CN114417674A - Finite element calculation method for fillet square billet continuous casting solidification heat transfer - Google Patents
Finite element calculation method for fillet square billet continuous casting solidification heat transfer Download PDFInfo
- Publication number
- CN114417674A CN114417674A CN202210092697.4A CN202210092697A CN114417674A CN 114417674 A CN114417674 A CN 114417674A CN 202210092697 A CN202210092697 A CN 202210092697A CN 114417674 A CN114417674 A CN 114417674A
- Authority
- CN
- China
- Prior art keywords
- heat transfer
- square billet
- finite element
- unit
- temperature
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/08—Thermal analysis or thermal optimisation
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Geometry (AREA)
- General Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Continuous Casting (AREA)
Abstract
The invention discloses a finite element calculation method for fillet square billet continuous casting solidification heat transfer, and relates to the technical field of steel continuous casting. The method comprises the steps of establishing a two-dimensional geometric model of the fillet square billet according to the section size of the fillet square billet; carrying out meshing on the two-dimensional geometric model of the fillet square billet, and establishing a two-dimensional finite element model of the fillet square billet; aiming at the problem of fillet square billet continuous casting solidification heat transfer, a fillet square billet two-dimensional finite element solidification heat transfer model is established; and calculating the temperature field change in the continuous casting process by using a fillet square billet two-dimensional finite element solidification heat transfer model. The method fully considers the special condition that the square blank usually has round corners in the actual production, adopts the triangular units, and can simulate and calculate any curve of the boundary of the area by using segmented straight lines when the grid is dense enough, so that the calculation precision is ensured to a certain extent; the finite element method is adopted for calculation, so that the calculation precision is improved; and proper boundary conditions are selected according to different cold regions, so that the full-flow solidification heat transfer of the fillet square billet continuous casting production is simulated more accurately.
Description
Technical Field
The invention relates to the technical field of steel continuous casting, in particular to a finite element calculation method for fillet square billet continuous casting solidification heat transfer.
Background
The square billet is a billet with a square cross section produced by a continuous casting machine and is widely used for processing sectional materials, wires and the like. The steel produced by the square billet is rich in variety and almost covers the whole carbon content range of the steel. In recent years, with the continuous development of the steel industry, the variety of the square billet alloy is gradually expanded, and the content of the square billet alloy is gradually increased. With the increase of the alloy content, the crack sensitivity of the steel grade is improved, various quality defects are more easily generated in the continuous casting process, and the requirement on the cooling uniformity is stronger.
Transverse cracks often appear at the corners of the billet. When the casting blank is straightened at 700-900 ℃, because elements such as microalloy Nb, V, Al, B and the like are combined with nitrogen in steel to form nitride and are precipitated at the grain boundary at the temperature, the surface of the casting blank has transverse cracks under the action of straightening stress, and the blank temperature of the casting blank in a straightening area needs to be more than 900 ℃. The subcutaneous cracks mostly occur at 1/4 of the thickness of the square billet, and the tiny cracks are vertical to the surface, the main reason is that the surface temperature of the casting blank repeatedly changes to cause phase change, the shell of the blank is heated to expand, the solidification front edge causes tensile strain, when the tensile strain at a certain local position exceeds the limit deformation value of the position, the fracture phenomenon is generated, and the fracture phenomenon continues to expand along the interface of two-phase tissues to finally form the cracks. Therefore, a reasonable secondary cooling zone cooling system needs to be established, and the surface temperature return of the casting blank is prevented from exceeding 100 ℃/m. The triangular region cracks are mainly due to uneven cooling along the width direction of the casting blank, in the final stage of solidification, part of molten steel in a higher-temperature region in the casting blank is not solidified, an adjacent lower-temperature region is basically solidified, when the tensile stress borne by the solidification front edge exceeds the critical value of steel, a blank shell is torn, and cracks are formed if adjacent molten steel cannot be fully filled, so that a secondary cooling system needs to be reasonably designed.
Therefore, the uniform cooling of the round-corner square billet in the crystallizer and the secondary cooling zone plays an important role in reducing the surface and internal defects of the casting billet. In order to realize uniform cooling of the fillet square billet, an online square billet regulating and controlling system is established, the temperature change condition of the fillet square billet at each moment is predicted quickly and accurately, and the cooling water amount is regulated in real time. The key point of the on-line billet regulation and control system lies in the determination of a solidification heat transfer core algorithm, namely the establishment of a billet solidification heat transfer model.
In the prior art, chinese patent "simulation and recurrence system of bloom continuous casting production process" with document No. CN 101559480B adopts rectangular meshes to divide tracking units, corners of a square billet are often rounded corners in actual production, the rectangular meshes are adopted for approximate simulation, the calculation accuracy on the boundary is greatly reduced, and the calculated corner temperature does not accord with the actual temperature; in chinese patent CN101347822B, "method for detecting continuous casting of bloom in-line temperature field and method for controlling secondary cooling water", the tracking units are divided by rectangular grids, and the calculation accuracy cannot be guaranteed; the chinese patent CN 100561383C, "secondary cooling of slab continuous casting and off-line simulation system under dynamic soft reduction" mainly solves the technical problem of excessive adjustment of parameters under dynamic soft reduction in production practice, and the patent does not consider how to handle fillet.
