the liquid phase, columnar crystalline phase, and equiaxed crystalline phase are as follows:

[0146] (twenty three);

[0147] (twenty four);

[0148] (25);

[0149] In the formula, h l h e h c These represent the enthalpy values ​​of the liquid phase, equiaxed crystalline phase, and columnar crystalline phase, respectively; k l k e k c T represents the thermal conductivity of the liquid phase, equiaxed crystalline phase, and columnar crystalline phase, respectively; l T e T c The temperature of the liquid phase, equiaxed crystalline phase, and columnar crystalline phase; Q le Q lc Q ec Both represent the average energy transfer rate between phases, Q le Q is the average interphase energy transfer rate between the liquid phase and the equiaxed crystalline phase. lc Q is the average interphase energy transfer rate between the liquid phase and the columnar crystalline phase. ec The average energy transfer rate between the equiaxed and columnar crystal phases;

[0150] Calculating V-shaped segregation requires considering the back diffusion phenomenon between the solid and liquid phases. The back diffusion equation supplements the diffusion mechanism between the lever rule and the Scherrer rule, as shown in the following formula:

[0151] (26);

[0152] (27);

[0153] (28);

[0154] (29);

[0155] (30);

[0156] In the formula, γ is the diffusion coefficient between 0 and 1; α m To correct the Fourier number; α f λ is the Fourier number calculated at the local solidification time; λ2 is the distance of the secondary dendrite shoulder, t f Local solidification time (specifically, local solidification time refers to the time when the liquid steel is cooled and undergoes a solidification transition); α c To enhance the anti-diffusion coefficient, the value is 0.1; D s T is the diffusion coefficient of the solute in the solid phase; m This refers to the local solidification temperature (specifically, the temperature at the solid-liquid interface). M l M is the average mass transfer rate between the liquid and solid phases. l =M le +M lc M S M is the average mass transfer rate between the solid and liquid phases. S =-M l .

[0157] In this embodiment, the electromagnetic stirrer at the solidification end is installed on the round billet continuous casting machine at the following position: Figure 1 As shown, a traveling wave electromagnetic stirrer 3 is installed at the solidification end of the round billet continuous casting machine 4. Molten steel is injected into the crystallizer 2 from the submerged entry nozzle 1, undergoes a cooling process, and finally solidifies. The position of the electromagnetic stirrer at the solidification end on the square billet continuous casting machine is as follows: Figure 2 As shown, a traveling wave electromagnetic stirrer 3 is also installed at the solidification end of the billet continuous casting machine 5. The molten steel is injected into the crystallizer 2 from the submerged entry nozzle 1, and after cooling, the molten steel finally solidifies and forms the shape. The electromagnetic stirring at the solidification end of the round billet continuous casting machine and the square billet continuous casting machine can control the strong flow of molten steel in the liquid phase cavity of the billet through electromagnetic force, enhance the solidification feeding ability, promote solute diffusion, expand the equiaxed crystal zone of the continuous casting billet, eliminate V-shaped segregation and inclusions, and achieve the purpose of producing high-quality and high-grade steel products.

[0158] In this embodiment, Figure 3 and Figure 4 This diagram illustrates the use of linear electromagnetic stirring at the end of solidification to eliminate V-shaped segregation. The traveling-wave linear electromagnetic stirrer generates electromagnetic force that acts on the mushy region, increasing the migration speed of equiaxed crystals and enhancing the solute diffusion capacity during solidification. This eliminates V-shaped segregation and inclusions, improves the internal quality of the cast billet, and achieves the goal of producing high-quality, high-grade steel.

[0159] Figure 3 and Figure 4 The difference is that, Figure 3Enable dual-side stirring mode for the traveling wave linear electromagnetic stirrer. Figure 4 Enable single-sided stirring mode for the linear electromagnetic stirrer.

[0160] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the claims of the present invention.

