CN108446505B - Method for calculating solidification heat transfer of casting blank in funnel crystallizer - Google Patents
Method for calculating solidification heat transfer of casting blank in funnel crystallizer Download PDFInfo
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Abstract
The invention provides a method for calculating solidification heat transfer of a casting blank in a funnel crystallizer, and relates to the technical field of steelmaking continuous casting. Firstly, looking up physical parameters of obtained steel, copper plates and cooling water, establishing 1/4 casting blank-crystallizer finite element models, and giving corresponding physical parameters; then establishing an interface heat transfer model coupling liquid slag layer distribution, solid slag layer distribution and air gap distribution; finally, setting a contact body and a contact relation; loading initial conditions and boundary conditions; loading a creep constitutive equation; and defining an analysis project, and submitting calculation in a parallel mode until the hot surface temperature of the copper plate reaches a steady state. The method for calculating the solidification heat transfer of the casting blank in the funnel crystallizer can accurately describe the dynamic distribution of liquid mold powder, solid mold powder and air gaps in the process of producing a sheet billet by continuous casting of the funnel crystallizer, the temperature distribution and the contact state of a crystallizer copper plate and a solidified billet shell, the shrinkage and deformation of the casting blank and other thermal/mechanical behaviors in the process of solidifying the sheet billet.
Description
Technical Field
The invention relates to the technical field of steelmaking continuous casting, in particular to a method for calculating solidification heat transfer of a casting blank in a funnel crystallizer.
Background
The continuous casting and rolling process of thin slabs originated in the last 80 th century and is a new short-process hot-rolled strip steel production process. As a core component of the continuous casting of the thin slab, the funnel crystallizer directly determines the production efficiency and the product surface of the continuous casting and rolling production line of the thin slab. The system knows the solidification heat transfer behavior of the billet shell in the funnel crystallizer in the thin slab continuous casting production process, and is the premise and the basis for improving the structure of the funnel crystallizer and developing a novel efficient funnel crystallizer. Because the solidification process of steel in the funnel crystallizer has the characteristic of black box, the heat transfer behavior in the crystallizer is difficult to describe in all directions in the traditional physical experiment, and at present, the heat transfer behavior in the funnel crystallizer is mostly researched by adopting a numerical simulation method.
In the actual production process of the sheet bar, because the structure of the inner cavity of the molten pool area of the funnel crystallizer is complex and is influenced by the dynamic deformation and shrinkage of the bar shell, the heat transfer behaviors of interfaces such as a protective slag film, an air gap and the like are obviously different from the traditional production of the sheet bar, so the solidification behavior of the bar shell in the funnel crystallizer is more complex than that of the traditional sheet bar, and the numerical simulation difficulty is higher.
The paper entitled "Modeling the thin-slab continuous-casting mold" studied the influence of the drawing speed, the thickness of the copper plate, etc. on the heat transfer behavior of the inner shell of the crystallizer during the casting process by establishing a three-dimensional finite element model. However, the influence of key heat transfer influencing factors of the crystallizer such as liquid and solid mold powder distribution, air gap formation and expansion in the crystallizer on the heat transfer of the casting blank is not considered in the model, so that the solidification heat transfer behavior rule of the casting blank in the funnel crystallizer cannot be truly reflected. Entitled "Thermal and mechanical behavor of copper molds with thin-slab casting (I): plant three and chemical modification "and" Thermal and mechanical beer of hopper molds thin-slab casting (II): the Mold crack formation "article studied the stress versus strain relationship of copper plates under cyclic loading. The crystallizer copper plate is taken as a research object of the model, and the influence of the contact state between the copper plate and a casting blank and the dynamic distribution behavior of the protective slag film on the evolution of the temperature field of the copper plate is not considered, so that the heat transfer and deformation behavior of the copper plate can not be truly reflected.
The invention patent with the application number of CN201310355699.9 discloses a continuous casting crystallizer heat flow density determination method based on slag film and air gap dynamic distribution, which realizes the coupling analysis of casting blank-copper plate temperature and contact state, slag film and air gap distribution and casting blank solidification shrinkage in the conventional slab continuous casting process; however, the calculation method is based on a two-dimensional finite element model, and because of the funnel structure design that the width surface of the funnel crystallizer is continuously reduced from top to bottom, the two-dimensional model cannot describe the continuously reduced funnel structure deformation and casting blank deformation, so the method is not suitable for describing the actions of casting blank solidification heat transfer and the like in the funnel crystallizer;
the invention patent with the application number of CN201410652827.0 discloses a method for calculating the non-uniform distribution of the thicknesses of a liquid-state slag film, a solid-state slag film and an air gap of covering slag in a continuous casting crystallizer, and realizes the description of the non-uniform distribution of the thicknesses of the covering slag and the air gap in a conventional slab continuous casting crystallizer; the invention is also based on a two-dimensional model, and therefore can not be applied to describing the solidification heat transfer of the casting blank in the funnel crystallizer;
disclosure of Invention
Aiming at the defects of the prior art, the invention provides a method for calculating the solidification heat transfer of a casting blank in a funnel crystallizer, which realizes the accurate description of the dynamic heat transfer behavior of a billet shell in a thin slab funnel crystallizer.
