CN107657108B - Continuous casting billet macrosegregation prediction method - Google Patents
Continuous casting billet macrosegregation prediction method Download PDFInfo
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Abstract
The invention discloses a continuous casting billet macrosegregation prediction method, which is characterized by comprising the following steps: the method comprises the following steps: the method comprises the following steps of firstly, establishing a continuous casting solidification macrosegregation model to obtain the solute concentration distribution and temperature distribution condition in a continuous casting billet when the precipitation of inclusions is not considered; secondly, introducing an inclusion precipitation calculation model; according to the thermodynamic theory of impurity precipitation and the solute mass conservation law, calculating and obtaining the precipitation distribution condition of impurities in the casting blank, the solute consumption caused by impurity precipitation and the like; and thirdly, recalculating and correcting the solute concentration distribution calculated by the continuous casting macrosegregation model according to the solute concentration after the inclusion precipitation, and finally predicting and obtaining the solute macrosegregation distribution in the continuous casting blank considering the inclusion precipitation. The method for predicting the macrosegregation of the continuous casting billet has the advantages of lower cost and higher efficiency, and can more accurately predict the distribution condition of the macrosegregation of the solute in the continuous casting billet; the prediction result can be used for optimizing the continuous casting process and improving the quality of the continuous casting billet.
Description
Technical Field
The invention belongs to the field of control methods for continuous casting, solidification and molding of steel materials, and particularly relates to a continuous casting billet macrosegregation prediction method.
Background
The continuous casting billet is an initial steel product obtained by casting molten steel smelted by a steel smelting furnace through a continuous casting machine.
Segregation is the phenomenon that chemical components are not uniform in each part of the casting section and between crystal grains and grain boundaries after liquid alloy (molten steel) is solidified in a casting mold; segregation is an inherent characteristic of alloy solidification and is one of important quality defects of a continuous casting billet in the molten steel continuous casting process; it has a great influence on the service life and the service performance of the alloy product. There are three types of segregation: namely, intragranular segregation, macrosegregation and specific gravity segregation. Here, macrosegregation (also referred to as "region segregation") refers to a phenomenon in which each macro region in a metal ingot (casting or continuous casting) has a nonuniform chemical composition. Macrosegregation can cause inhomogeneities in the structure and properties of the ingot (casting or strand). Macrosegregation is related to many factors such as material nature, casting conditions and cooling conditions, and although it cannot be absolutely avoided, it should be controlled within a certain range so as to ensure the casting quality.
Currently, in the process of continuous casting: the method is characterized in that molten steel solidification solute enrichment (a phenomenon that the concentration of solute is increased in a local area of a casting blank due to nonuniform selective crystallization and diffusion of the solute) and segregation phenomena are generated, and numerous researchers carry out a series of researches on macrosegregation, microsegregation and influence factors of the continuous casting blank by means of numerical simulation, experiments and the like; and the process technologies such as soft reduction, electromagnetic stirring, secondary cooling mode and the like are found to be effective methods for improving the solute macrosegregation of the continuous casting billet.
However, the above studies on macrosegregation of continuous casting slabs still have disadvantages:
the influence of the inclusion precipitation on the solute macrosegregation in the above research is generally carried out by an experimental detection method, and the experimental detection method for researching the mutual influence of the inclusion precipitation and the solute segregation is generally high in cost and low in efficiency, and the distribution of the solute and the inclusions in the whole macrosegregation section of the continuous casting billet in the continuous casting process cannot be completely and specifically obtained.
Based on the above, the applicant considers and designs a continuous casting billet macrosegregation prediction method which has lower cost and higher efficiency, can accurately predict the precipitation condition of the inclusions in the continuous casting billet and obtains solute segregation distribution considering the precipitation of the inclusions.
Disclosure of Invention
Aiming at the defects of the prior art, the technical problems to be solved by the invention are as follows: provided is a method for predicting macrosegregation of a continuous casting slab, which is lower in cost and higher in efficiency, can predict precipitation of inclusions in the continuous casting slab, and can obtain a solute segregation distribution considering the precipitation of inclusions.
In order to solve the technical problems, the invention adopts the following technical scheme:
a macrosegregation prediction method for a continuous casting billet is characterized by comprising the following steps: the method comprises the following steps:
the method comprises the following steps of firstly, establishing a continuous casting solidification macrosegregation model to obtain the solute concentration distribution and temperature distribution condition in a continuous casting billet when the precipitation of inclusions is not considered;
secondly, introducing an inclusion precipitation calculation model based on the solute concentration distribution and the temperature distribution condition in the continuous casting billet in the first step; according to the thermodynamic theory of impurity precipitation and the solute mass conservation law, calculating and obtaining the precipitation distribution condition of impurities in the casting blank, the solute consumption caused by impurity precipitation and the like;
and thirdly, recalculating and correcting the solute concentration distribution obtained by calculating the continuous casting macrosegregation model in the first step according to the solute concentration after the inclusions are separated out based on the calculation result in the second step, and finally predicting and obtaining the solute macrosegregation distribution in the continuous casting blank considering the inclusions.