Claims

1. A method of using a traveling magnetic field linear electromagnetic stirrer to control square billet V-segregation, characterized by: The electromagnetic stirrer is arranged at the solidification end of the continuous casting machine; the electromagnetic stirrer at the solidification end is a traveling wave linear electromagnetic stirrer; a numerical simulation prediction model of the linear electromagnetic stirring at the solidification end and the solidification growth of the continuous casting billet is constructed by an electromagnetic field calculation model of the traveling wave linear electromagnetic stirrer and a continuous casting multi-phase solidification physical model; the strength of the linear electromagnetic stirring at the solidification end is determined by solving the electromagnetic field calculation model; the time t0 value at which the slip velocity of the equiaxed crystal at the installation position of the electromagnetic stirrer at the solidification end is 0 m / s is obtained by solving the continuous casting multi-phase solidification physical model, and the distance between the center of the electromagnetic stirrer at the solidification end and the meniscus is calculated based on the time t0 value, so that the installation position of the electromagnetic stirrer at the solidification end is determined; finally, the shell thickness of the billet at the solidification end is calculated from the columnar crystal growth thickness and the equiaxed crystal growth thickness, so as to guide the elimination of V segregation and the maximization of the internal quality defects of the continuous casting billet in the field production.

2. A method of using a traveling wave linear electromagnetic stirrer to control square billet V-segregation according to claim 1, characterized in that: The time t0 at which the slip velocity of the equiaxed crystal at the installation position of the electromagnetic stirrer at the solidification end is 0 m / s is obtained by the following formula: ； where v e is the equiaxed crystal slip velocity at the installation of the solidification end electromagnetic stirrer, t is the solidification time of the continuous casting billet; D l is the liquid phase solute diffusion coefficient; , are the equilibrium concentrations at the solid-liquid interface, respectively, , T is the temperature in the unit cell, T f is the melting point of pure iron, m is the liquidus slope; c l is the concentration of the steel liquid; R e is the spherical radius of the equiaxed crystal; and k is the solute redistribution coefficient.

3. A method of using a traveling wave linear electromagnetic stirrer to control square billet V-segregation according to claim 2, characterized in that: The distance between the center position of the electromagnetic stirrer at the solidification end and the meniscus surface is shown in the following formula: ； where L is the distance from the center of the electromagnetic stirrer to the meniscus, V is the casting speed, and casting is the casting speed.

4. A method of using a traveling wave linear electromagnetic stirrer to control square billet V-segregation according to claim 3, characterized in that: The slab shell thickness of the continuously cast slab at the solidification end is given by the columnar crystal growth thickness S c and the equiaxed crystal growth thickness S e is added to give the following equation: ； where S is the shell thickness of the continuously cast billet at the end of solidification, v c is the columnar crystal growth rate, which is obtained from the following equation; ； wherein R f is the radius of the stem portion of the columnar crystal, R c is the radius of the tip portion of the columnar crystal; In is a constant and e is the base of the natural logarithm.

5. A method of using a traveling wave linear electromagnetic stirrer to control square billet V-segregation according to claim 4, characterized in that: The control equation of the electromagnetic field calculation model is as follows: (1)； (2)； (3)； (4)； where B is the magnetic induction; E is the electric field intensity; J is the current density vector; H is the magnetic field intensity of electromagnetic stirring; D is the electric flux density; is the partial derivative with respect to time; q is the charge density. The Ohm's law is simplified by ignoring the influence of the molten steel flow on the electromagnetic field as follows: (5)； where σ is the electrical conductivity; and e is the electrical conductivity; and The constitutive equation of the above formula (2) is as follows: (6)； (7)； In the formula, μ is the magnetic permeability; ε is the dielectric constant; In the numerical simulation of the end linear electromagnetic stirring and the solidification growth of continuous casting billets, since the electromagnetic force is a moment, the real part of the electromagnetic force vector complex is used, that is, the time-averaged electromagnetic stirring force F j The time-averaged electromagnetic stirring force F j is obtained by the following formula: (8)； (9)； where Re is the real part of the complex number; is the real part of the current density vector.