A method for calculating solidification heat transfer of a casting blank in a funnel crystallizer comprises the following steps:
step 1, looking up and acquiring physical parameters of steel according to simulated steel components, and simultaneously looking up and acquiring thermal physical parameters of a copper plate and cooling water used by a funnel crystallizer, and the method specifically comprises the following steps:
according to the mass percentage content of main elements in the steel grade to be simulated and poured, the liquidus temperature, the solidus temperature and the solidification latent heat of the steel are obtained by looking up and the changes of the thermal conductivity, the density, the specific heat and the thermal expansion coefficient of the steel grade along with the temperature in the solidification process; looking up and obtaining parameters of elastic modulus, Poisson ratio and yield limit of the steel at different temperatures and physical parameters of thermal conductivity, specific heat and density of a crystallizer copper plate and cooling water;
step 2, establishing a three-dimensional heat/force coupling finite element model according to a funnel crystallizer-casting blank system, wherein the specific method comprises the following steps:
step 2.1, establishing a three-dimensional geometric model of a combined structure of 1/2 wide-face crystallizer copper plates and 1/2 narrow-face crystallizer copper plates according to a structure diagram of the funnel crystallizer copper plates and the size of a casting blank casting section;
2.2, establishing a three-dimensional geometric model of 1/4 casting blank sections at a meniscus position according to the width of an upper opening of the funnel crystallizer, the taper of the narrow-face copper plate and the effective height of the crystallizer, wherein the height of the three-dimensional geometric model along the throwing direction is the effective height of the crystallizer;
step 2.3, importing the three-dimensional geometric model established in the step 2.1 and the step 2.2 into mesh division software to generate an unstructured mesh file approved by current mainstream finite element business software;
step 2.4, importing the wide and narrow copper plates and the casting blank grid file generated in the step 2.3 into nonlinear finite element analysis software, and constructing 1/2 wide copper plates, 1/2 narrow copper plates and 1/4 casting blanks into a 1/4 crystallizer-casting blank finite element model according to the section size and taper in the actual casting process;
step 2.5, inputting the steel physical parameters and the copper plate physical parameters determined in the step 1 into finite element calculation software, and correspondingly distributing the parameters to unit grids of the casting blank or the copper plate;
step 3, establishing a casting blank-crystallizer interface heat transfer model with a coupling protective slag layer and air gap distribution in a secondary development environment supported by finite element software;
step 4, setting contact bodies, initial conditions, boundary conditions and working condition analysis on the 1/4 crystallizer-casting blank finite element model established in the step 2, submitting a calculation task in a parallel calculation mode, moving a casting blank node at a meniscus to a lower opening of a crystallizer at a throwing speed, and calculating a first period, wherein the specific method comprises the following steps:
step 4.1, respectively setting contact body types of the copper plate of the funnel crystallizer and the casting blank, and contact relations and contact types between the copper plate and the casting blank;
the contact body type of the casting blank is set as a deformable body, and the copper plate is set as a heat-transferable rigid body;
the contact relation between the casting blank and the copper plate is a deformation body-heat-transferable rigid body, and the contact type is set as contact;
step 4.2, setting initial conditions of model calculation:
setting the initial temperature of a copper plate and the initial temperature of a casting blank;
step 4.3, setting mechanical and heat transfer boundary conditions of model calculation:
setting the temperature gradient, the heat flux density and the displacement of the upper node of the symmetrical surface of the casting blank and the upper node of the symmetrical surface of the copper plate along the normal phase to be 0;
applying interface heat transfer boundary conditions on the surface of the casting blank and the hot surface of the copper plate, wherein the interface heat flow density is determined by an interface heat transfer coefficient, the surface temperature of the casting blank and the hot surface temperature of the copper plate, and the interface heat transfer coefficient is determined by calculating and solving the model established in the step 3;
the lowest node of the casting blank moves downwards along the casting direction at the casting speed;
applying ferrostatic pressure at the solidification front of the casting blank, wherein the value of the ferrostatic pressure is determined by the vertical distance from the point to the meniscus;
applying a convection heat transfer boundary condition on the surface of the copper plate water tank;
4.4, establishing a creep constitutive equation and describing the creep behavior of the steel under the high-temperature condition;
step 4.5, setting a model analysis working condition:
setting the analysis working condition of the model as 'transient heat/machine creep', wherein the analysis time is the time required for a meniscus node to move to the lower opening of the crystallizer at the throwing speed;