Preferably, in the second step, an inclusion precipitation calculation model is introduced based on the solute concentration distribution and the temperature distribution in the continuous casting billet in the first step; according to the inclusion precipitation thermodynamic theory and the solute mass conservation law, the method calculates and obtains the precipitation distribution condition of the inclusions in the casting blank, the consumption of the inclusions to the solute and the like, and finally predicts and obtains the solute macrosegregation distribution' in the continuous casting blank considering the inclusion precipitation, and comprises the following steps:
(1) determine whether impurities are separated out
Judging whether impurities in the continuous casting billet can be separated out or not by combining the obtained solute concentration distribution and temperature distribution in the continuous casting billet based on the thermodynamic theoretical basis of impurity separation;
the thermodynamic judgment method for whether inclusions are precipitated is as follows:
the chemical reaction formula of the reactant or solute element M and N for generating the inclusion MN is as follows:
M+N＝MN
ΔGΘ＝A+BT
ΔG＝ΔGΘ+RTlnKMN
in the above formula,. DELTA.GΘThe standard gibbs free energy for chemical reaction to generate MN, and Δ G is the gibbs free energy for chemical reaction to generate MN, and the unit is: j/mol; t is the reaction temperature in K; omegaMAnd ωNConcentrations of reactants M and N, wt%, respectively; f. ofMAnd fNActivity interaction coefficients of reactants M and N, respectively; a isMNIs the activity of product MN; r is an ideal gas constant, 8.314J/(mol.K); a and B are constants whose values are determined by the particular chemical reaction;
calculating the solute concentration distribution and temperature distribution (i.e. omega) in the slab according to the "first stepM，ωNAnd T) is substituted into the Delta G calculation formula, and whether the inclusion MN at the corresponding position in the casting blank can be separated out can be judged; in the chemical reaction, when delta G is less than 0, the chemical reaction can occur and generate an inclusion MN; otherwise, the chemical reaction can not be carried out, and no inclusion MN is generated;
(2) amount of impurity precipitated, solute consumption, and solute concentration calculation after impurity precipitation
If the inclusion MN can be precipitated, the concentration of the solute element M, N after the precipitation of the MN is calculated as follows:
after the inclusion MN is separated out, the concentration of solute element M, N is equal to the equilibrium concentration of reactant M, N at the corresponding temperature; at this time, Δ G is 0, that is:
in the formula, ωM,ep、ωN,epRespectively at corresponding temperaturesEquilibrium concentration of solute M, N after lower inclusion MN precipitation; when the inclusion MN is separated out, the content of solute element M, N in the inclusion MN needs to be ensured to be stoichiometric ratio, namely:
according to the law of conservation of solute mass, there are:
ΔωM＝ωM-ωM,eq
ΔωN＝ωN-ωN,eq
ΔωMN＝ΔωM+ΔωN
ωM、ωNthe concentrations of the solutes M, N before the inclusions MN are precipitated, respectively; mM、MNRelative atomic masses of solute element M, N, respectively; delta omegaM、△ωNConsumption of solute M, N for inclusion precipitation, respectively; delta omegaMNAnd (4) for the precipitation amount of the inclusion MN, obtaining the precipitation distribution of the inclusion MN in the whole continuous casting billet in the continuous casting process according to the calculation result of the precipitation amount of the inclusion MN.
Preferably, the calculation result in the second step is: concentration Δ ω of solute M, N consumed by precipitation of inclusion MNM、△ωNAnd concentration ω of solute M, N after precipitation of inclusion MNM’、ωN’(i.e.,. omega.)M,ep、ωN,ep)；
And in the third step, recalculating the solute concentration distribution calculated by the continuous casting macrosegregation model according to the solute concentration after the inclusion precipitation based on the calculation result in the second step comprises correcting the solute concentration distribution calculated by the continuous casting macrosegregation model according to the calculated solute concentration result after the inclusion precipitation is considered, and finally predicting and obtaining the solute macrosegregation distribution in the continuous casting billet considering the inclusion precipitation.
Preferably, the step of establishing a continuous casting solidification macro-segregation model to obtain the solute concentration distribution and the temperature distribution in the continuous casting slab without considering the inclusion precipitation in the first step includes:
(1) establishing continuous casting macroscopic three-dimensional model
The continuous casting macroscopic three-dimensional model is used for coupling and calculating the flow, heat transfer solidification and solute element transmission phenomena of molten steel in a continuous casting billet in the continuous casting process, and finally obtaining the solute concentration distribution and temperature distribution conditions in the continuous casting billet;
the establishment of the continuous casting macroscopic three-dimensional model comprises the following parts: establishing a geometric model of a continuous casting blank, dividing meshes, selecting a control equation, and setting initial conditions and boundary conditions; wherein the control equations include a flow equation, a heat transfer solidification equation, and a solute transport equation;
setting the heat transfer boundary conditions of the continuous casting secondary cooling section continuous casting billet surface in the boundary conditions, wherein the water flow density distribution of the continuous casting billet surface is actually measured according to the arrangement of cooling nozzles in the actual continuous casting process, so that the heat flow density of each area of the continuous casting billet surface is calculated, and the heat flow density is loaded to the continuous casting billet surface in a continuous casting macroscopic three-dimensional model through a User Defined Function (UDF) to perform continuous casting billet solidification heat transfer calculation; due to the arrangement characteristics of nozzles and the cooling characteristics of a casting blank in the actual continuous casting process, the water flow density distribution on the surface of the continuous casting blank is not uniform, so that a plurality of cooling areas with different cooling strengths are formed on the surface of the casting blank; when the continuous casting macroscopical three-dimensional model is built, the difference of the cooling intensity of the surface of the casting blank is considered aiming at the setting of the heat transfer boundary condition of the surface of the continuous casting blank, and the surface of the casting blank is divided into a plurality of cooling areas according to the change of the cooling intensity, so that the heat transfer boundary condition of the continuous casting macroscopical three-dimensional model is more in line with the reality, and the accuracy of model calculation is improved.
(2) And performing analog simulation coupling calculation on the flowing, heat transfer and solute transfer behaviors in the continuous casting process based on the established continuous casting macroscopic three-dimensional model to obtain the solute concentration distribution and temperature distribution condition in the continuous casting blank when the inclusion precipitation is not considered.
