Quantitative analysis method and device for casting blank macrosegregation changing along with casting parameters

Abstract

The invention relates to the technical field of square billet continuous casting in the ferrous metallurgical industry, and provides a quantitative analysis method and device for the change of casting billet macrosegregation along with casting parameter, the method comprises the following steps: taking a representative small volume unit from a small square billet, and deducing to obtain a macrosegregation expression at a certain position of the casting billet; establishing a two-dimensional solidification heat transfer model of the casting blank; calculating a solidification rate and a solid fraction value by using a two-dimensional solidification heat transfer model; and the solidification rate and the solid-phase fraction value are substituted into a macrosegregation expression, and macrosegregation values of different positions of the section of the small high-carbon steel square billet casting blank are obtained through calculation. In this way, quantitative calculation and analysis of the influence of different continuous casting parameters on the macrosegregation of the casting blank can be achieved, and a powerful tool is provided for accurate research and macrosegregation control.

Description

Technical Field

[0001] Embodiments of the present invention generally relate to the technical field of bloom continuous casting in the iron and steel metallurgy industry, and particularly to a method and device for quantitative analysis of the change of macrosegregation of cast billets with casting parameters. Background Art

[0002] Macrosegregation is a prominent problem affecting the homogeneity of high-carbon steel bloom. The macrosegregation inside the cast billet often cannot be eliminated through the heating and rolling processes, which is likely to lead to the precipitation of carbides and the formation of abnormal structures. During the processing of downstream products, failure problems caused by macrosegregation are extremely likely to occur. In order to improve production efficiency, continuous casting has become the main production method for high-carbon steel. Therefore, studying the macrosegregation problem of high-carbon steel during continuous casting has great practical significance. Currently, the influence of continuous casting parameters on macrosegregation is mainly studied through experiments, and there are few established theoretical quantitative analysis models. Therefore, the understanding of the influence of continuous casting parameters on macrosegregation is mainly a trend-based understanding, but no quantitative analysis of mathematical models has been formed. Summary of the Invention

[0003] To solve the above problems, the present invention realizes quantitative calculation and analysis of the influence of different continuous casting parameter conditions on the macrosegregation of cast billets by establishing a mathematical analysis model related to continuous casting process parameters.

[0004] According to an embodiment of the present invention, there are provided a method and device for quantitative analysis of the change of macrosegregation of cast billets with casting parameters.

[0005] In the first aspect of the present invention, there is provided a method for quantitative analysis of the change of macrosegregation of cast billets with casting parameters. The method includes:

[0006] Step 1: During the solidification process of the bloom molten steel continuous casting, a representative small volume unit is taken at the solidification front, and the macrosegregation expression at a certain position of the cast billet is derived through the law of conservation of mass and the law of conservation of solute.

[0007] Step 2: Taking the continuous casting billet produced by a specific continuous caster as the research object, a two-dimensional solidification heat transfer model of the cast billet is established by using the slicing method.

[0008] Step 3: Input the casting parameters of the actual casting process into the two-dimensional solidification heat transfer model, calculate the solidification rate at the solidification front of the cast billet by using the two-dimensional solidification heat transfer model, and calculate the solid fraction values corresponding to the positions where the solidification front moves to different positions of the cast billet based on the isotherm distribution of the cross-section of the cast billet at different time periods.

[0009] Step 4: Substitute the solidification rate and solid fraction values calculated by the solidification heat transfer model into the macrosegregation expression to calculate the macrosegregation values at different positions of the cross-section of the high-carbon steel bloom cast billet.

[0010] Furthermore, the macrosegregation expression described in step one is as follows:

[0011]

[0012] In the formula, S i is the macrosegregation value, In the formula, g s is the solid volume fraction, K is the solute distribution coefficient, β is the solidification shrinkage coefficient, ρ s is the solid density, ρ l is the liquid density, u is the solidification rate, v l,rel is the relative flow velocity of the liquid phase.

[0013] Furthermore, the small volume unit described in step one is used to reflect the multi-phase microstructure characteristics of the continuous casting billet solidification process; within this small volume unit, the volume fractions, temperatures, enthalpies, and concentrations of each phase are uniform, set as a constant and varying with time; within this small volume unit, solutes enter or leave the small volume unit through the relative movement of the liquid phase, and the influence of diffusion is not considered.

[0014] Furthermore, when establishing the two-dimensional solidification heat transfer model of the continuous casting billet in step two, the following assumptions are made for the model according to the actual production situation of the continuous casting process:

[0015] 1) The steel liquid surface in the mold is adiabatic and the liquid surface remains stable;

[0016] 2) The physical properties of steel are piecewise constants in the liquid state, the solid-liquid two-phase region, and the solid state, and are isotropic;

[0017] 3) The continuous casting billet is uniformly cooled in all directions in the same cooling section;

[0018] 4) To simplify the calculation process, it is assumed that the thermal conductivity of the solid phase region of the continuous casting billet is a function of temperature. At the same time, due to the convective movement of the molten steel in the liquid phase region, an equivalent thermal conductivity is used to characterize the enhanced heat transfer process in the liquid phase region;

[0019] 5) The heat transfer between the roll surfaces and the continuous casting billet surface in the pouring path is added to the convective heat transfer coefficient of the secondary cooling water by using the method of correction factors.