setting each unit of the model to be judged before each increment step in the solving process is started, if the unit is positioned between the meniscus and the lower port of the crystallizer, activating the unit to participate in heat/computer coupling calculation, and otherwise, freezing the unit to not participate in any calculation;
when each increment step is finished, writing the thickness of the liquid protective slag film, the thickness of the solid protective slag film and the thickness of the air gap obtained when the interface heat transfer coefficient is calculated into a post-processing file;
4.6, performing region division on all units of the model, activating parallel computation, and submitting tasks to a solver;
step 5, continuously calculating 1/4 crystallizer-casting blank finite element models for a plurality of calculation cycles until the temperature of the crystallizer reaches a steady state, and completing the calculation of the solidification heat transfer of the casting blank in the funnel crystallizer, wherein the specific method comprises the following steps:
step 5.1, judging whether the current period is a second calculation period, if so, repositioning the grid of the unit at the end of the first calculation period in the step 4, and storing the unit as a new finite element calculation file; otherwise, the unit when the last calculation cycle is finished is subjected to grid relocation, and the unit is stored as a new finite element calculation file;
step 5.2, importing the material properties used in the step 4 into a new finite element calculation file additionally stored in the step 5.1, and distributing the material properties to the casting blank and the copper plate unit in the current calculation period again;
step 5.3, expanding the casting blank unit at the meniscus in the opposite direction of the throwing, wherein the expansion length is the effective height of the crystallizer;
step 5.4, setting the contact body and the contact relation of the model according to the step 4.1;
step 5.5, setting the calculation initial conditions of the model:
judging whether the current calculation period is the second calculation period or not, if so, taking the temperature of each node at the end of the first calculation period in the step 4 as an initial condition, and initializing the temperature of the casting blank and the copper plate unit except the newly generated unit in the step 5.3 in the current period; otherwise, initializing the temperatures of the casting blank units and the copper plate units in the current period except the newly generated units in the step 5.3 by taking the temperature of each node at the end of the calculation of the previous calculation period as an initial condition;
setting the initial temperature of the unit newly generated in the step 5.3 in the current calculation period as the pouring temperature;
step 5.6, respectively completing the setting of mechanical and heat transfer boundary conditions of the finite element model, the loading of a creep constitutive equation and the definition of an analysis working condition according to the methods of the steps 4.3 to 4.6, dividing a calculation area, and calculating in a parallel calculation mode;
and 5.7, monitoring the hot surface temperature of the copper plate in the calculation process, if the hot surface temperature of the copper plate does not change obviously any more or enters into periodic change, indicating that the crystallizer-casting blank heat transfer system in the current calculation period reaches a steady state, terminating the calculation, and extracting the calculation results of the temperature, the contact state, the casting blank deformation, the slag layer and the air gap distribution of the casting blank-copper plate system from a post-processing file, otherwise, repeatedly executing the steps 5.1-5.6 to finish the calculation of the next calculation period until the hot surface temperature of the copper plate reaches the stability.
According to the technical scheme, the invention has the beneficial effects that: the method for calculating the solidification heat transfer of the casting blank in the funnel crystallizer can accurately describe the dynamic distribution of liquid mold powder, solid mold powder and air gaps in the process of producing a sheet billet by continuous casting of the funnel crystallizer, the temperature distribution and the contact state of a crystallizer copper plate and a solidified billet shell, the shrinkage and deformation of the casting blank and other thermal/mechanical behaviors in the process of solidifying the sheet billet.
Drawings
FIG. 1 is a flowchart of a method for calculating a casting blank solidification heat transfer in a funnel crystallizer according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a three-dimensional geometric model of 1/2 wide-faced copper slabs and 1/2 narrow-faced copper slabs provided by an embodiment of the invention;
FIG. 3 is a schematic diagram of an 1/4 funnel crystallizer-billet finite element model, wherein (a) is a front view, (b) is a bottom view, (c) is a right side view, and (d) is a side view;
FIG. 4 is a schematic diagram illustrating the temperature distribution of the copper plate of the funnel mold-casting blank mold according to the embodiment of the present invention;
FIG. 5 is a schematic diagram of a slab temperature distribution of a funnel crystallizer-slab model according to an embodiment of the present invention;
fig. 6 is a schematic diagram of the distribution of the wide-surface air gap of the funnel crystallizer-casting blank model according to the embodiment of the present invention.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
In this embodiment, a CSP funnel crystallizer of a certain steel mill is taken as an example, and the casting blank solidification heat transfer in the funnel crystallizer is calculated by using the method for calculating the casting blank solidification heat transfer in the funnel crystallizer.
