CN116776668A - Method for calculating solidification shrinkage of billet shell in billet continuous casting crystallizer - Google Patents
Method for calculating solidification shrinkage of billet shell in billet continuous casting crystallizer Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 85
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- 230000008023 solidification Effects 0.000 title claims abstract description 72
- 229910052802 copper Inorganic materials 0.000 claims abstract description 112
- 239000010949 copper Substances 0.000 claims abstract description 112
- RYGMFSIKBFXOCR-UHFFFAOYSA-N Copper Chemical compound [Cu] RYGMFSIKBFXOCR-UHFFFAOYSA-N 0.000 claims abstract description 110
- 229910000831 Steel Inorganic materials 0.000 claims abstract description 80
- 239000010959 steel Substances 0.000 claims abstract description 80
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- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 claims description 32
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- OKTJSMMVPCPJKN-UHFFFAOYSA-N Carbon Chemical compound [C] OKTJSMMVPCPJKN-UHFFFAOYSA-N 0.000 description 3
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- 229910052799 carbon Inorganic materials 0.000 description 3
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Abstract
The invention provides a method for calculating solidification shrinkage of a billet shell in a billet continuous casting crystallizer, and relates to the technical field of steelmaking continuous casting. Firstly, establishing relevant parameters for simulation calculation of a billet continuous casting crystallizer; physical parameters of steel, a crystallizer copper pipe and cooling water are obtained; then, based on structural parameters of the billet continuous casting crystallizer, establishing a billet continuous casting crystallizer simulation model; setting initial conditions and boundary conditions of the model; constructing a shell-crystallizer interface heat transfer model, and performing coupling analysis on the distribution of liquid, solid mold flux and air gaps in a slag channel to quantitatively describe the influence of heat transfer medium distribution on the shell-crystallizer interface heat transfer; constructing a crystallizer-cooling water interface heat transfer model, analyzing the flow and heat exchange of cooling water outside a copper pipe, and quantitatively describing the heat transfer behavior of the crystallizer-cooling water interface; finally, setting the solving parameters of the simulation model of the billet continuous casting crystallizer, submitting the simulation operation, and analyzing the solidification heat transfer and shrinkage behavior of the billet shell in the billet continuous casting crystallizer.
Description
Technical Field
The invention relates to the technical field of steelmaking continuous casting, in particular to a method for calculating solidification shrinkage of a billet shell in a billet continuous casting crystallizer.
Background
The billets produced by continuous casting are main blanks of sectional materials and wire rods, and steel bars, wire rods, section steel, flat steel and the like processed by the billets are widely applied to civil fields such as building bridges, automobile manufacturing, furniture home appliances, ships and oceans and the like, and provide important support for national economic development. Because the billet drawing speed is higher, the problem of insufficient contact between the initial setting billet shell and the crystallizer copper pipe is particularly remarkable, uneven heat transfer is easy to cause, cracks on the surface and the skin of a casting blank are caused, the production quality of a downstream rolling processing link is threatened, the product degradation and even waste judgment can be caused when serious, and huge economic loss is caused for enterprises, so that the continuous casting method has become a common technical problem to be solved urgently for continuous casting high-efficiency and high-quality production of billets.
In order to control the quality defects of the surfaces and the subcutaneous surfaces of the billets caused by poor contact, the solidification shrinkage characteristics and the growth rules of the initial billet shells in the crystallizer are required to be comprehensively known, and on the basis, the inner cavity structure of the existing crystallizer is optimized, the taper design is improved, and the heat transfer uniformity of the interfaces between the billet shells and the copper tubes is improved. In short, the control of the dynamic shrinkage behavior and the evolution rule of the initial billet shell in the crystallizer is a key for developing a novel billet continuous casting crystallizer so as to inhibit cracks on the surface of a casting blank and improve the product quality.
Because the solidification process of steel in the crystallizer has the characteristic of 'black box', and a plurality of influencing factors, including water gap flow distribution, copper pipe structure, billet shell-copper pipe contact, casting powder performance and distribution, cooling water temperature and flow velocity and the like, the complex physical behavior and phenomenon in the crystallizer are difficult to comprehensively describe in the traditional physical experiment, so that the solidification behavior of the billet shell in the continuous casting crystallizer is mostly studied by adopting a numerical simulation method at present. On the other hand, in the actual production process, the billet continuous casting crystallizer generally adopts a nonlinear taper compensation design, and is influenced by dynamic deformation and shrinkage of the billet shell, the dynamic distribution condition of the casting powder film and the air gap in the slag channel is complex, and the contact state between the billet shell and the copper pipe of the crystallizer is difficult to quantitatively describe, so that the simulation calculation of solidification and shrinkage of the billet shell in the billet continuous casting crystallizer is more difficult.
In view of the above problems, the invention patent application numbers CN201110181557.6 and CN201110181559.5 disclose a calculation method and a calculation system for the solidification and heat transfer process of a continuous casting crystallizer. The system comprises three parts, namely a model data initializing module, a data operating module and a result outputting module, wherein the initializing module and the data operating module are respectively packaged with a one-dimensional heat transfer calculation model for calculating solidification and heat transfer of a shell at the center of a large surface in a crystallizer, the outputting module can store and output a calculation result to a visualization device, and the visualization device is specific to a boundary description problem encountered in the process of solving the one-dimensional heat transfer problem, the patent application number of CN201110044391.3 discloses a calculation method for heat flow density in the solidification and heat transfer process of a continuous casting crystallizer, and proposes a method for calculating heat flow density distribution of the surface of the shell by taking the thickness of the solidified shell at the lower opening of the continuous casting crystallizer of a square billet as a standard, converting the thickness into molten steel in unit volume, and then calculating the volume of the solidified shell in unit time to obtain heat released in the solidification process. The method is mostly used for calculating the solidification growth of the billet shell in the continuous casting process of the square billet, and the calculated current thickness of the billet shell is compared with the critical thickness of the billet shell, so that the occurrence risk of steel leakage accidents can be monitored in real time. However, the calculation method is relatively simple, does not relate to mechanical behaviors such as solidification shrinkage, contact deformation and the like of the billet shell, and cannot quantitatively describe non-uniform heat transfer occurring in continuous casting crystallization of the billet, so that the calculation method is not helpful for solving quality problems such as surface and subcutaneous cracks and the like in continuous casting production of the current billet.