Compared with the prior art, the method for predicting the macrosegregation of the continuous casting billet has the following beneficial technical effects:
1. the method for predicting the macrosegregation of the continuous casting billet considers the influence of the precipitation of the inclusions on the solute segregation (namely the precipitation of the inclusions consumes the concentration of the solute, so that the solute segregation is influenced), and the prediction result of the macrosegregation of the solute of the continuous casting billet is more accurate and reasonable.
The applicant finds out through research that: the solute concentration of the corresponding position of the casting blank can be reduced by the precipitation of the inclusions in the molten steel continuous casting solidification process, so that the segregation degree of the casting blank can be effectively inhibited. As shown in fig. 1, in the process of solidifying continuous casting molten steel, solute elements are segregated and enriched in a solidification two-phase region, and the concentration of the solute is increased; when the concentration of the solute reaches a certain range, impurities are separated out; after the impurities are precipitated, the solute concentration of the surrounding area of the impurities is correspondingly influenced and reduced, so that the solute concentration and the segregation distribution condition of the solidified casting blank are finally influenced.
Because, the applicant takes the findings in "1" above into consideration in the slab macrosegregation prediction method of the present invention: in the solidification process of the continuous casting billet, the segregation enrichment of solute at the solidification front of molten steel can promote the precipitation of inclusions, and the precipitation of the inclusions can cause the change of a solute concentration field in a corresponding area of the casting billet, so that the distribution of the solute in the solidification process of the continuous casting billet and the segregation condition of the solute of the continuous casting billet are influenced finally.
Therefore, the influence of impurity precipitation is fully considered in the segregation prediction process; and accurately predicting solute segregation behavior in the continuous casting molten steel solidification process by adopting a numerical simulation method to obtain the consumption of impurity precipitation caused by solute segregation enrichment in the molten steel solidification process on the solute concentration in the casting blank and the prediction result of the final solute segregation distribution of the macroscopic section of the continuous casting blank.
2. The method can obtain the influence of impurity precipitation on the macrosegregation of the solute and the final solute segregation distribution condition of the casting blank; according to the prediction result, the continuous casting production process system can be adjusted in time, so that the macrosegregation distribution of solutes in the continuous casting billet is improved, and finally the quality of the continuous casting billet is effectively controlled.
By adopting the prediction result of the continuous casting billet macrosegregation prediction method, the continuous casting production process system can be relatively adjusted to control the macrosegregation degree of the continuous casting billet, so that a continuous casting billet product meeting the quality requirement is obtained. The specific adjusting method can comprise the following steps: and adjusting the cooling water distribution of the secondary cooling section of the casting blank in the continuous casting process to control the solidification and cooling of the casting blank, so that the solidification path and the cooling time of the casting blank are changed, the concentration distribution, the temperature distribution and the precipitation distribution of inclusions in the casting blank are changed, and the macrosegregation distribution of solutes in the casting blank is finally improved, so that the quality of the casting blank is controlled.
3. Aiming at the molten steel multi-component system continuous casting process, the continuous casting billet macrosegregation prediction method establishes a continuous casting billet solute macrosegregation prediction model based on the continuous casting molten steel solidification and cooling process and considering inclusion precipitation; the prediction model specifically comprises a continuous casting macroscopical three-dimensional model for coupling flow, heat transfer solidification and solute transfer and an inclusion precipitation calculation model. According to the prediction model, the interaction relation between solute segregation enrichment and inclusion precipitation in the molten steel solidification and cooling process is researched and analyzed, and the distribution rule of the inclusions and the solute segregation on the whole continuous casting blank macroscopic section is finally obtained through prediction. The method for predicting the macrosegregation of the continuous casting billet has the characteristics of low cost and high efficiency.
4. The prediction method of the invention shows that the precipitation of the inclusions is beneficial to inhibiting and reducing the macrosegregation of solute, so that the distribution of solute elements on the macrosegregation section of the casting blank is more uniform. In addition, the prediction method of the present invention can obtain a macroscopic precipitation distribution of inclusions in the cast slab.
Drawings
FIG. 1 is a schematic diagram of solute segregation enrichment and inclusion precipitation in a continuous casting process.
FIG. 2 is a schematic flow chart of the method for predicting macrosegregation of a continuous casting slab.
FIG. 3(a) is a graph showing the concentration distribution of solute Mn in the center longitudinal section (width direction) of the slab, irrespective of the precipitation of MnS inclusions.
FIG. 3(b) is a graph showing the distribution of the concentration of solute Mn in the center longitudinal section (width direction) of a slab in consideration of the precipitation of MnS inclusions using the method for predicting macrosegregation of a slab according to the present invention.
FIG. 3(c) is a graph showing the concentration distribution of solute S on the center longitudinal section (width direction) of the slab, without considering the precipitation of MnS inclusions.
FIG. 3(d) is a graph showing the concentration distribution of solute S on the center longitudinal section (width direction) of the slab in consideration of MnS inclusion precipitation by the method for predicting macrosegregation of a slab according to the present invention.
Fig. 4 considers the influence of precipitation of MnS inclusions on the concentration distribution of solute S, Mn on the center line (width direction) of an ingot (a) solute S and (b) solute Mn.
FIG. 5 is a diagram showing a MnS inclusion precipitation distribution on a central longitudinal section (width direction) of a continuous casting slab by using the macrosegregation prediction method of the continuous casting slab of the invention.
FIG. 6 shows the distribution of MnS inclusion precipitation amount on the casting slab center line (width direction).