A method for calculating the solidification heat transfer of a casting blank in a funnel crystallizer is shown in figure 1 and comprises the following steps:
step 1, according to the mass percent of main elements in a steel grade QST420TM produced by the CSP continuous casting and rolling production line of the steel plant, looking up and obtaining physical parameters of the steel grade at different temperatures and the heat conductivity coefficient, specific heat and density of a copper plate and cooling water used by a funnel crystallizer;
the main elements and the percentage contents thereof in the steel QST420TM are respectively C0.047, Si0.022, Mn1.004, P0.015 and S0.0038, the liquidus temperature and the solidus temperature are respectively 1799.6K and 1776.1K, the solidification latent heat is 280kJ/kg, the specific heat of the liquid steel and the solid steel is respectively 0.8 kJ/(kg.K) and 0.6 kJ/(kg.K), and the specific heat of the steel in a two-phase region is obtained by interpolation of the specific heat of the liquid steel and the solid steel; the thermal conductivity, density and linear thermal expansion coefficient of the steel QST420TM at different temperatures are shown in Table 1:
TABLE 1 thermal conductivity, density, coefficient of linear thermal expansion of steel QST420TM at different temperatures
The modulus of elasticity of steel can be determined by the following formula:
E＝968-2.33T+1.9×10-3T2-5.18×10-7T3
wherein E is the elastic modulus, GPa; t is temperature, DEG C; the yield limit of steel at different temperatures can be set to 1/1000, which is the modulus of elasticity at that temperature;
the poisson's ratio of steel can be found by the following formula:
v＝0.278+8.23×10-5T
wherein v is the Poisson's ratio;
by consulting the data, the physical parameters of the copper plate of the funnel crystallizer and the cooling water can be determined, and the specific numerical values are shown in table 2:
TABLE 2 physical Properties of copper plate and Cooling Water
Step 2, establishing a three-dimensional 1/4 casting blank-crystallizer heat/machine coupling finite element model according to a steel mill CSP funnel crystallizer copper plate structure diagram, on-site assembly requirements, taper setting and other equipment and process parameters, wherein the specific implementation process comprises the following steps: establishing a geometric model, dividing grids, assembling parts and setting physical parameters;
2.1, establishing a three-dimensional geometric model of 1/2 wide-surface copper plates and 1/2 narrow-surface copper plates shown in the figure 2 according to a three-dimensional modeling software SpaceClaim for a CSP funnel crystallizer copper plate blue chart of a steel mill;
step 2.2, according to the on-site funnel crystallizer assembling requirements, including the width of an upper opening of the crystallizer, the taper of a narrow-face copper plate and the effective height of the crystallizer, establishing a three-dimensional geometric model of 1/4 casting blank sections at a meniscus position, wherein the height of the three-dimensional geometric model along the throwing direction is the effective height of the crystallizer;
step 2.3, respectively importing the three-dimensional geometric models established in the step 2.1 and the step 2.2 into ICEM software, and carrying out mesh division on the three-dimensional geometric models to generate an unstructured mesh file with a suffix name of pat;
step 2.4, importing the wide and narrow copper plates and the casting blank grid file generated in the step 2.3 into a nonlinear finite element analysis software MSC.Marc, and constructing 1/2 wide copper plates, 1/2 narrow copper plates and 1/4 casting blanks into a 1/4 crystallizer-casting blank finite element model shown in figure 3 according to the section size and taper in the actual casting process;
in this embodiment, the width of the upper opening of the crystallizer is fixed to 1110, and the back taper of the narrow-face copper plate is 0.9%.
And 2-5, inputting the steel physical parameters and the copper plate physical parameters acquired in the step 1 into a nonlinear finite element software MSC.
Step 3, under a secondary development environment supported by finite element software MSC.Marc, establishing a casting blank-crystallizer interface heat transfer model with a coupling protective slag layer and air gap distribution, wherein the specific modeling process and parameters are selected as follows:
the thermal resistance of the liquid slag layer is calculated by the following formula:
in the formula, Rliq、
Respectively is total thermal resistance of a liquid slag layer, heat conduction term thermal resistance of the liquid slag layer and radiation term thermal resistance of the liquid slag layer, and the unit is m2K/W；dliq、kliq、EliqRespectively the thickness, the heat conductivity and the light absorption of the liquid slag layer, and the units are m, W/(m.K) and m-1；εs、εfThe emissivity of the casting blank and the emissivity of the casting powder are respectively; t iscry、TsRespectively the crystallization temperature of the covering slag and the surface temperature of the casting blank, and the unit is K; σ is Boltzmann constant, and has a value of 5.67 × 10-8W/(m2·K4)；rfIs the refractive index;
the solid slag layer thermal resistance is calculated by the following formula:
in the formula, Rsol、
Respectively is total thermal resistance of a solid slag layer, thermal conduction term thermal resistance of the solid slag layer and radiation term thermal resistance of the solid slag layer, and the unit is m2K/W；dsol、ksol、EsolRespectively the thickness, the heat conductivity and the light absorption of the solid slag layer, and the units are m, W/(m.K) and m-1；εmThe emissivity of the crystallizer; t isa、TbAre the interface temperatures, and the units are K;
the air gap thermal resistance is calculated by:
in the formula, Rair、