The patent application CN202011400751.4 discloses a method for calculating solidification heat transfer of a continuous casting blank by considering non-uniform secondary cooling. The method aims at establishing a multi-stage calculation unit along the direction of drawing a billet based on the structure and technological parameters of a site continuous casting machine, calculating water distribution in a spray range of a nozzle by adopting an interpolation method, obtaining water distribution on the surface of a continuous casting billet through superposition treatment, setting an initial temperature field of a two-dimensional slice model of the continuous casting billet based on the water distribution, determining the slice position of the continuous casting billet according to the drawing speed and the solidification time, calling corresponding cooling conditions, further determining coefficients and source terms of a discrete linear equation set of solidification and heat transfer, finally calling a linear equation set solver, solving the temperature field of the continuous casting billet, and outputting a calculation result. In addition, the invention patent with the application number of CN202210092697.4 discloses a method for calculating the finite element of the solidification heat transfer of round-corner square billets, which fully considers the round-corner geometric characteristics of square billets in actual production, adopts a triangle unit to establish a two-dimensional solidification heat transfer finite element model, calculates the temperature change of the solidification billet shells of the round-corner square billets in the continuous casting process (comprising a crystallizer and a secondary cooling zone), and further calculates the shrinkage of the billet shells along the section direction according to the solidification shrinkage characteristics of steel. The method has great progress in calculation precision, and particularly has more detailed description on multi-nozzle compound spraying in a secondary cooling area, however, the method has the defects on the heat transfer description in a crystallizer, and the blank shell shrinkage behavior under the comprehensive heat transfer condition is not further explored.
Aiming at the defect problems of casting blank cracks and the like, the invention patent with application numbers of CN202111274295.8 and CN201510997828.3 proposes to eliminate central shrinkage and crack defects in the continuous casting production process of the low-carbon steel billets by controlling the superheat degree of molten steel, adjusting the water quantity of a secondary cooling zone, reducing the drawing speed, optimizing the electromagnetic stirring process parameters and the like. The core idea is to control the surface temperature of the casting blank by adjusting the spraying structure of the secondary cooling area and the water yield, so that the casting blank passes through the straightening area at higher temperature and higher plasticity, and the transverse crack of the inner arc side corner of the casting blank caused by the withdrawal and straightening force is avoided. The method can improve the internal quality of the continuous casting billet, and is not applicable to the surface and subcutaneous crack defects of the casting billet caused by uneven heat transfer of a crystallizer.
The paper entitled "thermodynamic behavior in billet continuous casting crystallizer under different process conditions" proposes that by establishing a billet continuous casting crystallizer thermo-force coupling finite element model, the thermo-mechanical behavior of an initial billet shell in the crystallizer under different drawing speeds is researched, and further, the influence of process parameters such as molten steel superheat degree, crystallizer taper, drawing speed and the like on the temperature and stress of the billet shell is analyzed, so that theoretical basis is provided for improving the process parameters and improving the surface quality of a casting blank. However, this study did not take into account the contact between the shell and the copper tube of the crystallizer, and the dynamic non-uniform distribution of the heat transfer medium in the slag track, the calculation of which with respect to the solidification heat transfer of the shell was not completely convincing.
It can be seen that in the continuous casting field of billets, the prior art mostly uses secondary cooling and mechanical pressing as research objects, optimizes spraying and pressing processes, and improves the internal quality of billets. The patent and research related to the calculation of solidification shrinkage of the blank shell in the crystallizer are rare, and the consideration factors are not comprehensive, so that the stress and deformation behavior of the initial-set blank shell under the real and complex conditions cannot be accurately described. In the face of the current and vigorous market competition environment, an accurate and effective method for calculating solidification shrinkage of billet shells in a billet continuous casting crystallizer is developed, and the method has very important practical significance and economic value for improving the inner cavity structure of the crystallizer, optimizing the heat transfer uniformity of the crystallizer and improving the surface quality of products and the economic benefits of enterprises.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a method for calculating solidification shrinkage of a billet shell in a billet continuous casting crystallizer, which is used for coupling analysis of billet shell-copper pipe contact, solid (liquid) covering slag distribution and air gap generation expansion, and comprehensively and accurately mathematically describing behaviors such as initial solidification billet shell contact, shrinkage, solidification, deformation and the like in the crystallizer on the basis.