[0020] Furthermore, based on the assumptions made for the model, the two-dimensional Fourier heat transfer equation is used to calculate the continuous casting billet solidification process, and the equation is as follows:

[0021]

[0022] In this model, the latent heat of solidification is processed by the equivalent specific heat capacity method, that is, by amplifying the specific heat capacity to slow down the temperature change rate in this region and realizing the equivalent release of latent heat. The equivalent specific heat capacity of the two-phase region after processing is calculated by the following formula:

[0023]

[0024] Wherein, ρ is the density of the molten steel, kg·m -3 ; λ is the thermal conductivity of the molten steel, W·m -1 ·°C -1 ; c is the specific heat capacity of the steel, J·kg -1 ·°C -1 ; T is the temperature at a certain moment, °C; t is the time, s; x is the width direction of the slab, m; y is the thickness direction of the slab, m; T L is the liquidus temperature of the steel, °C; T S is the solidus temperature of the steel, °C; C S and C L are the specific heat capacities of the solid phase and liquid phase of the steel respectively, J·kg -1 ·°C -1 ; L f is the latent heat of solidification of the steel, kJ·kg -1 .

[0025] Furthermore, when calculating using the two-dimensional solidification heat transfer model in step three, the casting direction is regarded as adiabatic, and the boundary conditions mainly include the heat transfer processes on the wide and narrow faces of the slab, mainly including three parts: heat transfer in the mold, heat transfer in the secondary cooling zone, and heat transfer by air-cooled radiation.

[0026] Furthermore, in the mold stage of the slab, the average heat flux density in this stage can be calculated according to the measured cooling water volume in the mold and the temperature difference at the inlet and outlet. The calculation formula is as follows:

[0027]

[0028] The instantaneous heat flux density distributed along the casting direction in the mold, the calculation formula is as follows:

[0029]

[0030] Wherein, is the average heat flux density in the mold, W·m-2; q mold is the instantaneous heat flux density in the mold, W·m-2; ρ w is the density of the cooling water, kg·m-3; Q w is the cooling water flow rate in the mold, L·min-1; C w is the specific heat capacity of the cooling water, J·kg-1·°C-1; ΔT w is the temperature difference between the inlet and outlet water temperatures of the mold, °C; S eff is the effective contact area between the molten steel and the mold, m 2 ; L is the distance from the position of the required instantaneous heat flux density to the meniscus, m; L mis the effective length of the mold, m; ν is the casting speed of the billet, m·min -1 .

[0031] Furthermore, in the secondary cooling zone stage of the billet, the heat fluxes, heat flux densities and heat transfer coefficients of each zone are calculated through the heat transfer coefficient, and the formulas are as follows:

[0032] q sec = h(T b - T w )

[0033] h = α·W β + n

[0034] In the formula, q sec is the heat flux density on the surface of the billet in the secondary cooling zone, W·m -2 ; h is the convective heat transfer coefficient in the secondary cooling zone, W·m -2 ·°C -1 ; T b is the surface temperature of the billet, °C; T w is the cooling water temperature, °C; W is the water flow density, L·m -2 ·s -1 ; α, β, n are constants related to the equipment in the secondary cooling zone and are determined according to the actual production process.

[0035] The secondary cooling zone is divided into two types: full water cooling and mist cooling. The calculation formulas for the heat transfer coefficients of different cooling types are as follows:

[0036] Water cooling zone:

[0037] h = 420W 0.351 × η

[0038] Mist cooling zone:

[0039] h = 1570W 0.55 (1 - 0.0075T w )

[0040] In the formula, η is the coefficient related to the cooling roll and is adjusted according to the actual situation; h is the heat transfer coefficient.

[0041] Furthermore, in the air cooling zone stage of the billet, the heat transfer mainly occurs through the radiative heat transfer with the surrounding environment. The calculation formula for the heat flux density is as follows:

[0042] Q a = εσ[(T b + 273) 4 - (T a + 273) 4 )

[0043] In the formula, Q aq is the heat flux density, ε is the radiation coefficient with a value of 0.9; σ is the Stefan-Boltzmann constant with a value of 5.67×10 -8 , W·m -2 ·℃ -4 ; T b is the surface temperature of the continuous casting slab, in °C; T a is the ambient temperature, in °C.

[0044] In the second aspect of the present invention, there is provided an apparatus for quantitatively analyzing the change of macrosegregation of continuous casting slabs with casting parameters. The apparatus includes:

[0045] Macrosegregation expression derivation module: used to take a representative small volume unit at the solidification front during the continuous casting solidification process of small billet molten steel, and derive the macrosegregation expression at a certain position of the continuous casting slab through the law of conservation of mass and the law of conservation of solute;

[0046] Two-dimensional solidification heat transfer model establishment module: used to take the continuous casting slab produced by a specific continuous casting machine as the research object, and establish a two-dimensional solidification heat transfer model of the continuous casting slab by using the slicing method. The slice moves downward from the mold to the full roll zone, secondary cooling zone and air cooling zone in sequence;

[0047] Two-dimensional solidification heat transfer model calculation module: used to input the casting parameters of the actual casting process into the two-dimensional solidification heat transfer model, calculate the solidification rate at the solidification front of the continuous casting slab by using the two-dimensional solidification heat transfer model, and calculate the solid fraction values corresponding to different positions of the continuous casting slab when the solidification front moves to different positions based on the isothermal line distribution of the cross section of the continuous casting slab at different time periods;

[0048] Macrosegregation value calculation module: used to substitute the solidification rate and solid fraction values calculated by the solidification heat transfer model into the macrosegregation expression to calculate the macrosegregation values at different positions of the cross section of the small billet of high carbon steel continuous casting slab.