Respectively is air gap total thermal resistance, air gap heat conduction term thermal resistance and air gap radiation term thermal resistance, and the unit is m2K/W；dair、kair、EairRespectively the thickness of the air gap, the thermal conductivity of the air gap and the light absorption of the air gap, and the units are m, W/(m.K) and m-1；TmIs the temperature of the hot surface of the crystallizer and has the unit of K;
the solid slag layer-crystallizer interfacial thermal resistance is determined by the following formula:
in the formula, RintRepresents the thermal resistance of the interface of the solid slag layer and the crystallizer and has the unit of m2K/W；
Because the heat fluxes of all the medium layers are equal, the following relations exist among the liquid slag layer, the solid slag layer and the air gap layer:
By solving the above formula, the dynamic distribution of the liquid mold flux, the solid mold flux and the air gap can be obtained, so that the thermal resistance of each medium layer can be further obtained;
the heat transfer coefficient between the shell and the copper plate is determined by the following formula:
wherein h is the heat exchange coefficient of the crystallizer-casting blank interface and the unit is W/(m)2·K)；
Obtaining physical parameters of the casting powder required for calculating interface heat transfer by detecting the physical characteristics of the CSP casting powder on site; specific values of the parameters used for solving the above formula in this embodiment are shown in table 3:
TABLE 3 solving physical parameters required for the crystallizer-casting blank interface heat transfer model
Step 4, setting contact bodies, initial conditions, boundary conditions and working condition analysis on the 1/4 crystallizer-casting blank finite element model established in the step 2, submitting a calculation task in a parallel calculation mode, moving a casting blank node at a meniscus to a lower opening of a crystallizer at a throwing speed, and calculating a first period, wherein the specific method comprises the following steps:
step 4.1, respectively setting contact body types of the copper plate of the funnel crystallizer and the casting blank, and contact relations and contact types between the copper plate and the casting blank;
the contact body type of the casting blank is set as a deformable body, and the copper plate is set as a heat-transferable rigid body;
the contact relation between the casting blank and the copper plate is a deformation body-heat-transferable rigid body, and the contact type is set as contact;
step 4.2, setting initial conditions of model calculation:
the initial temperature of the casting blank node is set to be the pouring temperature, namely 1824K, and the initial temperature of the copper plate is set to be 323K.
4.3, setting mechanical and heat transfer boundary conditions of model calculation;
the displacement of the upper node of the symmetrical surface of the casting blank and the upper node of the symmetrical surface of the copper plate along the normal phase is 0; the freedom degree of the copper plate node is 0, and the displacement along each direction is 0; the lowest layer of the casting blank, namely a node close to the meniscus, moves downwards along the casting direction at the casting speed of 4.0 m/s;
considering that the ferrostatic pressure acts on the solidification front in the actual production process, the position of the solidification front needs to be determined firstly in the process of applying the ferrostatic pressure; in the present example, the solidus temperature, i.e. 1776K, is taken as the temperature of the solidification front and the position of the solidification front is determined therefrom; in the process of loading mechanical boundary conditions, averaging the 8-node temperature of each casting blank unit, if the solidus temperature is just between the average temperatures of two adjacent units, applying ferrostatic pressure on the surface of a shared unit of the two adjacent units, otherwise, not applying any load in the period; the specific value of the ferrostatic pressure is determined by the following formula:
P＝ρmolten gh
wherein, P is the ferrostatic pressure and the unit is Pa; rhomeltenThe density of the molten steel is 7200kg/m3(ii) a g is the acceleration of gravity in m/s2(ii) a h is the depth of the molten pool in m;
applying a contact heat transfer boundary condition on the surface of the casting blank and the hot surface of the copper plate, wherein the heat flow density can be represented by the following formula:
q＝h(Ts-Tm)
wherein q is the interface heat flux density and has the unit W/(m)2) (ii) a h is the heat exchange coefficient of the crystallizer-casting blank interface and the unit is W/(m)2·K)；TsAnd TmThe temperatures of the surface of the casting blank and the hot surface of the copper plate are respectively expressed by K; the interface heat exchange coefficient in the above formula is obtained by the interface heat transfer model established in the step 3; it is worth noting that by solving a nonlinear equation set in the model, the thickness of the liquid slag layer, the thickness of the solid slag layer and the thickness of the air gap are obtained along with the interface heat exchange coefficient and are stored in a post-processing file;
setting the heat flux density of the upper edge normal phase of the symmetrical surfaces of the casting blank and the copper plate to be 0 and the temperature gradient to be 0;
setting the heat transfer mode of the crystallizer copper plate water tank side as convection heat transfer, and assuming that the temperature of cooling water is linearly changed from an inlet (309K) to an outlet (317K), the heat transfer coefficient of the cooling water is determined by the following formula:
in the formula, hwIs the convective heat transfer coefficient and has the unit of W/(m)2·K)，ρw、vw、kw、μw、cwThe density, flow rate, heat conductivity coefficient, dynamic viscosity and specific heat of cooling water are respectively, and the unit of each variable is kg/m3M/s, W/(m.K), Pa.s, J/(kg.K); d is the hydraulic diameter of the water tank, and the unit is m;