In order to solve the technical problems, the invention adopts the following technical scheme: the method for calculating the solidification shrinkage of the billet shell in the billet continuous casting crystallizer comprises the following steps:
step 1, establishing relevant parameters for simulation calculation of a billet continuous casting crystallizer; the related parameters comprise structural parameters of the crystallizer, steel grade components, pulling speed and superheat degree, cooling water flow of the crystallizer and inlet and outlet water temperature; the structural parameters of the crystallizer comprise a copper pipe structure of the crystallizer, coating distribution, an external water jacket structure, a casting section size, a taper of the crystallizer and an effective working height of the crystallizer;
step 2, obtaining physical parameters of steel, a crystallizer copper pipe and cooling water according to the related parameters established in the step 1 and calculated by simulation, wherein the specific process is as follows:
step 2-1, according to steel type components, establishing high-temperature physical parameters of steel, wherein the parameters comprise solid/liquidus of the steel, phase fraction in a solidification process, density, specific heat, enthalpy value, heat conductivity, linear thermal expansion coefficient, elastic modulus and Poisson ratio evolution;
step 2-2, according to the texture of the crystallizer copper pipe, establishing thermal physical parameters of a copper matrix and thermal physical parameters of a coating, wherein the thermal coefficients, specific heats and densities of the copper matrix at all temperatures and the thermal coefficients, specific heats and densities of the coating are specifically included;
step 2-3, physical parameters of circulating cooling water of the casting site crystallizer are established, wherein the physical parameters comprise water density, specific heat, heat conductivity coefficient and viscosity;
step 3, establishing a small square billet continuous casting crystallizer simulation model based on structural parameters of the small square billet continuous casting crystallizer; considering that the continuous casting of the small square billets mostly adopts an arc-shaped crystallizer, namely an asymmetric structure, 1:1, modeling an equal proportion relation, wherein the specific operation is as follows:
step 3-1. According to the crystallizer copper tube structure established in step 1, 1 is performed on the crystallizer copper tube: 1, geometric modeling, namely truly reflecting the inner cavity structure of the small square billet crystallizer and nonlinear taper compensation;
step 3-2, performing grid division on the established geometric model of the copper tube of the crystallizer, and constructing a finite element model of the copper tube of the crystallizer;
step 3-3, refining the inner surface grid of the crystallizer copper tube in the finite element model of the crystallizer copper tube, and distinguishing the copper matrix grid from the plating grid;
step 3-4, endowing the copper matrix grids and the coating grids with the thermal physical parameters of the copper matrix and the coating thermal physical parameters of the coating established in the step 2-2 respectively;
step 3-5. According to the casting section size and the effective working height of the crystallizer established in the step 1, establishing 1:1, a steel casting flow geometric model;
step 3-6, mesh division is carried out on the established geometric model of the steel casting flow, and a finite element model of the steel casting flow is constructed;
step 3-7, endowing the steel casting grid with the high-temperature physical parameters of the steel established in the step 2-1;
step 3-8, according to the crystal copper pipe structure and the external water jacket structure established in the step 1, establishing 1 for cooling water of a crystallizer: 1 geometric modeling;
step 3-9, performing grid division on the established geometric model of the cooling water to construct a limited volume model of the cooling water;
step 3-10, endowing the physical property parameters of the circulating cooling water of the crystallizer established in the step 2-3 with cooling water grids;
step 3-11, according to the crystallizer assembly process, assembling and integrating the crystallizer copper pipe grid established in the step 3-4, the steel casting grid established in the step 3-7 and the cooling water grid established in the step 3-10 to ensure that the space position of each assembly body is consistent with that of the billet continuous casting crystallizer, thereby obtaining a multi-physical field coupling simulation model of the steel casting flow-crystallizer copper pipe-cooling water system, namely a billet continuous casting crystallizer simulation model;
step 4, setting initial conditions and boundary conditions of a simulation model of the billet continuous casting crystallizer, wherein the specific operation is as follows:
step 4-1, setting a steel casting flow as a deformed body, wherein a crystallizer copper pipe is a rigid body;
step 4-2, setting initial temperatures of the steel casting flow and cooling water of the crystallizer according to the superheat degree and the inlet water temperature established in the step 1, and setting the initial temperature of a copper pipe of the crystallizer to be 25 ℃;
step 4-3, setting the space displacement of the copper pipe of the crystallizer to be 0, and simultaneously, enabling the steel casting flow to move towards the lower opening of the crystallizer at the blank pulling speed established in the step 1;
and 4-4, applying a load to the unit surface, which is vertical to the surface of the steel casting flow, of the steel casting flow grid unit, and simulating the ferrostatic pressure born by the solidification front in the continuous casting process, wherein the concrete steps are as follows:
step 4-4-1, before each time increment step of the continuous casting process simulation calculation is started, judging whether each grid unit is positioned at the solidification front according to the node temperature in the grid unit, if the node temperature in the grid unit is higher than or lower than the solidus temperature, judging that the grid unit is a non-solidification front unit, and if part of the node temperature in the grid unit is higher than the solidus and part of the node temperature is lower than the solidus, judging that the grid unit is a solidification front unit;
step 4-4-2, extracting coordinates of a solidification front unit, calculating the depth of a molten pool where the grid unit is currently located according to the coordinates, further calculating the hydrostatic pressure of molten steel at the position, and applying the hydrostatic pressure to the corresponding grid unit surface;
step 4-4-3, for the non-solidification front unit, the load applied on the grid unit surface is 0;
step 4-5, setting the flow rate of cooling water according to the flow rate of cooling water of the crystallizer established in the step 1;
step 5, constructing a blank shell-crystallizer interface heat transfer model, and performing coupling analysis on the distribution of liquid, solid mold flux and air gaps in a slag channel, and quantitatively describing the influence of heat transfer medium distribution on blank shell-crystallizer interface heat transfer;
in the actual continuous casting production process of the small square billets, three heat transfer mediums, namely liquid slag, solid slag and air gaps, exist between a billet shell and a copper pipe of a crystallizer, wherein the liquid slag film thermal resistance is calculated by the following formula:
wherein R is thermal resistance, superscripts c and rad respectively represent a heat conduction item and a radiation item, and subscript liq represents a liquid slag layer; d. k and E are respectively the thickness of the slag layer, the heat conductivity coefficient and the absorbance; epsilon is emissivity, and subscripts s and f respectively represent casting blanks and covering slag; t is the temperature, and the subscript cry represents the crystallization temperature of the mold flux; sigma is the Boltzmann constant; r is the refractive index;