Detailed Description
The technical solution of the present invention is explained in detail below:
a macrosegregation prediction method for a continuous casting billet comprises the following steps:
the method comprises the following steps of firstly, establishing a continuous casting solidification macrosegregation model to obtain the solute concentration distribution and temperature distribution condition in a continuous casting billet when the precipitation of inclusions is not considered;
secondly, introducing an inclusion precipitation calculation model based on the solute concentration distribution and the temperature distribution condition in the continuous casting billet in the first step; according to the thermodynamic theory of impurity precipitation and the solute mass conservation law, calculating and obtaining the precipitation distribution condition of impurities in the casting blank, the solute consumption caused by impurity precipitation and the like;
and thirdly, recalculating the solute concentration distribution obtained by calculating the corrected continuous casting macrosegregation model according to the solute concentration after the inclusion precipitation based on the calculation result in the second step, and finally predicting and obtaining the solute macrosegregation distribution in the continuous casting blank considering the inclusion precipitation.
Because segregation is a common quality defect in continuous casting billets, severe macrosegregation will affect the mechanical properties and service life of steel, and increase production cost. In the process of solidifying the continuous casting molten steel, solute elements are segregated and enriched at the solidification front, and when the concentration of the solute elements at the solidification front reaches a certain degree and meets the inclusion precipitation conditions, inclusions are precipitated in the process of solidifying the molten steel; the precipitation of the inclusions influences the solute concentration distribution of the continuous casting blank and the final distribution of the macrosegregation of the casting blank.
Therefore, when the macrosegregation prediction method of the continuous casting billet simulates and predicts the macrosegregation of the solute of the continuous casting billet, the factors of impurity precipitation are considered, and the prediction result is more accurate and reasonable; the prediction result can be used for optimizing the continuous casting process and improving the quality of the continuous casting billet.
Wherein, the step of establishing a continuous casting solidification macrosegregation model to obtain the solute concentration distribution and temperature distribution condition in the continuous casting billet when the inclusion precipitation is not considered comprises the following steps:
(1) continuous casting macroscopic three-dimensional model established by using Fluent software
The continuous casting macroscopic three-dimensional model is used for coupling and calculating the flow, heat transfer solidification and solute element transmission phenomena of molten steel in a continuous casting billet in the continuous casting process, and finally obtaining the solute concentration distribution and temperature distribution in the continuous casting billet;
the establishment of the continuous casting macroscopic three-dimensional model comprises the following parts:
a. establishing continuous casting billet geometric model and mesh division
Adopting computer aided engineering software (when in implementation, the computer aided engineering software can adopt ICEM software) to establish a continuous casting billet geometric dimension model, and carrying out structured grid division on the continuous casting billet geometric dimension model; (Fluent software considers each calculation grid as a calculation unit and carries out analog simulation calculation of corresponding continuous casting process aiming at each calculation unit)
b. Selection of control equations
The control equation comprises a flow equation, a heat transfer solidification equation and a solute transport equation, and specifically comprises the following steps:
(a) equation of flow
In the continuous casting process, the flow of the molten steel is controlled through a continuity equation; the continuity equation, mass conservation equation, which expresses that the difference in the mass of fluid flowing into and out of the control body per unit time is equal to the change in mass in the control body due to the change in density, is as follows:
the equation of momentum is expressed as follows:
SBis a source of hot solute buoyancy, SPIs a velocity source term; the expressions are respectively:
CL,m,0is the solute concentration at the temperature of the liquid phase, AmushyIs a constant of mushy zone, vpIs the pull rate, ε is a constant of 0.001; (continuous casting forced convection area molten steel mainly generates turbulent flow, the direct solution of a turbulent three-dimensional transient control equation is complex, and the turbulent characteristic is mainly reflected by a turbulent kinetic energy equation and a turbulent dissipation rate equation at present, so that the calculation process is simplified);
(b) heat transfer solidification equation
The heat transfer and solidification equations of the continuous casting billet are as follows:
h is the enthalpy of the material, λeffEffective thermal conductivity;
(c) equation of solute transport
The solute conservation equation for a solid-liquid system is expressed as:
Sdifand SC,conRespectively, a diffusion source item and a convection source item, wherein the expressions are respectively:
at the solid-liquid interface at the solidification front, a lever model is adopted for the micro distribution of solutes:
Cm＝fLCL,m+fSCS,m
CS,mand CL,mThe solute concentrations at the two sides of the solid phase and the liquid phase at the solidification front are respectively as follows:
description of the drawings: in the process of casting blank solidification, the casting blank solidification process is generally divided into three areas: an outer solid phase region, an intermediate two-phase region, an inner liquid phase region; the liquid phase → the two-phase region → the solid phase when the molten steel is solidified; the junction of the solid phase and the liquid phase is called a solidification front;
c. setting of initial conditions and boundary conditions
Introducing an additional condition and solving the additional condition through the control equation, wherein the additional condition is called a definite condition, and the definite condition comprises an initial condition and a boundary condition;
the initial condition is an initial state that the system should satisfy at an initial time; for a molten steel continuous casting system, the initial conditions comprise molten steel heat transfer, initial temperature, initial speed, initial solute concentration and the like of the whole casting blank region at the beginning of the flowing process, namely molten steel casting temperature, blank drawing speed, solute components, steel physical parameters and the like in the continuous casting process;
the boundary conditions include values of flow variables and thermal variables at boundaries, which refer to the laws of time and space variation of the variables or first derivatives thereof solved on the boundaries of the solution domain;
the boundary conditions of the macroscopic three-dimensional model are set as follows:
1) entry boundary condition
Molten steel flows into a casting blank (a crystallizer section) from a submerged nozzle, and the submerged nozzle is used as an inlet of a model; the mass conservation and the throwing speed are comprehensively considered at the molten steel inlet speed; estimating the turbulent kinetic energy and the dissipation rate of the turbulent energy at the water gap by using a semi-empirical formula; the mathematical expression is:
εinlet＝Cμ 3/4k3/2/l
2) free surface
A free surface, i.e. the casting mould meniscus; on this free surface, the gradient of all variables along the normal to the liquid surface is zero:
the velocity component perpendicular to the surface is set to zero:
ux,surface＝0
3) plane of symmetry
The setting of the boundary conditions of the symmetry plane is the same as for the free surface, i.e. the initial normal gradients of all variables on the symmetry plane are zero, the velocity component perpendicular to the symmetry plane is zero:
uy,symmetry＝0
uz,symmetry＝0
4) outlet boundary condition
The outlet of the model is positioned at the bottom of the casting blank calculation area; the flow field at the outlet can be considered to be fully developed and the normal gradient along the section is set to zero for all variables:
5) boundary condition of crystallizer wall surface
At the crystallizer wall, the velocity perpendicular to the wall is zero, and the velocity component parallel to the wall is determined by the wall function; the casting blank and the wall surface have no solute element transfer, namely the dissipation flux of each element on the wall of the crystallizer is zero;
6) boundary condition of heat transfer
In the process of solidifying and cooling continuous casting molten steel, the cooling strength of each area of a casting blank is determined by the heat flux density on the surface of the casting blank; when the model is set, the cooling intensity of the surface of each area of the crystallizer section of the continuous casting billet and each section of the secondary cooling is correspondingly set according to the actual continuous casting process;
setting the continuous casting secondary cooling continuous casting billet surface heat transfer boundary conditions in the boundary conditions needs to actually measure the surface water flow density distribution of the continuous casting billet according to the arrangement of cooling nozzles in the actual continuous casting process, so that the heat flow density of each area on the surface of the continuous casting billet is calculated, and the heat flow density is loaded to the surface of the continuous casting billet in a continuous casting macroscopic three-dimensional model through a User Defined Function (UDF) to perform solidification heat transfer calculation of the continuous casting billet. Due to the arrangement characteristics of nozzles and the cooling characteristics of a casting blank in the actual continuous casting process, the water flow density distribution on the surface of the continuous casting blank is not uniform, so that a plurality of cooling areas with different cooling strengths are formed on the surface of the casting blank; when the continuous casting macroscopical three-dimensional model is built, the difference of the cooling intensity of the surface of the casting blank is considered aiming at the setting of the heat transfer boundary condition of the surface of the continuous casting blank, and the surface of the casting blank is divided into a plurality of cooling areas according to the change of the cooling intensity, so that the heat transfer boundary condition of the continuous casting macroscopical three-dimensional model is more in line with the reality, and the accuracy of model calculation is improved.
(2) And performing analog simulation coupling calculation on the flowing, heat transfer and solute transfer behaviors in the continuous casting process based on the continuous casting macroscopical three-dimensional model established by using Fluent software to obtain the solute concentration distribution and temperature distribution in the continuous casting billet.
From the above, the continuous casting macroscopical three-dimensional model has all the contents: the establishment and grid division of the geometric model of the continuous casting billet, the selection of a control equation, and the setting of boundary conditions and initial conditions are all carried out by depending on Fluent software.
The Fluent software is a current international popular Commercial Fluid Dynamics (CFD) software, all phenomena related to fluid, heat transfer, chemical reaction and the like can be correspondingly simulated by using the Fluent software, has rich physical models, advanced numerical methods and powerful pre-and post-processing functions, and is widely applied to the aspects of aerospace, automobile design, metallurgy and chemical engineering and the like.
Introducing an inclusion precipitation calculation model based on the solute concentration distribution and the temperature distribution in the continuous casting slab in the first step in the second step; according to the inclusion precipitation thermodynamic theory and the solute mass conservation law, the method calculates and obtains the precipitation distribution condition of the inclusions in the casting blank, the consumption of the inclusions to the solute and the like, and finally predicts and obtains the solute macrosegregation distribution' in the continuous casting blank considering the inclusion precipitation, and comprises the following steps:
(1) determine whether impurities are separated out
Judging whether impurities in the continuous casting billet can be separated out or not by combining the obtained solute concentration distribution and temperature distribution in the continuous casting billet based on the thermodynamic theoretical basis of impurity separation;
the thermodynamic judgment method for whether inclusions are precipitated is as follows:
the chemical reaction formula of the reactant or solute element M and N for generating the inclusion MN is as follows:
M+N＝MN
ΔGΘ＝A+BT
ΔG＝ΔGΘ+RTlnKMN
in the above formula,. DELTA.GΘThe standard gibbs free energy for chemical reaction to generate MN, and Δ G is the gibbs free energy for chemical reaction to generate MN, and the unit is: j/mol; t is the reaction temperature in K; omegaMAnd ωNConcentrations of reactants M and N, wt%, respectively; f. ofMAnd fNActivity interaction coefficients of reactants M and N, respectively; a isMNIs the activity of product MN; r is an ideal gas constant, 8.314J/(mol.K); a and B are constants whose values are determined by the particular chemical reaction;
calculating the solute concentration distribution and temperature distribution (i.e. omega) in the slab according to the "first stepM，ωNAnd T) is substituted into the Delta G calculation formula, and whether the inclusion MN at the corresponding position in the casting blank can be separated out can be judged; in the chemical reaction, when delta G is less than 0, the chemical reaction can occur and generate an inclusion MN; otherwise, the chemical reaction cannot proceedAnd then MN is generated without impurities;
(2) amount of impurity precipitated, solute consumption, and solute concentration calculation after impurity precipitation
If the inclusion MN in a certain region in the casting blank meets the precipitation condition, namely can be precipitated, the consumption of solute element M, N for the precipitation of the inclusion MN and the concentration calculation method of solute element M, N after the precipitation of the inclusion MN are as follows:
after MN is separated out, the concentration of solute elements M, N in the area in the casting blank is equal to the equilibrium concentration of reactant M, N at the corresponding temperature; at this time, Δ G is 0, that is:
in the formula, ωM,ep、ωN,epRespectively is the equilibrium concentration of solute M, N after the inclusion MN is precipitated under corresponding temperature; when the inclusion MN is separated out, the content of solute element M, N in the inclusion MN needs to be ensured to be stoichiometric ratio, namely:
according to the law of conservation of solute mass, there are:
ΔωM＝ωM-ωM,eq
ΔωN＝ωN-ωN,eq
ΔωMN＝ΔωM+ΔωN
ωM、ωNthe concentrations of the solutes M, N in the regions in the casting blank before the separation of the inclusions MN are respectively determined; mM、MNRelative atomic masses of solute element M, N, respectively; delta omegaM、△ωNConsumption of solute M, N for inclusion MN precipitation, respectively; delta omegaMNFor the precipitation amount of the inclusion MN, the precipitation distribution of the inclusion MN in the whole continuous casting billet in the continuous casting process can be obtained according to the calculation result of the precipitation amount of the inclusion MN;
wherein, the first stepAnd on the basis of the calculation result in the second step, recalculating the solute concentration distribution calculated by the corrected continuous casting macrosegregation model according to the solute concentration after the inclusion precipitation, and finally predicting and obtaining the solute macrosegregation distribution in the continuous casting blank considering the inclusion precipitation, wherein the calculation step comprises the following steps: from the results of the second step, the concentration Δ ω of the solute M, N consumed by the precipitation of the inclusion MN is obtainedM、△ωNAnd concentration ω of solute M, N after precipitation of inclusion MNM’、ωN’(i.e.,. omega.)M,ep、ωN,ep) (ii) a The concentration of the solute M, N (i.e.,. omega.). omega. after the inclusion MN is precipitated is calculated according to the aboveM,ep、ωN,ep) And recalculating and correcting the solute concentration distribution calculated by the continuous casting macrosegregation model, and finally predicting and obtaining the solute macrosegregation distribution in the continuous casting blank considering inclusion precipitation.
The macrosegregation prediction method of the continuous casting slab of the invention is described below with reference to specific examples:
the continuous casting slab in this example was a high-sulfur steel slab in which precipitation of MnS inclusions was mainly observed.
A macrosegregation prediction method for continuous casting billets (a flow diagram is shown in figure 2), which comprises the following steps:
the method comprises the following steps of firstly, establishing a continuous casting solidification macrosegregation model to obtain the concentration distribution and temperature distribution rule of solute in a continuous casting billet when the precipitation of inclusions is not considered;
(1) continuous casting macroscopic three-dimensional model established by using Fluent software
a. Establishing continuous casting billet geometric model and mesh division
The width and thickness of the continuous casting slab is 1530 x 190mm, and only a quarter area of the continuous casting slab is calculated due to the symmetry of the continuous casting slab; after the grid division, there are 552385 grid computing units.
b. Establishing a governing equation
c. Setting initial conditions and boundary conditions
Initial conditions: the casting blank pulling speed is 1.0 m/mim; the initial temperature of the molten steel is 1811K; the molten steel mainly comprises elements C, Si, Mn, P, S and Fe, wherein the initial components Mn-1.38% and S-0.4%.
Boundary conditions: the heat transfer boundary condition of the surface of the continuous casting billet is that the heat flux density of each area on the surface of the continuous casting billet is calculated according to the water flow density distribution on the surface of the continuous casting billet obtained by actual measurement, and the heat flux density is loaded to the surface of the continuous casting billet in a three-dimensional model through a User Defined Function (UDF), so that the solidification heat transfer calculation is carried out.
(2) Based on the continuous casting macroscopical three-dimensional model established by using Fluent software, simulation coupling calculation is carried out on the flowing, heat transfer and solute transmission behaviors in the continuous casting process, and the solute concentration distribution in the continuous casting blank when the inclusion precipitation is not considered is obtained (as shown in fig. 3(a) and fig. 3 (c)).
Secondly, introducing an inclusion precipitation calculation model based on the solute concentration and temperature distribution result in the casting blank; according to the inclusion precipitation thermodynamic theory and the solute mass conservation law, the precipitation distribution rule of the inclusions in the casting blank, the consumption of the inclusions to the solute by precipitation and the like are calculated and obtained, so that the solute macrosegregation distribution in the continuous casting blank considering the inclusion precipitation is finally obtained by prediction:
(1) determine whether impurities are separated out
The thermodynamic judgment of whether the inclusion MnS is precipitated or not is based on the following:
when the concentrations of solutes Mn and S in corresponding regions in a casting blank exceed the MnS precipitation equilibrium concentration of inclusions in molten steel, MnS reacts and precipitates, and the precipitation standard Gibbs free energy is as follows:
ΔGΘ＝-165146+90.84T
based on the solute concentration and the temperature distribution obtained by the first-step macroscopic three-dimensional model calculation, whether inclusions MnS in corresponding regions in the casting blank are precipitated or not can be calculated and judged according to an inclusion precipitation calculation model;
(2) amount of impurity precipitated, solute consumption, and solute concentration calculation after impurity precipitation
Calculating the solute concentration and temperature distribution obtained by the first-step macroscopic three-dimensional model, and calculating the precipitation amount of the inclusions MnS in the corresponding region in the casting blank by combining an inclusion precipitation calculation model (according to the precipitation amount calculation result of the inclusions MnS, the precipitation distribution of the inclusions MnS in the whole continuous casting blank in the continuous casting process can be obtained), the consumption of the inclusions Mn and S due to the precipitation of the inclusions MnS, and the concentrations of the solutes Mn and S in the corresponding region in the casting blank after the inclusions MnS are precipitated;
and thirdly, recalculating the solute concentration distribution obtained by correcting the calculation of the continuous casting macrosegregation model according to the solute concentration after the inclusion precipitation based on the calculation result in the second step, and finally predicting and obtaining the solute macrosegregation distribution in the continuous casting blank considering the inclusion precipitation:
according to the result of the second step, the concentrations of Mn and S consumed by the precipitation of MnS inclusions are obtainedMn、△ωSAnd the concentrations of Mn and S in the solute after MnS inclusion precipitationMn’、ωS’(i.e.,. omega.)Mn,ep、ωS,ep) (ii) a The concentrations of the solutes Mn and S (i.e.,. omega. omega.) after the precipitation of MnS as the inclusion are calculated according to the calculationMn,ep、ωS,ep) And recalculating and correcting the solute concentration distribution calculated by the continuous casting macrosegregation model, and finally predicting and obtaining the solute macrosegregation distribution in the continuous casting blank considering inclusion precipitation.