4.4, establishing a creep constitutive equation and describing the creep behavior of the steel under the high-temperature condition;
considering that steel has creep behavior under high temperature conditions, a traditional elastic-plastic model cannot accurately describe the creep behavior, so the following calculation formula is used in the embodiment to describe the stress-strain relationship of the creep stage:
n＝6.365-4.521×10-3T+1.439×10-6T2
m＝-1.362+5.761×10-4T+1.982×10-8T2
in the formula (I), the compound is shown in the specification,
respectively, the equivalent strain rate and the equivalent stress, respectively, are in units of s-1And MPa; c is a pre-exponential factor, the value of which is related to the carbon content wc in the steel; n is the temperature-dependent index of the equivalent stress, and m is the temperature-dependent index of time; q is the ratio of the creep activation energy to the gas constant, and has a value of 17160K-1(ii) a t is time in units of s;
step 4.5, setting the analysis working condition of the model;
setting the analysis working condition type of the model as transient heat/machine creep, wherein the whole working condition time is 15s, and because the CSP stable casting speed is 4m/s and the effective height of the crystallizer is 1m, the time for moving the unit at the meniscus to the lower opening of the crystallizer at the casting speed needs 15 s;
setting each increment step in the solving process to judge each unit before starting, if the current position of each unit is just below a meniscus of the crystallizer and above a lower opening of the crystallizer, activating the unit to participate in mechanical and heat transfer calculation, otherwise, freezing the unit to not participate in any calculation and not to be displayed in a post-processing file;
when each increment step is finished, writing the dynamic distribution of the liquid and solid protective slag layers and the air gaps obtained simultaneously along with the interface heat transfer coefficient in the process of calculating the heat transfer of the casting blank-copper plate interface into a post-processing file;
4.6, performing region division on all units of the model, activating parallel computation, and submitting tasks to a solver;
step 5, continuously calculating 1/4 crystallizer-casting blank finite element models for a plurality of calculation cycles until the temperature of the crystallizer reaches a steady state, and completing the calculation of the solidification heat transfer of the casting blank in the funnel crystallizer, wherein the specific method comprises the following steps:
step 5.1, judging whether the current period is the second calculation period, if so, repositioning the grid of the unit at the end of the first calculation period in the step 4, and storing the unit as a new finite element calculation file (. mud file); otherwise, the grid of the unit at the end of the calculation in the previous calculation cycle is repositioned, and the grid is saved as a new finite element calculation file (. mud file);
step 5.2, importing the material properties used in the step 4 into a new finite element calculation file additionally stored in the step 5.1, and distributing the material properties to the casting blank and the copper plate unit in the current calculation period again;
step 5.3, expanding the casting blank unit at the meniscus in the opposite direction of the throwing, wherein the expansion length is the effective height of the crystallizer;
in this embodiment, the vertical distance from the meniscus of the crystallizer to the lower port is equal to 1 m.
Step 5.4, setting the contact body and the contact relation of the model according to the step 4.1;
step 5.5, setting the calculation initial conditions of the model:
judging whether the current calculation period is the second calculation period or not, if so, taking the temperature of each node at the end of the first calculation period in the step 4 as an initial condition, and initializing the temperature of the casting blank and the copper plate unit except the newly generated unit in the step 5.3 in the current period; otherwise, initializing the temperatures of the casting blank units and the copper plate units in the current period except the newly generated units in the step 5.3 by taking the temperature of each node at the end of the calculation of the previous calculation period as an initial condition;
setting the initial temperature of the unit newly generated in the step 5.3 in the current calculation period as the pouring temperature, namely 1824K;
step 5.6, respectively completing the setting of mechanical and heat transfer boundary conditions of the finite element model, the loading of a creep constitutive equation and the definition of an analysis working condition according to the methods of the steps 4.3 to 4.6, dividing a calculation area, and calculating in a parallel calculation mode;
and 5.7, monitoring the hot surface temperature of the copper plate in the calculation process, if the hot surface temperature of the copper plate does not change obviously any more or enters into periodic change, indicating that the crystallizer-casting blank heat transfer system in the current calculation period reaches a steady state, terminating the calculation, and extracting the calculation results of the temperature, the contact state, the casting blank deformation, the slag layer and the air gap distribution of the casting blank-copper plate system from a post-processing file, otherwise, repeatedly executing the steps 5.1-5.6 to finish the calculation of the next calculation period until the hot surface temperature of the copper plate reaches the stability.
In this embodiment, after the calculation is completed, calculation results such as the funnel crystallizer copper plate temperature shown in fig. 4, the casting blank temperature shown in fig. 5, the copper plate-casting blank contact state, the liquid slag layer, the solid slag layer, and the dynamic distribution of the air gap shown in fig. 6 are extracted from the msc.