the thermal resistance of the slag fixing film is calculated by the following formula:
wherein, the subscript sol represents a slag fixing layer; the subscript m represents a crystallizer; t (T) a 、T b All are interface temperatures;
the air gap thermal resistance is calculated by the following formula:
wherein the subscript air represents an air gap layer;
the heat exchange coefficient between the blank shell and the copper plate is determined by the following steps:
wherein h is the interface heat exchange coefficient, R int Heat transfer resistance for the interface;
embedding the blank shell-crystallizer interface heat transfer model into a finite element model of a crystallizer system, solving the distribution of liquid, solid slag layers and air gaps, and obtaining interface heat exchange coefficients;
step 6, constructing a crystallizer-cooling water interface heat transfer model, analyzing the flow and heat exchange of cooling water outside the copper pipe, and quantitatively describing the heat transfer behavior of the crystallizer-cooling water interface;
the crystallizer-cooling water interface heat transfer model is shown in the following formula:
in the method, in the process of the invention,is a dimensionless temperature; t (T) m And T w The temperature of the cold surface of the copper pipe of the crystallizer and the temperature of the center of the grid unit adjacent to the wall surface of the water gap are respectively; q is the heat flux density of the crystallizer-cooling water interface; ρ w And c w The density and specific heat of water respectively; c (C) μ Is constant; k is turbulent energy; pr is the Planck constant; y is a dimensionless distance; y is w The distance from the center of each adjacent unit to the wall surface; />Is the dimensionless temperature boundary layer thickness; kappa is the Karman constant; e is an empirical constant; e' is a wall roughness constant; pr (Pr) t Is the turbulent planter number, mu l Is the molecular viscosity;
step 7, setting solving parameters of a simulation model of the billet continuous casting crystallizer, wherein the solving parameters comprise relaxation variables and termination conditions; the termination condition takes the temperature of the crystallization copper pipe as a criterion, if the temperature of the crystallizer copper pipe is not changed any more, the heat transfer in the steel casting flow-crystallizer copper pipe-cooling water system is considered to reach dynamic balance, and the calculation can be terminated at the moment;
step 8, submitting simulation operation, extracting a calculation result after the operation is finished, and analyzing solidification heat transfer and shrinkage behaviors of a billet shell in the billet continuous casting crystallizer; the calculation result comprises covering slag distribution, air gap layer distribution, blank shell solidification, heat transfer, deformation and crystallizer copper pipe temperature distribution in the small square blank continuous casting crystallizer.
The beneficial effects of adopting above-mentioned technical scheme to produce lie in: the method for calculating the solidification shrinkage of the billet shell in the billet continuous casting crystallizer provided by the invention has the advantages that the consideration factors are more comprehensive, the dynamic distribution of slag channel covering slag in the billet continuous casting crystallizer and the generation and expansion of an air gap layer can be coupled and analyzed, meanwhile, the quantitative description of the contact of the billet shell and a copper pipe of the crystallizer is included, the non-uniform heat transfer behavior of the billet shell and the evolution rule thereof are accurately calculated, the space shrinkage rule of the billet shell in the solidification process is further obtained, and a theoretical basis is provided for optimizing the taper and the inner cavity structure of the crystallizer.
Drawings
FIG. 1 is a flow chart of a method for calculating solidification shrinkage of a billet shell in a billet continuous casting crystallizer provided by an embodiment of the invention;
FIG. 2 is a schematic diagram of a geometric model of a billet crystallizer copper pipe provided by an embodiment of the invention;
fig. 3 is a diagram of a result of dividing copper pipe grids of a billet continuous casting crystallizer provided by an embodiment of the invention;
FIG. 4 is a schematic diagram of a geometric model of a billet according to an embodiment of the present invention;
FIG. 5 is a schematic diagram of an assembled steel cast strand-crystallizer system provided in an embodiment of the present invention;
FIG. 6 is a schematic diagram of distribution of mold flux of a slag runner obtained by coupling analysis according to an embodiment of the present invention;
fig. 7 is a schematic diagram of the solidification shrinkage deformation of the blank shell according to the embodiment of the present invention, where (a) is displacement in the x direction and (b) is displacement in the y direction.
Detailed Description
The following describes in further detail the embodiments of the present invention with reference to the drawings and examples. The following examples are illustrative of the invention and are not intended to limit the scope of the invention.
In the embodiment, the 08 carbon structural steel with the casting section of 120 multiplied by 120mm is taken as an example, and the method for calculating the solidification shrinkage of the billet shell in the billet continuous casting crystallizer is adopted to comprehensively and accurately describe the actions of contact, shrinkage, solidification, deformation and the like of the initial billet shell in the crystallizer.
In this embodiment, a method for calculating solidification shrinkage of a billet shell in a billet continuous casting crystallizer, as shown in fig. 1, includes the following steps:
step 1, establishing relevant parameters for simulation calculation of a billet continuous casting crystallizer (namely a simulation object); the related parameters comprise structural parameters of the crystallizer, steel grade components, pulling speed and superheat degree, cooling water flow of the crystallizer and inlet and outlet water temperature; the structural parameters of the crystallizer comprise a copper pipe structure of the crystallizer, coating distribution, an external water jacket structure, a casting section size, a taper of the crystallizer and an effective working height of the crystallizer;
in this example, the steel grade composition is shown in Table 1, the usual drawing speed under the general working condition is 2.6m/min, the superheat degree is 25 ℃, the cooling water quantity of the crystallizer is 160m3/h, the inlet water temperature is 29 ℃, the outlet water temperature is 34 ℃, and the inlet water temperature difference is 5 ℃. The copper pipe structure of the crystallizer is shown in figure 2, the inner surface coating of the copper pipe structure is uniformly transited from 0.5mm of the upper opening to 1.5mm of the lower opening, the taper of the crystallizer is distributed in a nonlinear manner, and the effective height is 700mm.
TABLE 1 main component (wt%) of 08 carbon structural steel
| C | Si | Mn | P | S |
| 0.09 | 0.27 | 0.5 | 0.03 | 0.03 |
And 2, obtaining physical parameters of steel, a crystallizer copper pipe and cooling water by calculating or referring to data according to the related parameters of the simulation calculation established in the step 1, wherein the specific process is as follows:
step 2-1, according to steel type components, establishing high-temperature physical parameters of steel, wherein the parameters comprise solid/liquidus of the steel, phase fraction in a solidification process, density, specific heat, enthalpy value, heat conductivity, linear thermal expansion coefficient, elastic modulus and Poisson ratio evolution; in the embodiment, the high-temperature physical parameters of the steel are obtained mainly by applying professional physical parameter calculation software JMatPro.