[0049] The present invention realizes the quantitative calculation and analysis of the influence of different continuous casting parameter conditions on the macrosegregation of continuous casting slabs by establishing a mathematical analysis model related to continuous casting process parameters.

[0050] It should be understood that the content described in the "Summary of the Invention" section is not intended to limit the key or important features of the embodiments of the present invention, nor is it used to limit the scope of the present invention. Other features of the present invention will become easily understood through the following description.

[0051] Advantages of the present invention:

[0052] 1. Establish a quantitative analysis model: By establishing a mathematical analysis model related to continuous casting process parameters, it is possible to achieve quantitative calculation and analysis of the influence of different continuous casting parameters on the macrosegregation of the billet, making up for the deficiency that the influence of previous continuous casting parameters on macrosegregation was mainly a trend understanding and lacked quantitative analysis by a mathematical model, and providing a powerful tool for accurately studying and controlling macrosegregation;

[0053] 2. Reflect the characteristics of the microstructure: The representative small volume unit (RVE) taken at the solidification front can fully reflect the multi-phase microstructure characteristics of the billet solidification process, enabling more accurate study of the relationship between macrosegregation and microstructure, and helping to deeply understand the formation mechanism of macrosegregation;

[0054] 3. Consider multiple factors comprehensively: The model takes into account various factors that cause relative movement of the liquid phase at the solidification front, such as solidification shrinkage, thermal shrinkage, and deformation under external force, and comprehensively analyzes the influence of these factors on macrosegregation, making the research results more in line with the actual production situation;

[0055] 4. Verification with actual production: By comparing with the actual production practice of 70 steel and its inspection results, the reliability and practical application value of the analysis model are verified, increasing the credibility and practical guiding significance of the model, and helping to apply the model to judge and control macrosegregation in actual production;

[0056] 5. Coupled multi-physics field calculation: A solidification heat transfer model is established to calculate the solidification rate and relative flow velocity. By considering the increase in liquid phase flow velocity caused by thermal shrinkage through a thermo-mechanical coupling model, it is possible to more accurately simulate the complex physical phenomena in the continuous casting process and provide more comprehensive information for the study of macrosegregation; BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In combination with the accompanying drawings and with reference to the following detailed description, the above and other features, advantages and aspects of the embodiments of the present invention will become more apparent. Among them:

[0058] Figure 1 Shows a method flow chart of quantitative analysis of the macrosegregation of a billet changing with pouring parameters according to an embodiment of the present invention;

[0059] Figure 2 Shows a schematic diagram of a slice of the solidification heat transfer model of a billet according to an embodiment of the present invention;

[0060] Figure 3 Shows a schematic diagram of the sampling position of the macrosegregation of a billet according to an embodiment of the present invention;

[0061] Figure 4 Shows a block diagram of a device for quantitative analysis of the macrosegregation of a billet changing with pouring parameters according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0062] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Apparently, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0063] According to the embodiments of the present invention, a method and device for quantitatively analyzing the macrosegregation of a continuous casting slab with the change of casting parameters are proposed. By establishing a mathematical analysis model related to continuous casting process parameters, quantitative calculation and analysis of the influence of different continuous casting parameter conditions on the macrosegregation of the continuous casting slab are realized.

[0064] The following elaborates on the principles and spirit of the present invention in detail with reference to several representative embodiments of the present invention.

[0065] Figure 1 It is a schematic flow chart of a method for quantitatively analyzing the macrosegregation of a continuous casting slab with the change of casting parameters according to an embodiment of the present invention. The method includes:

[0066] Step 1: During the solidification process of the small billet molten steel continuous casting, a representative small volume unit is taken at the solidification front, and the macrosegregation expression at a certain position of the continuous casting slab is derived through the law of conservation of mass and the law of conservation of solute.

[0067] Step 2: Taking the continuous casting slab produced by a specific continuous casting machine as the research object, a two-dimensional solidification heat transfer model of the continuous casting slab is established by using the slicing method.

[0068] Step 3: Input the casting parameters of the actual casting process into the two-dimensional solidification heat transfer model, calculate the solidification rate at the solidification front of the continuous casting slab by using the two-dimensional solidification heat transfer model, and calculate the solid fraction values corresponding to the positions where the solidification front moves to different positions of the continuous casting slab based on the isothermal line distribution of the cross-section of the continuous casting slab at different time periods.

[0069] Step 4: Substitute the solidification rate and solid fraction values calculated by the solidification heat transfer model into the macrosegregation expression to calculate the macrosegregation values at different positions of the cross-section of the small billet of high-carbon steel continuous casting slab.