6. A method of using a traveling wave linear electromagnetic stirrer to control square billet V-segregation according to claim 5, wherein: The continuous casting multi-phase solidification physical model includes a columnar crystal growth model, an equiaxed crystal growth model, a mass conservation equation, a momentum conservation equation, a solute conservation equation and an energy conservation equation; In the columnar crystal growth model, the columnar crystal is defined as a cylinder growing perpendicular to the cooling wall and having a cone-like tip; firstly, the columnar crystal is restricted to a radius of R. f Grown within a cylindrical volume, R f It is derived from the geometric arrangement of crystals and the spacing of primary dendrites. If the crystals are arranged in an orderly manner, then... If the crystals are arranged in an alternating pattern, then Furthermore, considering that the cylinder exists independently, its internal mass and solute must be conserved, as shown in the following formula: (10)； (11)； wherein p l , p s , p c are the densities of the liquid, solid and columnar phases; f l , f s , f c are the volume fractions of the liquid, solid and columnar phases; c c is the columnar solute concentration; And the amount of solute discharged from the molten steel while the columnar crystal grows is equal to the change amount of the solute in the molten steel, as shown in the following formula: (12)； Thus, the columnar crystal growth rate is obtained as follows: (13)； wherein is the columnar crystal growth rate, W c is the columnar crystal cross-sectional area; l l,c is the columnar crystal initial length in the numerical simulation model; In the model of equiaxed grain growth, equiaxed grains are assumed to be movable spherical particles; therefore, the diameter of equiaxed grain spherical growth is obtained by The nucleation process of equiaxed grains adopts a three-parameter homogeneous nucleation model, and the specific expression is as follows: (14)； where N e is the rate of equiaxed crystal nucleation; d e is the diameter of equiaxed crystal globule growth; f e is the volume fraction of equiaxed crystals; n is the density of equiaxed crystal grains; n max is the maximum nucleation density of equiaxed grains; ΔT is the degree of undercooling of the liquid steel; ΔT N is the average nucleation undercooling; ΔT σ is the standard deviation of the grain distribution; The mass conservation equations of the liquid phase, the columnar crystal phase and the equiaxed crystal phase are as follows: (15)； (16)； (17)； wherein u l , u c , and u e are the velocities of the liquid steel, the columnar phase, and the equiaxed phase, respectively; M le is the average mass transfer rate between the liquid phase and the equiaxed phase, M lc is the average mass transfer rate between the liquid phase and the columnar phase, and M ec is the average mass transfer rate between the equiaxed phase and the columnar phase. The momentum conservation equations of the liquid phase and the equiaxed crystal phase are as follows: (18)； (19)； wherein ρ l , ρ e are the densities of the liquid steel and the equiaxed phase, respectively; P is the static pressure of the liquid steel; , are the stress-strain tensors of the liquid and equiaxed phases, respectively; The solute conservation equations of the liquid phase, the equiaxed crystal phase and the columnar crystal phase are as follows: (20)； (21)； (22)； wherein c l , c e , c c represent the solute concentration in the liquid phase, the equiaxed crystal phase, and the columnar crystal phase, respectively; C le is the average solute transfer rate between the liquid phase and the equiaxed crystal phase, C lc is the average solute transfer rate between the liquid phase and the columnar crystal phase, and C ec is the average solute transfer rate between the equiaxed crystal and the columnar crystal. The energy conservation equations of the liquid phase, the columnar crystal phase and the equiaxed crystal phase are as follows: (23)； (24)； (25)； wherein h l , h e , h c respectively represent the enthalpy of liquid phase, equiaxed crystal phase, and columnar crystal phase; k l , k e , k c respectively represent the thermal conductivity of liquid phase, equiaxed crystal phase, and columnar crystal phase; T l , T e , T c Tm is the temperature of the liquid phase, the equiaxed crystal phase, the columnar crystal phase; Q le Q is the average energy transmission rate between the liquid phase and the equiaxed crystal phase, Q lc Q is the average energy transmission rate between the liquid phase and the columnar crystal phase, Q ec Q is the average energy transmission rate between the equiaxed crystal phase and the columnar crystal phase.

7. A method of using a traveling wave linear electromagnetic stirrer to control square billet V-segregation according to claim 6, characterized in that: When calculating the V segregation, the continuous casting multi-phase solidification physical model needs to consider the back diffusion phenomenon between the solid and liquid phases, and a back diffusion equation is established; the back diffusion equation supplements the diffusion mechanism between the lever rule and the Scheil rule, as shown in the following formula: (26)； (27)； (28)； (29)； (30)； where γ is a diffusion coefficient between 0 and 1; α m is the Fourier number to be corrected; α f is the Fourier number to be calculated at the local solidification time; λ2is the distance of the secondary dendrite arm, t f is the local solidification time; α c is the enhanced counter-diffusion coefficient with a value of 0.1; D s is the diffusion coefficient of the solute in the solid phase; T m is the local solidification temperature; M l is the average mass transfer rate between liquid and solid phase, M l = M le + M lc ; M S is the average mass transfer rate between solid and liquid phase, M S = -M l .

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