Step 2-2, according to the texture of the crystallizer copper pipe, establishing thermal physical parameters of a copper matrix and thermal physical parameters of a coating, wherein the thermal coefficients, specific heats and densities of the copper matrix at all temperatures and the thermal coefficients, specific heats and densities of the coating are specifically included;
in this example, the physical parameters of the copper tube required for calculation were obtained by referring to the relevant data, as shown in table 2, wherein the specific heat and density of the copper matrix can be regarded as being well-established, and the thermal conductivity varies with the temperature. The plating layer on the inner surface of the copper tube can be regarded as a constant in all physical properties.
TABLE 2 physical parameters of copper tube parts of crystallizer
Step 2-3, physical parameters of circulating cooling water of the casting site crystallizer are established, wherein the physical parameters comprise water density, specific heat, heat conductivity coefficient and viscosity;
in this example, physical properties of the cooling water circulated in the crystallizer under the ordinary conditions were checked, and the results are shown in table 3. Since the temperature change of the cooling water flowing through the crystallizer is small, the physical property parameter thereof can be regarded as a constant.
TABLE 3 physical parameters of circulating cooling water of crystallizer
| Parameters (parameters) | Density (kg/m 3) | Specific heat (J/(kg. K)) | Thermal conductivity (W/(m.K)) | Viscosity (kg/(m.s)) |
| Value taking | 998.2 | 4182 | 0.6 | 0.0006 |
Step 3, establishing a small square billet continuous casting crystallizer simulation model based on structural parameters of the small square billet continuous casting crystallizer; considering that the continuous casting of the small square billets mostly adopts an arc-shaped crystallizer, namely an asymmetric structure, 1:1, modeling an equal proportion relation, wherein the specific operation is as follows:
step 3-1. According to the crystallizer copper tube structure established in step 1, 1 is performed on the crystallizer copper tube: 1, geometric modeling, namely truly reflecting the inner cavity structure of the small square billet crystallizer and nonlinear taper compensation;
in this embodiment, according to the copper tube structure of the on-site billet continuous casting crystallizer, 1 is established in spaceclaim: 1, as shown in figure 3, meanwhile, special attention should be paid to the taper setting of the crystallizer in the modeling process, and the structure of the inner cavity of the crystallizer is truly reflected;
step 3-2, performing grid division on the established geometric model of the copper tube of the crystallizer, and constructing a finite element model of the copper tube of the crystallizer;
and (3) importing the geometric model of the crystallizer copper pipe into finite element software MSC.Marc, and performing grid division. Considering the overall structure of the copper tube of the crystallizer, the hexahedral unit is adopted for grid division in the embodiment, and the result is shown in fig. 3.
Step 3-3, refining the inner surface grid of the crystallizer copper tube in the finite element model of the crystallizer copper tube, and distinguishing the copper matrix grid from the plating grid;
in the embodiment, a surface layer thinning technology is applied in MSC.Marc, a coating grid with the thickness of 0.5mm is separated from the inner surface of a copper pipe of a crystallizer, and then the thickness distribution of the coating is changed by adjusting the nodes of the coating grid, so that the coating is gradually transited from 0.5mm of an upper opening to 1.5mm of a lower opening along the direction of drawing a blank.
Step 3-4, endowing the copper matrix grids and the coating grids with the thermal physical parameters of the copper matrix and the coating thermal physical parameters of the coating established in the step 2-2 respectively;
step 3-5. Establishing 1 in space according to the casting section size and the effective working height of the crystallizer established in step 1:1, a steel casting flow geometric model, as shown in fig. 4, fully represents the three-dimensional space structure of the steel casting flow in a crystallizer;
step 3-6, mesh division is carried out on the established geometric model of the steel casting flow, and a finite element model of the steel casting flow is constructed;
and (3) importing the steel casting flow geometric model into MSC.Marc finite element software, and adopting hexahedral units to divide the steel casting flow geometric model into grids. Considering that the tensile billet force of the solidified billet shell continuously moves downwards under the actual continuous casting condition, the steel casting flow unit also needs to realize the downward movement in the corresponding finite element simulation, so the steel casting flow unit at the meniscus should be reversely extended along the billet drawing direction, and the reverse extension distance in the embodiment is 2000mm.
Step 3-7, endowing the steel casting grid with the high-temperature physical property parameters of the steel established by the JMatPro calculation in the step 2-1;
step 3-8. According to the crystal copper pipe structure and the external water jacket structure established in the step 1, establishing 1 for crystallizer cooling water in space: 1 geometric modeling;
and 3-9, introducing the built cooling water geometric model into an ICEM to carry out grid division, wherein the grid type is hexahedral unit. Constructing a cooling water limited volume model;
step 3-10, endowing the physical property parameters of the circulating cooling water of the crystallizer established in the step 2-3 with cooling water grids;
and (3) introducing the cooling water grid into fluid computing software fluent, and setting according to the physical property parameters of the water at normal temperature, which are referred to in the step (2-3).
Step 3-11, according to the crystallizer assembly process, assembling and integrating the crystallizer copper pipe grid established in the step 3-4, the steel casting grid established in the step 3-7 and the cooling water grid established in the step 3-10 to ensure that the space position of each assembly body is consistent with that of the billet continuous casting crystallizer, thereby obtaining a multi-physical field coupling simulation model of the steel casting flow-crystallizer copper pipe-cooling water system, namely a billet continuous casting crystallizer simulation model;
in this embodiment, the finite element model of the copper tube of the crystallizer established in the step 3-4 and the finite element model of the steel casting stream established in the step 3-7 are combined, and the spatial relative position of the copper tube of the crystallizer and the steel casting stream is adjusted so that the outer surface of the casting stream contacts the inner surface of the copper tube of the crystallizer, as shown in fig. 5. In addition, the spatial position of the cooling water grid in the fluent is adjusted to be matched with the outer surface of the copper pipe of the crystallizer.