[0070] It should be noted that although the operations of the method of the present invention are described in a specific order in the above embodiments and the accompanying drawings, this does not require or imply that these operations must be performed in this specific order, or that all the operations shown must be performed to achieve the desired result. Additionally or alternatively, some steps may be omitted, multiple steps may be combined into one step for execution, and / or one step may be decomposed into multiple steps for execution.

[0071] To provide a clearer explanation of the method for quantitatively analyzing the macrosegregation of the above-mentioned continuous casting billets with changes in casting parameters, the following will be described in conjunction with a specific embodiment. However, it should be noted that this embodiment is only for better explaining the present invention and does not constitute an improper limitation of the present invention.

[0072] The following will further illustrate in more detail the method for quantitatively analyzing the macrosegregation of continuous casting billets with changes in casting parameters by taking a specific example:

[0073] Step 1: During the continuous casting solidification process of small square billet molten steel, a representative small volume unit is taken at the solidification front, and the macrosegregation expression at a certain position of the continuous casting billet is derived through the law of conservation of mass and the law of conservation of solute.

[0074] Specifically, during the continuous casting solidification process of molten steel, as solidification progresses, solutes are continuously enriched in the solution at the solidification front. Due to reasons such as solidification shrinkage, thermal shrinkage, and deformation caused by external forces, relative movement occurs in the liquid phase at the solidification front, thereby forming macrosegregation in the continuous casting billet. To quantitatively analyze the influence of the relative movement of the enriched solution on macrosegregation, a representative small volume unit (RVE) is taken at the solidification front. On the one hand, this small unit can fully reflect the multiphase microstructure characteristics of the continuous casting billet solidification process. At the same time, within this small unit, the volume fractions, temperatures, enthalpies, and concentrations of the constituent phases are uniform and can be set as a constant that changes with time. In addition, solutes enter or leave the small unit through the relative movement of the liquid phase within this small unit, and the influence of diffusion is not considered.

[0075] For this representative volume unit, according to the law of conservation of mass, we have:

[0076]

[0077] In the formula, t is time, is the average density, ρ l is the liquid phase density, g l is the liquid phase volume fraction, v l,rel is the relative flow velocity of the liquid phase. Similarly, from the law of conservation of solute of the small unit, we have:

[0078]

[0079] In the formula, is the initial average solute concentration of the representative volume unit, C l represents the liquid phase solute concentration.

[0080] Expanding the above formula gives:

[0081]

[0082] Substituting Equation (3) into Equation (1) gives:

[0083]

[0084] The change in solute mass within the small unit is equal to the sum of the solute mass changes in the liquid and solid phases. Thus, the following equation can be obtained:

[0085]

[0086] where C s is the solute concentration in the solid phase, is the average concentration in the solid phase, ρ s is the density of the solid phase, g s is the volume fraction of the solid phase.

[0087] Since no gas phase is generated, then:

[0088] g s + g l = 1 (6)

[0089] Converting gives:

[0090] g s = 1 - g l (7)

[0091] Substituting Equation 7 into Equation (5), assuming the density of the solid phase is constant, and letting the solute partition coefficient After expanding Equation (5), the following can be obtained:

[0092]

[0093] From the relationship between the average density and the densities of each phase, it can be obtained that:

[0094]

[0095] Substituting Equation (9) into Equation (4) and combining it with Equation (8) gives:

[0096]

[0097] Let the solidification shrinkage coefficient and substitute g s = 1 - g l into Equation (10) to obtain:

[0098]

[0099] The temperature T within the unit can be expressed as:

[0100]

[0101] The above equation can be further expressed as:

[0102]

[0103] Wherein, represents the direction and distance of the isotherm moving in the x, y, and z directions, and can be expressed by the following formula:

[0104]

[0105] Wherein, is the vector component in the x direction, is the vector component in the y direction, is the vector component in the z direction.

[0106] Since the flow in the cross-sectional direction of the billet is much smaller than that in the casting speed direction, its solidification process can be equivalent to unidirectional solidification in the opposite direction of the casting direction. Therefore, only the casting x direction is considered here, and Equation (13) can be converted to:

[0107]

[0108] Since the temperature and liquid-phase solute concentration in the representative unit are uniform and change with time t, the following can be obtained:

[0109]

[0110] The above formula is transformed to:

[0111]

[0112] Let u be the solidification rate, and the negative sign indicates that the temperature gradient is opposite to the moving direction of the isotherm. At this time, horizontal heat transfer in the cross-section is not considered, and only the casting speed direction is considered. Therefore, it is assumed that the solidification direction is opposite to the casting speed direction, and the following can be obtained:

[0113]

[0114] Similarly, the moving speed of the isoconcentration line is the same as that of the isotherm, so the following can be obtained:

[0115]

[0116] Substituting Equation (19) into Equation (11) gives:

[0117]

[0118] Assume g s = 1 C is the initial average concentration of the small unit, and the above formula is integrated to obtain:

[0119]

[0120] It can be obtained through mass conservation that:

[0121] (ρ l g l v l,rel +ρ s g s v c ) = ρ s v c (22)

[0122] Transforming the above equation gives:

[0123]

[0124] Substituting Equation (23) into Equation (21) and letting The macroscopic segregation expression S at a certain position of the continuous casting slab i (where i represents the specific segregation element) can be expressed as:

[0125]

[0126] Step 2: Taking the continuous casting slab produced by a specific continuous caster as the research object, using the slicing method, a two-dimensional solidification heat transfer model of the slab is established. The slice moves downward from the mold to the full roller zone, secondary cooling zone, and air cooling zone in sequence.