A calculation flow chart of the inclusion precipitation calculation model is shown in fig. 1. Obtaining a MnS inclusion precipitation distribution diagram on the central longitudinal section of the continuous casting billet as shown in figure 5; the distribution of MnS precipitation amount of inclusions on the center line (width direction) of the cast slab is shown in FIG. 6. The concentration distributions of the solute Mn and S in the central longitudinal section of the slab in consideration of the inclusion precipitation are shown in FIGS. 3(b) and 3 (d); the influence of MnS inclusion on the distribution of the concentration of solute S, Mn on the center line (width direction) of the cast slab is considered as shown in FIG. 4.
Next, the "final prediction acquisition of the macrosegregation distribution of solute in the slab with inclusion precipitation taken into consideration" prediction result obtained by the above-described example is compared with the result without inclusion precipitation taken into consideration:
FIG. 3(a) is a graph showing the concentration distribution of solute Mn in the center longitudinal section (width direction) of the slab, irrespective of the precipitation of MnS inclusions.
FIG. 3(b) is a graph showing the distribution of the concentration of solute Mn in the center longitudinal section (width direction) of a slab in consideration of the precipitation of MnS inclusions using the method for predicting macrosegregation of a slab according to the present invention.
FIG. 3(c) is a graph showing the concentration distribution of solute S on the center longitudinal section (width direction) of the slab, without considering the precipitation of MnS inclusions.
FIG. 3(d) is a graph showing the concentration distribution of solute S on the center longitudinal section (width direction) of the slab in consideration of MnS inclusion precipitation by the method for predicting macrosegregation of a slab according to the present invention.
As can be seen from a comparison between fig. 3(a) and 3(b) and fig. 3(c) and 3(d), when MnS inclusion precipitation is considered, the concentrations of the solutes Mn and S are reduced in the corresponding regions in the cast slab; and the concentration distribution of solute in the continuous casting billet is more uniform, especially solute element S. FIG. 4 also shows that on the central line (width direction) of the casting blank, the precipitation of MnS inclusions effectively reduces the concentrations of the solutes Mn and S in the corresponding regions of the casting blank; when MnS is considered to be precipitated, the segregation degree of solute Mn is reduced from 0.9-1.21 to 0.85-1.02, and the segregation degree of solute S is reduced from 0.89-1.48 to 0.81-1.12 on the central line of a casting blank; the average degrees of segregation of the solutes Mn and S were reduced by 9.0% and 15.6%, respectively. This shows that the solute segregation degree in the central area of the continuous casting billet is reduced after MnS is considered to be precipitated, and the distribution of the solutes Mn and S is more uniform. Therefore, when the solute macrosegregation in the continuous casting and solidification process of molten steel is predicted, the influence of inclusion precipitation on the solute segregation distribution cannot be ignored; after the inclusion precipitation factor is considered, the prediction result of the solute macrosegregation can be more accurate.
According to the forecasting result of the solute macrosegregation of the continuous casting billet, the continuous casting production process system can be correspondingly adjusted, so that the flowing, solidification heat transfer and solute transmission behaviors of molten steel in the continuous casting process are changed, and the aim of controlling and improving the solute macrosegregation of the continuous casting billet is fulfilled.
The above is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various changes and modifications can be made without departing from the technical solution, and the technical solution of the changes and modifications should also be considered as falling within the scope of the claims.