In this embodiment, the heat transfer behavior of a CSP funnel crystallizer of a certain steel mill is preliminarily analyzed by combining the following drawings:
as can be seen from the attached FIG. 4, the temperature distribution of the hot surface of the copper plate of the CSP funnel crystallizer in the factory is extremely uneven, a large temperature difference exists at the meniscus, and a large thermal strain is induced at the meniscus of the copper plate by a large temperature gradient in the casting process, so that large plastic deformation is very likely to occur in the area. When the crystallizer is offline and cooled to room temperature, the place where plastic deformation occurs can generate concentrated stress, and surface cracks of the copper plate are easily caused. In order to avoid the situation, the reduction of the width of the water tank on the back of the copper plate and the increase of the number of the water tanks can be considered properly so as to reduce the non-uniformity of the hot surface temperature of the copper plate during production.
As can be seen from FIGS. 5 and 6, inside the mold, a thick air gap exists at the corner of the wide side of the cast slab and the off-angle region, and the presence of the air gap causes a high temperature in the off-angle region of the cast slab. Considering that the strength of the steel is obviously reduced under the high-temperature condition, the high temperature of the deviation angle area is very likely to make the blank shell not bear huge ferrostatic pressure, and further cause the steel leakage accident. In order to avoid the phenomenon, the back taper of the copper plate along the thickness direction is properly increased so as to compensate the shrinkage of the casting blank corner along the thickness direction, reduce the thickness of the air gap and reduce the temperature of the casting blank deviation angle as much as possible.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions and scope of the present invention as defined in the appended claims.
Claims (3)
1. A method for calculating solidification heat transfer of a casting blank in a funnel crystallizer is characterized by comprising the following steps: the method comprises the following steps:
step 1, looking up and acquiring physical parameters of steel according to simulated steel components, and looking up and acquiring thermophysical parameters of a copper plate and cooling water used by a funnel crystallizer;
step 2, establishing a three-dimensional heat/force coupling finite element model according to a funnel crystallizer-casting blank system;
step 2.1, establishing a three-dimensional geometric model of a combined structure of 1/2 wide-face crystallizer copper plates and 1/2 narrow-face crystallizer copper plates according to a structure diagram of the funnel crystallizer copper plates and the size of a casting blank casting section;
2.2, establishing a three-dimensional geometric model of 1/4 casting blank sections at a meniscus position according to the width of an upper opening of the funnel crystallizer, the taper of the narrow-face copper plate and the effective height of the crystallizer, wherein the height of the three-dimensional geometric model along the throwing direction is the effective height of the crystallizer;
step 2.3, importing the three-dimensional geometric model established in the step 2.1 and the step 2.2 into mesh division software to generate an unstructured mesh file approved by current mainstream finite element business software;
step 2.4, importing the wide and narrow copper plates and the casting blank grid file generated in the step 2.3 into nonlinear finite element analysis software, and constructing 1/2 wide copper plates, 1/2 narrow copper plates and 1/4 casting blanks into a 1/4 crystallizer-casting blank finite element model according to the section size and taper in the actual casting process;
step 2.5, inputting the steel physical parameters and the copper plate physical parameters determined in the step 1 into finite element calculation software, and correspondingly distributing the parameters to unit grids of the casting blank or the copper plate;
step 3, establishing a casting blank-crystallizer interface heat transfer model with a coupling protective slag layer and air gap distribution in a secondary development environment supported by finite element software;
step 4, setting contact bodies, initial conditions, boundary conditions and working condition analysis on the 1/4 crystallizer-casting blank finite element model established in the step 2, submitting a calculation task in a parallel calculation mode, moving a casting blank node at a meniscus to a lower opening of a crystallizer at a throwing speed, and calculating a first period;
step 4.1, respectively setting contact body types of the copper plate of the funnel crystallizer and the casting blank, and contact relations and contact types between the copper plate and the casting blank;
the contact body type of the casting blank is set as a deformable body, and the copper plate is set as a heat-transferable rigid body;
the contact relation between the casting blank and the copper plate is a deformation body-heat-transferable rigid body, and the contact type is set as contact;
step 4.2, setting initial conditions of model calculation:
setting the initial temperature of a copper plate and the pouring temperature of a casting blank;
step 4.3, setting mechanical and heat transfer boundary conditions of model calculation:
setting the temperature gradient, the heat flux density and the displacement of the upper node of the symmetrical surface of the casting blank and the upper node of the symmetrical surface of the copper plate along the normal phase to be 0;
applying interface heat transfer boundary conditions on the surface of the casting blank and the hot surface of the copper plate, wherein the interface heat flow density is determined by an interface heat transfer coefficient, the surface temperature of the casting blank and the hot surface temperature of the copper plate, and the interface heat transfer coefficient is determined by calculating and solving the model established in the step 3;
the lowest node of the casting blank moves downwards along the casting direction at the casting speed;
applying ferrostatic pressure to the solidification front of the casting blank, wherein the value of the ferrostatic pressure is determined by the vertical distance from the point of applying the ferrostatic pressure to a meniscus;
applying a convection heat transfer boundary condition on the surface of the copper plate water tank;
4.4, establishing a creep constitutive equation and describing the creep behavior of the steel under the high-temperature condition;
step 4.5, setting a model analysis working condition:
setting the analysis working condition of the model as 'transient heat/machine creep', wherein the analysis time is the time required for a meniscus node to move to the lower opening of the crystallizer at the throwing speed;
setting each unit of the model to be judged before each increment step in the solving process is started, if the unit is positioned between the meniscus and the lower port of the crystallizer, activating the unit to participate in heat/computer coupling calculation, and otherwise, freezing the unit to not participate in any calculation;
when each increment step is finished, writing the thickness of the liquid protective slag film, the thickness of the solid protective slag film and the thickness of the air gap obtained when the interface heat transfer coefficient is calculated into a post-processing file;
4.6, performing region division on all units of the model, activating parallel computation, and submitting tasks to a solver;
and 5, continuously calculating 1/4 crystallizer-casting blank finite element models for a plurality of calculation cycles until the temperature of the crystallizer reaches a steady state, and finishing the calculation of the solidification heat transfer of the casting blank in the funnel crystallizer.