[0127] Specifically, taking the continuous casting slab produced by a specific continuous caster as the research object, using MSC.Marc software, a geometric mathematical model is established. The width direction is selected as the x-axis, the thickness direction is the y-axis, and the casting direction is the z-axis.

[0128] To simplify the equations and boundary conditions while maintaining rationality, when establishing the solidification heat transfer model of the slab, the following assumptions are made for the model according to the actual production situation of the continuous casting process:

[0129] (1) The steel liquid surface in the mold is adiabatic and the liquid surface remains stable;

[0130] (2) The physical properties of steel are piecewise constants in the liquid state, solid-liquid two-phase region, and solid state, and are isotropic;

[0131] (3) The slab is uniformly cooled in all directions in the same cooling section;

[0132] (4) To simplify the calculation process, it is assumed that the thermal conductivity of the solid phase region of the slab is a function of temperature. At the same time, due to the convective motion of the molten steel in the liquid phase region, the equivalent thermal conductivity is used to characterize the enhanced heat transfer process in the liquid phase region;

[0133] (5) The heat transfer between the roll surfaces and the slab surface in the pouring path is added to the convective heat transfer coefficient of the secondary cooling water by using the method of correction coefficients;

[0134] Based on the above assumptions, the two-dimensional Fourier heat transfer equation is used to calculate the solidification process of the continuous casting slab, and the equation is as follows:

[0135]

[0136] In this model, the latent heat of solidification is treated by the equivalent specific heat capacity method, that is, in the form of enlarged specific heat capacity to slow down the temperature change rate in this area and realize the equivalent release of latent heat. The calculation formula of the equivalent specific heat capacity in the two-phase region after treatment is as follows:

[0137]

[0138] In the formula, ρ is the density of molten steel, kg·m -3 ; λ is the thermal conductivity of molten steel, W·m -1 ·°C -1 ; c is the specific heat capacity of steel, J·kg -1 ·°C -1 ; T is the temperature at a certain moment, °C; t is the time, s; x is the width direction of the continuous casting slab, m; y is the thickness direction of the continuous casting slab, m; T L is the liquidus temperature of steel, °C; T S is the solidus temperature of steel, °C; C S and C L are the specific heat capacities of the solid phase and liquid phase of steel respectively, J·kg -1 ·°C -1 ; L f is the latent heat of solidification of steel, kJ·kg -1 .

[0139] When t = 0, that is, at the beginning of casting, the temperature of the molten steel in the mold is equal to the casting temperature, that is, the measured value of the tundish temperature:

[0140] T t＝0 = T 中包 (27)

[0141] During the calculation process of the solidification model, the drawing direction is regarded as adiabatic, and the boundary conditions are mainly the heat transfer processes on the wide and narrow surfaces of the continuous casting slab, including three parts: heat transfer in the mold, heat transfer in the secondary cooling zone, and heat transfer in the air-cooling radiation zone.

[0142] During the mold stage of the continuous casting slab, the average heat flux density in this stage can be calculated according to the measured mold cooling water volume and the temperature difference at the inlet and outlet. The calculation formula is as follows:

[0143]

[0144] The calculation formula of the instantaneous heat flux density distributed along the casting direction in the mold is as follows:

[0145]

[0146] Wherein, is the average heat flux density in the mold, W·m-2; q mold is the instantaneous heat flux density in the mold, W·m-2; ρ w is the density of the cooling water, kg·m-3; Q w is the cooling water flow rate of the mold, L·min-1; C w is the specific heat capacity of the cooling water, J·kg-1·℃-1; ΔT w is the temperature difference between the inlet and outlet of the mold, ℃; S eff is the effective contact area between the molten steel and the mold, m 2 ; L is the distance from the position of the instantaneous heat flux density to be obtained to the meniscus, m; L m is the effective length of the mold, m; v is the casting speed of the slab, m·min -1 .

[0147] It is difficult to directly calculate the heat flux density value in the secondary cooling zone, but the heat flux of each zone can be calculated through the heat transfer coefficient. The calculation formulas for the heat flux density and the heat transfer coefficient are as follows:

[0148] q sec = h(T b - T w ) (31)

[0149] h = α·W β + n (32)

[0150] Wherein, q sec is the heat flux density on the surface of the slab in the secondary cooling zone, W·m -2 ; h is the convective heat transfer coefficient in the secondary cooling zone, W·m -2 ·℃ -1 ; T b is the surface temperature of the slab, ℃; T w is the temperature of the cooling water, ℃; W is the water flow density, L·m -2 ·s -1 ; α, β, n are constants related to the secondary cooling zone equipment and are determined according to the actual production process.