Step 4, setting initial conditions and boundary conditions of a simulation model of the billet continuous casting crystallizer in the MSC.Marc and fluent respectively, wherein the specific operation is as follows:
step 4-1, setting a steel casting flow as a deformed body, wherein a crystallizer copper pipe is a rigid body;
step 4-2, setting initial temperatures of the steel casting flow and cooling water of the crystallizer according to the superheat degree and the inlet water temperature established in the step 1, and setting the initial temperature of a copper pipe of the crystallizer to be 25 ℃;
in this example, the ladle superheat degree in billet continuous casting is 25 ℃, and the liquidus temperature of 08 carbon structural steel can be calculated to be 1523 ℃ according to the steel grade composition, so the casting temperature in MSC.Marc software should be 1548 ℃. The initial temperature of the copper tube may be set at room temperature, i.e., 25 ℃. In addition, as can be seen from step 1, the temperature of the circulating cooling water at the inlet of the crystallizer in fluent software should be set to 29 ℃.
Step 4-3, setting the space displacement of the copper pipe of the crystallizer to be 0, and simultaneously, enabling the steel casting flow to move towards the lower opening of the crystallizer at the blank pulling speed established in the step 1;
in this embodiment, the displacement of each node on the copper pipe grid of the crystallizer along the x, y and z directions is set to be 0. Meanwhile, the displacement speed of the steel casting flow node at the lower opening of the crystallizer along the direction of drawing the blank is set to be 2.6m/min.
Step 4-4, the hydrostatic pressure of molten steel in the continuous casting process is considered to have important influence on the deformation behavior of the shell, so that a load is required to be applied to the unit surface, perpendicular to the surface of the steel casting flow, of the steel casting flow grid unit, the hydrostatic pressure of molten steel born by the solidification front in the continuous casting process is simulated, and the calculation result is more accurate, and the concrete steps are as follows:
and 4-4-1, applying surface load to the steel casting flow unit in the finite element model, and defining the load applied to the unit surface in the calculation process through secondary development. The specific calculation process is as follows: before each time increment step of the continuous casting process simulation calculation starts, judging whether each grid unit is positioned at a solidification front according to the node temperature in the grid unit, if the node temperature in the grid unit is larger than or smaller than the solidus temperature, judging the grid unit as a non-solidification front unit, and if part of the node temperature in the grid unit is higher than the solidus and part of the node temperature is lower than the solidus, judging the grid unit as a solidification front unit;
step 4-4-2, extracting coordinates of a solidification front unit, calculating the depth of a molten pool where the grid unit is currently located according to the coordinates, calculating the required applied hydrostatic pressure according to the following formula, and applying the hydrostatic pressure to the corresponding grid unit surface;
P＝ρgh
wherein P is the applied hydrostatic pressure of molten steel, g is the density of molten steel, and h is the depth of the molten pool.
Step 4-4-3. For non-solidification front cells, the load applied on the grid cell face is 0, i.e. p=0;
step 4-5, setting cooling water flow rate in fluent according to the crystallizer cooling water flow rate established in the step 1, wherein the cooling water flow rate is shown in the following formula:
v＝Q/s
wherein v is the set cooling water flow rate, Q is the cooling water flow rate of the crystallizer, and s is the water gap cross-sectional area of the crystallizer.
Step 5, constructing a shell-crystallizer interface heat transfer model through MSC.Marc secondary development, and performing coupling analysis on the distribution of liquid, solid mold flux and air gaps in a slag channel to quantitatively describe the influence of heat transfer medium distribution on the shell-crystallizer interface heat transfer;
in the actual continuous casting production process of the small square billets, three heat transfer mediums, namely liquid slag, solid slag and air gaps, exist between a billet shell and a copper pipe of a crystallizer, wherein the liquid slag film thermal resistance is calculated by the following formula:
wherein R is thermal resistance, superscripts c and rad respectively represent a heat conduction item and a radiation item, and subscript liq represents a liquid slag layer; d. k and E are respectively the thickness of the slag layer, the heat conductivity coefficient and the absorbance; epsilon is emissivity, and subscripts s and f respectively represent casting blanks and covering slag; t is the temperature, and the subscript cry represents the crystallization temperature of the mold flux; sigma is the Boltzmann constant, which is 5.67×10 -8 W/(m 2 ·K 4 ) The method comprises the steps of carrying out a first treatment on the surface of the r is the refractive index;
the thermal resistance of the slag fixing film is calculated by the following formula:
wherein, the subscript sol represents a slag fixing layer; the subscript m represents a crystallizer; t (T) a 、T b The interface temperature and the K are respectively;
the air gap thermal resistance is calculated by the following formula:
wherein the subscript air represents an air gap layer;
the heat exchange coefficient between the blank shell and the copper plate is determined by the following steps:
wherein h is the interface heat exchange coefficient, W/(m) 2 ·K)，R int Heat transfer resistance for the interface;
the above-mentioned shell-crystallizer interface heat transfer model is embedded in the finite element model of the crystallizer system, and the distribution of liquid, solid slag layer and air gap is solved, and the interface heat exchange coefficient is obtained, as shown in figure 6.