2. The method for calculating the solidification heat transfer of the casting blank in the funnel crystallizer according to claim 1, wherein: the physical parameters in the step 1 specifically comprise:
according to the mass percentage content of main elements in the steel grade to be simulated and poured, the liquidus temperature, the solidus temperature and the solidification latent heat of the steel are obtained by looking up and the changes of the thermal conductivity, the density, the specific heat and the thermal expansion coefficient of the steel grade along with the temperature in the solidification process; and looking up and obtaining the parameters of the elastic modulus, the Poisson ratio and the yield limit of the steel at different temperatures and the physical parameters of the thermal conductivity, the specific heat and the density of the copper plate of the crystallizer and the cooling water.
3. The method for calculating the solidification heat transfer of the casting blank in the funnel crystallizer according to claim 1, wherein: the specific method of the step 5 comprises the following steps:
step 5.1, judging whether the current period is a second calculation period, if so, repositioning the grid of the unit at the end of the first calculation period in the step 4, and storing the unit as a new finite element calculation file; otherwise, the unit when the last calculation cycle is finished is subjected to grid relocation, and the unit is stored as a new finite element calculation file;
step 5.2, importing the material properties used in the step 4 into a new finite element calculation file additionally stored in the step 5.1, and distributing the material properties to the casting blank and the copper plate unit in the current calculation period again;
step 5.3, expanding the casting blank unit at the meniscus in the opposite direction of the throwing, wherein the expansion length is the effective height of the crystallizer;
step 5.4, setting the contact body and the contact relation of the model according to the step 4.1;
step 5.5, setting the calculation initial conditions of the model:
judging whether the current calculation period is the second calculation period or not, if so, taking the temperature of each node at the end of the first calculation period in the step 4 as an initial condition, and initializing the temperature of the casting blank and the copper plate unit except the newly generated unit in the step 5.3 in the current period; otherwise, initializing the temperatures of the casting blank units and the copper plate units in the current period except the newly generated units in the step 5.3 by taking the temperature of each node at the end of the calculation of the previous calculation period as an initial condition;
setting the initial temperature of the unit newly generated in the step 5.3 in the current calculation period as the pouring temperature;
step 5.6, respectively completing the setting of mechanical and heat transfer boundary conditions of the finite element model, the loading of a creep constitutive equation and the definition of an analysis working condition according to the methods of the steps 4.3 to 4.6, dividing a calculation area, and calculating in a parallel calculation mode;
and 5.7, monitoring the hot surface temperature of the copper plate in the calculation process, if the hot surface temperature of the copper plate does not change obviously any more or enters into periodic change, indicating that the crystallizer-casting blank heat transfer system in the current calculation period reaches a steady state, terminating the calculation, and extracting the calculation results of the temperature, the contact state, the casting blank deformation, the slag layer and the air gap distribution of the casting blank-copper plate system from a post-processing file, otherwise, repeatedly executing the steps 5.1-5.6 to finish the calculation of the next calculation period until the hot surface temperature of the copper plate reaches the stability.
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| CN113319259B (en) * | 2021-06-07 | 2022-09-20 | 东北电力大学 | Bonding breakout logic judgment method based on space-time sequence characteristics |
| CN113705006B (en) * | 2021-08-30 | 2024-01-30 | 日照钢铁控股集团有限公司 | Sheet bar narrow surface of continuous casting machine copper plate abrasion prediction method |
| CN114357789B (en) * | 2022-01-10 | 2024-09-10 | 东北大学 | Method for setting taper angle of inner crystallizer of electroslag remelting hollow steel ingot and inner crystallizer |
| CN114626224A (en) * | 2022-03-18 | 2022-06-14 | 重庆大学 | Method for determining inner cavity taper of ultrahigh-pulling-speed square billet continuous casting crystallizer |
| CN116776668B (en) * | 2023-05-15 | 2024-01-26 | 河北工程大学 | Method for calculating solidification shrinkage of billet shell in billet continuous casting crystallizer |
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