[0151] The secondary cooling zone is divided into two types: full water cooling (foot roll section) and spray cooling. The calculation formulas for the heat transfer coefficient of different cooling types are as follows:

[0152] Water cooling zone:

[0153] h = 420W 0.351 × η (33)

[0154] Spray cooling zone:

[0155] h = 1570W 0.55 (1 - 0.0075T w) (34)

[0156] In the formula, η is a coefficient related to the cooling roll and is adjusted according to the actual situation; h is the heat transfer coefficient.

[0157] In the air-cooled zone, heat transfer mainly occurs through radiation heat transfer with the surrounding environment. The calculation formula for the heat flux density is as follows:

[0158] Qa = εσ[(T b + 273) 4 - (T a + 273) 4 (35)

[0159] In the formula, Q a is the heat flux density, ε is the radiation coefficient with a value of 0.9; σ is the Stefan-Boltzmann constant with a value of 5.67×10 -8 , W·m -2 ·℃ -4 ; T a is the surface temperature of the slab, in °C; T a is the ambient temperature, in °C.

[0160] Adopt the "slicing method" to establish a two-dimensional solidification heat transfer model of the slab. Assume that the slice moves downward from the mold to the full roll zone, secondary cooling zone, and air-cooled zone in sequence. The schematic diagram of the model and mesh division is as Figure 2 shown.

[0161] In this embodiment, through the above method for establishing the solidification heat transfer model, the temperature change curves of different parts of the slab at different positions from the meniscus are obtained for 70 steel with a cross-section of 160×160mm 2 under the pouring conditions of a cooling intensity of 0.35 L / min and a casting speed of 2.0 m / min (33.33 mm / s). The chemical composition of 70 steel is tested as follows: 0.70 weight percentage of carbon C, 0.28 weight percentage of silicon Si, 0.55 weight percentage of manganese Mn, 0.008 weight percentage of phosphorus P, 0.006 weight ratio of sulfur S, and the rest is iron Fe.

[0162] Step 3: Input the pouring parameters of the actual pouring process into the two-dimensional solidification heat transfer model, calculate the solidification rate u of the solidification front of the slab using the two-dimensional solidification heat transfer model, and calculate the corresponding solid fraction value g at the position where the solidification front moves to different positions of the slab based on the isothermal line distribution of the slab cross-section at different time intervals s .

[0163] In this embodiment, Figure 3It is a schematic diagram of the sampling positions for the macrosegregation of the continuous casting billet. Under the above pouring conditions calculated according to the solidification heat transfer model, the cross-sectional temperature distribution curves corresponding to different positions where the solidification front moves to the vertical line at the center of the cross-section of the continuous casting billet are obtained. The solidification rate u and the solid fraction g corresponding to different positions are calculated. s , and the specific calculated values are shown in Table 1.

[0164] Table 1

[0165] Position from the slab surface Solidification rate u (mm / s) <![CDATA[Solid fraction g s > 5 mm 0.367 0.121 40 mm 0.136 0.732 78 mm 1.189 0.996

[0166] Step 4: Substitute the solidification rate u and the solid fraction value g calculated by the solidification heat transfer model s into the expression of the macrosegregation value S i to calculate the macrosegregation values at different positions of the cross-section of the small bloom of high-carbon steel.

[0167] In this embodiment, according to the actual drawing speed (33.33 mm / s) during the pouring process of the small bloom, the solid fraction g at different positions s , the solidification rate u of the solidification front at different positions, and the distribution coefficient K of carbon element (for 70 high-carbon steel, K is taken as 0.34 here) are substituted into Equation (24) to calculate the macro carbon segregation index S corresponding to different positions on the vertical line at the center of the cross-section of the continuous casting billet under the above pouring conditions. C , and the specific calculated values are shown in Table 2.

[0168] Table 2

[0169]

[0170] In this embodiment, the drill chip detection method is used to detect the macrosegregation of carbon element at specific positions of the continuous casting billet. The diameter of the drill bit used is 5 mm. The cross-sectional sample of the continuous casting billet is drilled with this drill bit, and the obtained steel chips are chemically analyzed for the C element content by using a Leco carbon analyzer (Leco CS744). The macrosegregation index of carbon is defined as Ci / Co, where Ci is the carbon content of the drill sample at a specific sample position and Co is the carbon content measured in the molten steel in the tundish. The measured macrosegregation values of carbon element are shown in Table 2. It can be seen from the comparison between the calculated values and the measured values of the macrosegregation of carbon element at different positions of the continuous casting billet that the deviation between the two is within 1%, which further confirms the reliability and applicability of the above quantitative calculation method.

[0171] Based on the same inventive concept, the present invention also provides a device for quantitative analysis of the change of macrosegregation of continuous casting billet with pouring parameters. The implementation of this device can refer to the implementation of the above method, and the repeated parts will not be described again.