Step 6, constructing a crystallizer-cooling water interface heat transfer model, analyzing the flow and heat exchange of cooling water outside the copper pipe, and quantitatively describing the heat transfer behavior of the crystallizer-cooling water interface;
the crystallizer-cooling water interface heat transfer model is shown in the following formula:
in the method, in the process of the invention,is a dimensionless temperature; t (T) m And T w The temperature of the cold surface of the copper pipe of the crystallizer and the temperature of the center of the grid unit adjacent to the wall surface of the water gap are respectively; q is the heat flux density of the crystallizer-cooling water interface; ρ w And c w The density and specific heat of water respectively; c (C) μ Is constant 0.09; k is turbulent energy; pr is the Planck constant; y is a dimensionless distance; y is w The distance from the center of each adjacent unit to the wall surface; />Is the dimensionless temperature boundary layer thickness; kappa is Karman constant 0.42; e is an empirical constant of 9.79; e' is a wall roughness constant; pr (Pr) t Is the turbulent planter number, mu l Is the molecular viscosity;
step 7, setting solution parameters of a simulation model of the billet continuous casting crystallizer, wherein the solution parameters comprise a relaxation variable and a termination condition, in the embodiment, setting the relaxation variable to be 0.5, taking whether the temperature of a crystallization copper pipe reaches a steady state or not as a calculation termination condition, and if the temperature of the crystallization copper pipe does not change any more, considering that the heat transfer in a steel casting flow-crystallizer copper pipe-cooling water system reaches dynamic balance, and at the moment, stopping calculation;
and 8, submitting simulation operation in commercial software MpCCI to realize data transmission between the shell-crystallizer finite element model and the cooling water flow model. Extracting a calculation result after the calculation is finished, and analyzing solidification heat transfer and shrinkage behaviors of a billet shell in the billet continuous casting crystallizer, as shown in fig. 7; the calculation result comprises covering slag distribution, air gap layer distribution, blank shell solidification, heat transfer, deformation and crystallizer copper pipe temperature distribution in the small square blank continuous casting crystallizer.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced with equivalents; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions, which are defined by the scope of the appended claims.
Claims (10)
1. A method for calculating solidification shrinkage of a billet shell in a billet continuous casting crystallizer is characterized by comprising the following steps of: the method comprises the following steps:
step 1, establishing relevant parameters for simulation calculation of a billet continuous casting crystallizer;
step 2, obtaining physical parameters of steel, a crystallizer copper pipe and cooling water according to the related parameters established in the step 1 and calculated by simulation;
step 3, establishing a small square billet continuous casting crystallizer simulation model based on structural parameters of the small square billet continuous casting crystallizer; considering that the continuous casting of the small square billets mostly adopts an arc-shaped crystallizer, namely an asymmetric structure, 1:1, modeling an equal proportion relation;
step 4, setting initial conditions and boundary conditions of a simulation model of the billet continuous casting crystallizer;
step 5, constructing a blank shell-crystallizer interface heat transfer model, and performing coupling analysis on the distribution of liquid, solid mold flux and air gaps in a slag channel, and quantitatively describing the influence of heat transfer medium distribution on blank shell-crystallizer interface heat transfer;
step 6, constructing a crystallizer-cooling water interface heat transfer model, analyzing the flow and heat exchange of cooling water outside the copper pipe, and quantitatively describing the heat transfer behavior of the crystallizer-cooling water interface;
step 7, setting solving parameters of a simulation model of the billet continuous casting crystallizer, wherein the solving parameters comprise relaxation variables and termination conditions;
and 8, submitting simulation operation, extracting a calculation result after the operation is finished, and analyzing solidification heat transfer and shrinkage behaviors of a billet shell in the billet continuous casting crystallizer.
2. The method for calculating solidification shrinkage of billet shells in a billet continuous casting crystallizer according to claim 1, wherein the method comprises the following steps of: the related parameters comprise structural parameters of the crystallizer, steel grade components, pulling speed and superheat degree, cooling water flow of the crystallizer and inlet and outlet water temperature; the structural parameters of the crystallizer comprise a copper pipe structure of the crystallizer, coating distribution, an external water jacket structure, a casting section size, a taper of the crystallizer and an effective working height of the crystallizer.
3. The method for calculating solidification shrinkage of billet shells in a billet continuous casting crystallizer according to claim 2, wherein the method comprises the following steps of: the specific method of the step 2 is as follows:
step 2-1, according to steel type components, establishing high-temperature physical parameters of steel, wherein the parameters comprise solid/liquidus of the steel, phase fraction in a solidification process, density, specific heat, enthalpy value, heat conductivity, linear thermal expansion coefficient, elastic modulus and Poisson ratio evolution;
step 2-2, according to the texture of the crystallizer copper pipe, establishing thermal physical parameters of a copper matrix and thermal physical parameters of a coating, wherein the thermal coefficients, specific heats and densities of the copper matrix at all temperatures and the thermal coefficients, specific heats and densities of the coating are specifically included;
and 2-3, establishing physical parameters of circulating cooling water of the casting site crystallizer, wherein the physical parameters comprise water density, specific heat, heat conductivity coefficient and viscosity.
4. A method for calculating solidification shrinkage of a billet shell in a billet continuous casting mold according to claim 3, wherein: the specific method of the step 3 is as follows:
step 3-1. According to the crystallizer copper tube structure established in step 1, 1 is performed on the crystallizer copper tube: 1, geometric modeling, namely truly reflecting the inner cavity structure of the small square billet crystallizer and nonlinear taper compensation;
step 3-2, performing grid division on the established geometric model of the copper tube of the crystallizer, and constructing a finite element model of the copper tube of the crystallizer;
step 3-3, refining the inner surface grid of the crystallizer copper tube in the finite element model of the crystallizer copper tube, and distinguishing the copper matrix grid from the plating grid;
step 3-4, endowing the copper matrix grids and the coating grids with the thermal physical parameters of the copper matrix and the coating thermal physical parameters of the coating established in the step 2-2 respectively;
step 3-5. According to the casting section size and the effective working height of the crystallizer established in the step 1, establishing 1:1, a steel casting flow geometric model;
step 3-6, mesh division is carried out on the established geometric model of the steel casting flow, and a finite element model of the steel casting flow is constructed;
step 3-7, endowing the steel casting grid with the high-temperature physical parameters of the steel established in the step 2-1;
step 3-8, according to the crystal copper pipe structure and the external water jacket structure established in the step 1, establishing 1 for cooling water of a crystallizer: 1 geometric modeling;
step 3-9, performing grid division on the established geometric model of the cooling water to construct a limited volume model of the cooling water;
step 3-10, endowing the physical property parameters of the circulating cooling water of the crystallizer established in the step 2-3 with cooling water grids;
and 3-11, assembling and integrating the crystallizer copper pipe grid established in the step 3-4, the steel casting grid established in the step 3-7 and the cooling water grid established in the step 3-10 according to a crystallizer assembling process, so that the spatial positions of all assemblies are consistent with that of the billet continuous casting crystallizer, and obtaining a multi-physical field coupling simulation model of the steel casting flow-crystallizer copper pipe-cooling water system, namely a billet continuous casting crystallizer simulation model.