Claims (3)
1. A macrosegregation prediction method for a continuous casting billet is characterized by comprising the following steps: the method comprises the following steps:
the method comprises the following steps of firstly, establishing a continuous casting solidification macrosegregation model to obtain the solute concentration distribution and temperature distribution condition in a continuous casting billet when the precipitation of inclusions is not considered;
secondly, introducing an inclusion precipitation calculation model based on the solute concentration distribution and the temperature distribution condition in the continuous casting billet in the first step; calculating and obtaining the precipitation distribution condition of the inclusions in the casting blank and the consumption of the inclusions to solute by precipitation according to the thermodynamic theory of inclusion precipitation and the solute mass conservation law;
thirdly, recalculating and correcting the solute concentration distribution obtained by calculating the continuous casting macrosegregation model in the first step according to the solute concentration after the inclusions are separated out based on the calculation result in the second step, and finally predicting and obtaining the solute macrosegregation distribution in the continuous casting blank considering the inclusions;
introducing an inclusion precipitation calculation model based on the solute concentration distribution and the temperature distribution in the continuous casting slab in the first step in the second step; according to the inclusion precipitation thermodynamic theory and the solute mass conservation law, the method for calculating and obtaining the precipitation distribution condition of the inclusions in the casting blank and the solute consumption amount caused by the inclusion precipitation comprises the following steps:
(1) determine whether impurities are separated out
Judging whether impurities in the continuous casting billet can be separated out or not by combining the obtained solute concentration distribution and temperature distribution in the continuous casting billet based on the thermodynamic theoretical basis of impurity separation;
the thermodynamic judgment method for whether inclusions are precipitated is as follows:
the chemical reaction formula of the reactant or solute element M and N for generating the inclusion MN is as follows:
M+N＝MN
ΔGΘ＝A+BT
ΔG＝ΔGΘ+RTlnKMN
in the above formula,. DELTA.GΘThe standard gibbs free energy for chemical reaction to generate MN, and Δ G is the gibbs free energy for chemical reaction to generate MN, and the unit is: j/mol; t is the reaction temperature in K; omegaMAnd ωNConcentrations of reactants M and N, wt%, respectively; f. ofMAnd fNActivity interaction coefficients of reactants M and N, respectively; a isMNIs the activity of product MN; r is an ideal gas constant, 8.314J/(mol.K); a and B are constants whose values are determined by the particular chemical reaction;
calculating the solute concentration distribution and temperature distribution, i.e. omega, in the slab according to the "first stepM，ωNAnd T, substituting the sum into the Delta G calculation formula to judge whether the inclusion MN at the corresponding position in the casting blank can be separated out; in the chemical reaction, when delta G is less than 0, the chemical reaction can occur and generate an inclusion MN; otherwise, the chemical reaction can not be carried out, and no inclusion MN is generated;
(2) amount of impurity precipitated, solute consumption, and solute concentration calculation after impurity precipitation
If the inclusion MN can be precipitated, the concentration of the solute element M, N after the precipitation of the MN is calculated as follows:
after the inclusion MN is separated out, the concentration of solute element M, N is equal to the equilibrium concentration of reactant M, N at the corresponding temperature; at this time, Δ G is 0, that is:
in the formula, ωM,ep、ωN,epRespectively is the equilibrium concentration of solute M, N after the inclusion MN is precipitated under corresponding temperature; when the inclusion MN is separated out, the content of solute element M, N in the inclusion MN needs to be ensured to be stoichiometric ratio, namely:
according to the law of conservation of solute mass, there are:
ΔωM＝ωM-ωM,eq
ΔωN＝ωN-ωN,eq
ΔωMN＝ΔωM+ΔωN
ωM、ωNthe concentrations of the solutes M, N before the inclusions MN are precipitated, respectively; mM、MNRelative atomic masses of solute element M, N, respectively; delta omegaM、△ωNConsumption of solute M, N for inclusion precipitation, respectively; delta omegaMNAnd (4) for the precipitation amount of the inclusion MN, obtaining the precipitation distribution of the inclusion MN in the whole continuous casting billet in the continuous casting process according to the calculation result of the precipitation amount of the inclusion MN.
2. The slab macrosegregation prediction method of claim 1, characterized in that:
the calculation result in the second step is: concentration Δ ω of solute M, N consumed by precipitation of inclusion MNM、△ωNAnd concentration ω of solute M, N after precipitation of inclusion MNM’、ωN’ω is saidM’、ωN’I.e. omegaM,ep、ωN,ep；
And in the third step, recalculating the solute concentration distribution obtained by correcting the continuous casting macrosegregation model according to the solute concentration after the inclusion precipitation based on the calculation result in the second step comprises correcting the solute concentration distribution obtained by calculating the continuous casting macrosegregation model according to the calculated solute concentration result after the inclusion precipitation is considered, and finally predicting and obtaining the solute macrosegregation distribution in the continuous casting billet considering the inclusion precipitation.
3. The slab macrosegregation prediction method of claim 1, characterized in that:
the first step of establishing a continuous casting solidification macrosegregation model to obtain the solute concentration distribution and the temperature distribution condition in the continuous casting billet when the inclusion precipitation is not considered comprises the following steps:
(1) establishing continuous casting macroscopic three-dimensional model
The continuous casting macroscopic three-dimensional model is used for coupling and calculating the flow, heat transfer solidification and solute element transmission phenomena of molten steel in a continuous casting billet in the continuous casting process, and finally obtaining the solute concentration distribution and temperature distribution conditions in the continuous casting billet;
the establishment of the continuous casting macroscopic three-dimensional model comprises the following parts: establishing a geometric model of a continuous casting blank, dividing meshes, selecting a control equation, and setting initial conditions and boundary conditions; wherein the control equations include a flow equation, a heat transfer solidification equation, and a solute transport equation;
(2) and performing analog simulation coupling calculation on the flowing, heat transfer and solute transfer behaviors in the continuous casting process based on the established continuous casting macroscopic three-dimensional model to obtain the solute concentration distribution and temperature distribution condition in the continuous casting blank when the inclusion precipitation is not considered.
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| CN109614710B (en) * | 2018-12-12 | 2023-05-12 | 重庆大学 | Method for predicting element segregation three-dimensional characteristics of continuous casting blank based on random mathematic principle |
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| CN110750868A (en) * | 2019-09-20 | 2020-02-04 | 北京科技大学 | Method and system for predicting macrosegregation in continuous casting process on line |
| CN110765598A (en) * | 2019-10-11 | 2020-02-07 | 东北大学 | Method for predicting MnS inclusion precipitation condition in molten steel solidification process |
| CN110765599A (en) * | 2019-10-11 | 2020-02-07 | 东北大学 | Prediction method for AlN inclusion precipitation condition in molten steel solidification process |
| CN111899230B (en) * | 2020-07-15 | 2023-11-17 | 重庆大学 | Quality quantification and automatic multi-stage judgment method based on three-dimensional characteristics of steel casting blank macrostructure |
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