[0172] As Figure 4 shown, this device 100 includes:

[0173] Macrossegregation Expression Deduction Module 101: It is used to take a representative small volume unit at the solidification front during the continuous casting solidification process of billet molten steel, and deduce the macrossegregation expression at a certain position of the casting blank through the law of conservation of mass and the law of conservation of solute;

[0174] Two-dimensional Solidification Heat Transfer Model Establishment Module 102: It is used to take the continuous casting blank produced by a specific continuous casting machine as the research object, and establish a two-dimensional solidification heat transfer model of the casting blank by using the slicing method;

[0175] Two-dimensional Solidification Heat Transfer Model Calculation Module 103: It is used to input the pouring parameters of the actual pouring process into the two-dimensional solidification heat transfer model, calculate the solidification rate at the solidification front of the casting blank by using the two-dimensional solidification heat transfer model, and calculate the solid fraction values corresponding to the positions where the solidification front moves to different positions of the casting blank according to the isothermal line distribution of the cross-section of the casting blank at different time periods;

[0176] Macrossegregation Value Calculation Module 104: It is used to substitute the solidification rate and solid fraction values calculated by the solidification heat transfer model into the macrossegregation expression, and calculate the macrossegregation values at different positions of the cross-section of the high-carbon steel billet casting blank.

[0177] The device for quantitative analysis of the change of the macrossegregation of the casting blank with the pouring parameters proposed by the present invention realizes the quantitative calculation and analysis of the influence of different continuous casting parameter conditions on the macrossegregation of the casting blank by establishing a mathematical analysis model related to the continuous casting process parameters.

[0178] Although the spirit and principle of the present invention have been described with reference to several specific embodiments, it should be understood that the present invention is not limited to the specific embodiments disclosed, and the division of each aspect does not mean that the features in these aspects cannot be combined for benefit. This division is only for the convenience of expression. The present invention aims to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.

[0179] Regarding the limitations on the protection scope of the present invention, those skilled in the art should understand that based on the technical solutions of the present invention, various modifications or deformations that can be made by those skilled in the art without creative labor are still within the protection scope of the present invention.

Claims

1. A method for quantitatively analyzing the macroscopic segregation of a continuous casting billet with changes in casting parameters, characterized in that, The method includes: Step 1: During the continuous casting solidification process of small billet molten steel, a representative small volume unit is taken at the solidification front, and the macroscopic segregation expression at a certain position of the billet is derived through the law of conservation of mass and the law of conservation of solute; Step 2: Taking the continuous casting billet produced by a specific continuous caster as the research object, a two-dimensional solidification heat transfer model of the billet is established by using the slicing method; Step 3: Input the pouring parameters of the actual pouring process into the two-dimensional solidification heat transfer model, calculate the solidification rate at the solidification front of the billet by using the two-dimensional solidification heat transfer model, and calculate the solid fraction values corresponding to the positions where the solidification front moves to different positions of the billet based on the isotherm distribution of the billet cross-section at different time periods; Step 4: Substitute the solidification rate and solid fraction values calculated by the solidification heat transfer model into the macroscopic segregation expression, and calculate the macroscopic segregation values at different positions of the cross-section of the high-carbon steel small billet.

2. The method for quantitative analysis of the change of the macroscopic segregation of the continuous casting billet with the casting parameters according to claim 1, characterized in that The macroscopic segregation expression described in Step 1 is: In the formula, S i is the macroscopic segregation value, In the formula, g s is the solid volume fraction, K is the solute distribution coefficient, β is the solidification shrinkage coefficient, ρ s is the solid density, ρ l is the liquid density, u is the solidification rate, v l,rel is the relative flow velocity of the liquid phase.

3. The method for quantitative analysis of the change of the macroscopic segregation of the continuous casting billet with the casting parameters according to claim 1, characterized in that, The small volume unit described in Step 1 is used to reflect the multi-phase microstructure characteristics of the billet solidification process; the volume fractions, temperatures, enthalpies, and concentrations of each phase in this small volume unit are uniform, set as a constant and varying with time; within this small volume unit, solutes enter or leave the small volume unit through the relative movement of the liquid phase, and the influence of diffusion is not considered.

4. The method for quantitative analysis of the change of the macrosegregation of the casting blank with the casting parameters according to claim 1, characterized in that When establishing the two-dimensional solidification heat transfer model of the billet in Step 2, the following assumptions are made for the model according to the actual production situation of the continuous casting process: 1) The molten steel surface in the mold is adiabatic and the liquid surface remains stable; 2) The physical properties of steel are piecewise constants in the liquid state, the solid-liquid two-phase region, and the solid state, and are isotropic; 3) The billet is cooled uniformly in all directions in the same cooling section; 4) To simplify the calculation process, it is assumed that the thermal conductivity of the solid phase region of the billet is a function of temperature. At the same time, due to the convective motion of the molten steel in the liquid phase region, the equivalent thermal conductivity is used to characterize the enhanced heat transfer process in the liquid phase region; 5) The heat transfer between the rolls and the billet surface in the pouring path is added to the convective heat transfer coefficient of the secondary cooling water by using the method of correction coefficient.

5. The quantitative analysis method for the change of the macroscopic segregation of the continuous casting slab with the casting parameters according to claim 4, characterized in that, Based on the assumptions made for the model, the two-dimensional Fourier heat transfer equation is used to calculate the billet solidification process, and the equation is as follows: In this model, the latent heat of solidification is processed by the equivalent specific heat capacity method, that is, in the form of an enlarged specific heat capacity to slow down the temperature change rate in this region and realize the equivalent release of latent heat. The equivalent specific heat capacity of the two-phase region after processing is calculated by the following formula: Where ρ is the density of the molten steel, kg·m -3 ; λ is the thermal conductivity of the molten steel, W·m -1 ·℃ -1 ; c is the specific heat capacity of the steel, J·kg -1 ·℃ -1 ; T is the temperature at a certain moment, °C; t is the time, s; x is the width direction of the slab, m; y is the thickness direction of the slab, m; T L is the liquidus temperature of the steel, °C; T S is the solidus temperature of the steel, °C; C S and C L are the specific heat capacities of the solid phase and the liquid phase of the steel respectively, J·kg -1 ·℃ -1 ; L f is the latent heat of solidification of the steel, kJ·kg -1 .