5. The method for calculating solidification shrinkage of billet shells in a billet continuous casting crystallizer according to claim 4, wherein the method comprises the following steps of: the specific method of the step 4 is as follows:
step 4-1, setting a steel casting flow as a deformed body, wherein a crystallizer copper pipe is a rigid body;
step 4-2, setting initial temperatures of the steel casting flow and cooling water of the crystallizer according to the superheat degree and the inlet water temperature established in the step 1, and setting the initial temperature of a copper pipe of the crystallizer to be 25; DEG C
Step 4-3, setting the space displacement of the copper pipe of the crystallizer to be 0, and simultaneously, enabling the steel casting flow to move towards the lower opening of the crystallizer at the blank pulling speed established in the step 1;
step 4-4, applying load to the unit surface vertical to the surface of the steel casting flow in the steel casting flow grid unit, and simulating the ferrostatic pressure born by the solidification front in the continuous casting process;
and 4-5, setting the cooling water flow rate according to the cooling water flow rate of the crystallizer established in the step 1.
6. The method for calculating solidification shrinkage of billet shells in a billet continuous casting crystallizer according to claim 5, wherein the method comprises the following steps of: the specific method of the step 4-4 is as follows:
step 4-4-1, before each time increment step of the continuous casting process simulation calculation is started, judging whether each grid unit is positioned at the solidification front according to the node temperature in the grid unit, if the node temperature in the grid unit is higher than or lower than the solidus temperature, judging that the grid unit is a non-solidification front unit, and if part of the node temperature in the grid unit is higher than the solidus and part of the node temperature is lower than the solidus, judging that the grid unit is a solidification front unit;
step 4-4-2, extracting coordinates of a solidification front unit, calculating the depth of a molten pool where the grid unit is currently located according to the coordinates, further calculating the hydrostatic pressure of molten steel at the position, and applying the hydrostatic pressure to the corresponding grid unit surface;
step 4-4-3. For the non-solidifying front cells, the load applied on the grid cell face is 0.
7. The method for calculating solidification shrinkage of billet shells in a billet continuous casting crystallizer according to claim 5, wherein the method comprises the following steps of: the specific method in the step 5 is as follows:
in the actual continuous casting production process of the small square billets, three heat transfer mediums, namely liquid slag, solid slag and air gaps, exist between a billet shell and a copper pipe of a crystallizer, wherein the liquid slag film thermal resistance is calculated by the following formula:
wherein R is thermal resistance, superscripts c and rad respectively represent a heat conduction item and a radiation item, and subscript liq represents a liquid slag layer; d. k and E are respectively the thickness of the slag layer, the heat conductivity coefficient and the absorbance; epsilon is emissivity, and subscripts s and f respectively represent casting blanks and covering slag; t is the temperature, and the subscript cry represents the crystallization temperature of the mold flux; sigma is the Boltzmann constant; r is the refractive index;
the thermal resistance of the slag fixing film is calculated by the following formula:
wherein, the subscript sol represents a slag fixing layer; the subscript m represents a crystallizer; t (T) a 、T b All are interface temperatures;
the air gap thermal resistance is calculated by the following formula:
wherein the subscript air represents an air gap layer;
the heat exchange coefficient between the blank shell and the copper plate is determined by the following steps:
wherein h is the interface heat exchange coefficient, R int Heat transfer resistance for the interface;
and embedding the blank shell-crystallizer interface heat transfer model into a finite element model of a crystallizer system, solving the distribution of liquid, solid slag layers and air gaps, and obtaining an interface heat exchange coefficient.
8. The method for calculating solidification shrinkage of billet shells in a billet continuous casting crystallizer according to claim 7, wherein the method comprises the following steps of: the crystallizer-cooling water interface heat transfer model in the step 6 is shown in the following formula:
in the method, in the process of the invention,is a dimensionless temperature; t (T) m And T w The temperature of the cold surface of the copper pipe of the crystallizer and the temperature of the center of the grid unit adjacent to the wall surface of the water gap are respectively; q is the heat flux density of the crystallizer-cooling water interface; ρ w And c w The density and specific heat of water respectively; c (C) μ Is constant; k is turbulent energy; pr is the Planck constant; y is a dimensionless distance; y is w The distance from the center of each adjacent unit to the wall surface; />Is the dimensionless temperature boundary layer thickness; kappa is the Karman constant; e is an empirical constant; e' is a wall roughness constant; pr (Pr) t Is the turbulent planter number, mu l Is the molecular viscosity.
9. The method for calculating solidification shrinkage of billet shells in a billet continuous casting crystallizer according to claim 8, wherein the method comprises the following steps of: and 7, taking the temperature of the crystallization copper pipe as a criterion for the termination condition, and if the temperature of the crystallizer copper pipe is not changed any more, considering that the heat transfer in the steel casting flow-crystallizer copper pipe-cooling water system reaches dynamic balance, and terminating calculation at the moment.
10. The method for calculating solidification shrinkage of billet shells in a billet continuous casting crystallizer according to claim 9, wherein the method comprises the following steps: and 8, calculating the results including covering slag distribution, air gap layer distribution, blank shell solidification, heat transfer, deformation and crystallizer copper pipe temperature distribution in the small square blank continuous casting crystallizer.
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