6. The method for quantitative analysis of the macroscopic segregation of a continuous casting billet varying with casting parameters according to claim 1, characterized in that, When calculating by using the two-dimensional solidification heat transfer model described in Step 3, the casting direction is regarded as adiabatic, and the boundary conditions are mainly the heat transfer processes of the wide and narrow faces of the billet, including three parts: mold heat transfer, secondary cooling zone heat transfer, and air-cooled radiation zone heat transfer.

7. The method for quantitative analysis of the change of slab macrosegregation with casting parameters according to claim 6, characterized in that In the mold stage of the billet, the average heat flux density in this stage can be calculated according to the measured mold cooling water volume and the temperature difference at the inlet and outlet, and the calculation formula is as follows: The instantaneous heat flux density distributed along the casting direction of the mold is calculated by the following formula: In the formula, is the average heat flux density in the mold, W·m-2; q mold is the instantaneous heat flux density in the mold, W·m-2; ρ w is the density of the cooling water, kg·m-3; Q w is the flow rate of the mold cooling water, L·min-1; C w is the specific heat capacity of the cooling water, J·kg-1·℃-1; ΔT w is the temperature difference between the inlet and outlet of the mold cooling water, ℃; S eff is the effective contact area between the molten steel and the mold, m 2 ; L is the distance from the position of the instantaneous heat flux density to be obtained to the meniscus, m; L m is the effective length of the mold, m; v is the casting speed of the slab, m·min -1 .

8. The method for quantitative analysis of the change of the macroscopic segregation of the continuous casting billet with the casting parameters according to claim 6, characterized in that, In the secondary cooling zone stage of the billet, the heat fluxes of each zone are calculated through the heat transfer coefficient, and the heat flux density and heat transfer coefficient are calculated as follows: q sec = h(T b - T w ) h = α·W β + n where q sec is the surface heat flux density of the billet in the secondary cooling zone, W·m -2 ; h is the convective heat transfer coefficient in the secondary cooling zone, W·m -2 ·℃ -1 ; T b is the surface temperature of the continuous casting slab, °C; T w is the cooling water temperature, °C; W is the water flow density, L·m -2 ·s -1 ; α, β, and n are constants related to the secondary cooling zone equipment and are determined according to the actual production process. The secondary cooling zone is divided into two types: full water cooling and aerosol cooling. The calculation formulas for the heat transfer coefficients of different cooling types are as follows: Water cooling zone: h = 420W 0.351 × η Aerosol cooling zone: h = 1570W 0.55 (1 - 0.0075T w ) In the formula, η is a coefficient related to the cooling roll and is adjusted according to the actual situation; h is the heat transfer coefficient.

9. The quantitative analysis method for the change of the macrosegregation of the continuous casting slab with the casting parameters according to claim 6, characterized in that During the air-cooling zone stage of the continuous casting slab, heat transfer mainly occurs through radiative heat transfer with the surrounding environment. The calculation formula for the heat flux density is as follows: Q a = εσ[(T b + 273) 4 -(T a + 273) 4 ​ Where Q A is the heat flux density, ε is the radiation coefficient with a value of 0.9; σ is the Stefan-Boltzmann constant with a value of 5.67×10 -8 , W·m -2 ·°C -4 ; T b is the surface temperature of the continuous casting billet, °C; T a is the ambient temperature, °C.

10. An apparatus for quantitatively analyzing the macrosegregation of a continuous casting slab with changes in casting parameters, characterized in that, The device implements the method described in claims 1-9, including: Macro-segregation expression derivation module: used to take a representative small volume unit at the solidification front during the continuous casting solidification process of small billet molten steel, and derive the macro-segregation expression at a certain position of the continuous casting slab through the law of conservation of mass and the law of conservation of solutes; Two-dimensional solidification heat transfer model establishment module: used to take the continuous casting slab produced by a specific continuous casting machine as the research object, and establish a two-dimensional solidification heat transfer model of the continuous casting slab using the slicing method; Two-dimensional solidification heat transfer model calculation module: used to input the pouring parameters of the actual pouring process into the two-dimensional solidification heat transfer model, calculate the solidification rate at the solidification front of the continuous casting slab using the two-dimensional solidification heat transfer model, and calculate the corresponding solid fraction values when the solidification front moves to different positions of the continuous casting slab based on the isotherm distribution of the continuous casting slab cross-section at different time periods; Macro-segregation value calculation module: used to substitute the solidification rate and solid fraction values calculated by the solidification heat transfer model into the macro-segregation expression to calculate the macro-segregation values at different positions of the cross-section of the high-carbon steel small billet continuous casting slab.

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