In summary, although the establishment of the square billet solidification heat transfer model and the calculation of the temperature field at each moment in the continuous casting process have great significance for regulating and controlling cooling water in real time to realize uniform cooling of the round-corner square billet and improve the quality of a casting blank, the prior model fails to consider the round corner of the square billet and cannot accurately simulate the temperature change condition of the round-corner square billet in actual production.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a finite element calculation method for fillet square billet continuous casting solidification heat transfer, aiming at predicting the temperature change condition of each moment in the fillet square billet solidification process, promoting fillet square billet simulation and heat transfer analysis, establishing a fillet square billet online solidification heat transfer model, optimizing water distribution in a secondary cooling area, reducing fillet square billet surface defects and providing a theoretical basis for improving the casting blank quality.
The technical scheme of the invention is as follows:
in order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a finite element calculation method for fillet square billet continuous casting solidification heat transfer comprises the following steps:
step 1: establishing a two-dimensional geometric model of the fillet square billet by using finite element analysis software according to the section size of the fillet square billet;
step 2: performing mesh division on the two-dimensional geometric model of the fillet square billet obtained in the step (1), establishing a two-dimensional finite element model of the fillet square billet and storing mesh information;
and step 3: aiming at the problem of fillet square billet continuous casting solidification heat transfer, a fillet square billet two-dimensional finite element solidification heat transfer model is established;
and 4, step 4: and calculating the temperature field change in the continuous casting process by using a fillet square billet two-dimensional finite element solidification heat transfer model.
Further, according to the finite element calculation method of the fillet square billet continuous casting solidification heat transfer, the grid information comprises unit information, node information and boundary information; the unit information includes a unit number and a node included in the unit; the node information comprises a node number and a node coordinate; the boundaries comprise an upper boundary, namely an inner arc, a lower boundary, namely an outer arc, a left boundary, namely a left side arc, a right boundary, namely a right side arc and a fillet boundary; the boundary information includes cell information and node information existing on the boundary.
Further, according to the finite element calculation method of the fillet square billet continuous casting solidification heat transfer, the step 3 comprises the following steps:
step 3.1: constructing a finite element heat transfer basic equation;
step 3.2: constructing a finite element calculation model of the transient heat transfer problem;
step 3.3: and constructing a plane three-node triangular unit, and performing heat transfer analysis aiming at different heat transfer boundary conditions based on the unit.
Further, according to the finite element calculation method of the fillet square billet continuous casting solidification heat transfer, the method of the plane three-node triangular unit comprises the following steps: 3 nodes are encoded in a counter-clockwise direction as i, j,mand constructing a plane three-node triangular heat transfer unit.
Further, according to the finite element calculation method for the fillet square billet continuous casting solidification heat transfer, the step 4 comprises the following steps:
step 4.1: reading the information of the round-corner square billet steel type, the structural parameters of a continuous casting machine, the cold-state performance parameters of a nozzle and the continuous casting process parameters, and calculating the solidus temperature and the liquidus temperature;
step 4.2: importing the grid information of a fillet square billet two-dimensional finite element model;
step 4.3: determining a time step length; the time step is the time of each slice movement; the slice represents the fillet square billet two-dimensional finite element model;
step 4.4: judging a unit phase region, and calculating physical property parameters of the unit;
step 4.5: calculating a unit heat transfer matrix, a node load and a unit heat capacity matrix and integrating a total heat transfer matrix, a total temperature load and a total heat capacity matrix; the integrated total heat transfer matrix is that each unit heat transfer matrix is decomposed into sub-matrixes, and then the sub-matrixes of the blocks determined by each node sequence are filled into the total heat transfer matrix according to the unit node numbers in a 'number matching' mode; the integrated total temperature load and the integrated total heat capacity matrix are the same as the integrated total heat transfer matrix;
step 4.6: solving temperature fields, i.e. finite element two-dimensional unsteady heat-conduction control equations
And meanwhile, judging whether the slice position exceeds an air cooling area, if so, finishing the calculation, otherwise, continuing to move the slice, and turning to the step 4.4.
Further, according to the finite element calculation method of the fillet square billet continuous casting solidification heat transfer, the steel type information comprises a steel grade and chemical components; the structural parameters of the continuous casting machine comprise the height of a crystallizer, the structural parameters of a secondary cooling zone and the length of an air cooling zone; the secondary cooling area structural parameters comprise the number, the length, the inlet position and the outlet position of the secondary cooling areas; the cold-state performance parameters of the nozzle comprise a nozzle number, a test mounting height, a spraying infinitesimal size, a spraying infinitesimal number, a spraying shape, a spraying water flow and a spraying characteristic; the spraying characteristic refers to the water flow percentage of spraying microelements in the original spraying network obtained by a cold-state performance test experiment of the nozzle under the conditions of testing the installation height and vertically installing the nozzle; the continuous casting process parameters comprise casting temperature, casting speed, crystallizer water quantity and water temperature difference, secondary cooling water flow and water temperature of each zone, environment temperature and section size of a fillet square billet; the section size of the fillet square billet comprises a wide surface width, a narrow surface width and a fillet radius.
Further, according to the finite element calculation method of the fillet square billet continuous casting solidification heat transfer, the phase region refers to a liquid phase region, a solid phase region and a solid-liquid two-phase region; the physical parameters include unit density, unit specific heat, unit solid phase ratio and unit heat conduction coefficient.
Further, according to the finite element calculation method of the fillet square billet continuous casting solidification heat transfer, the method for judging the unit phase region comprises the following steps: and calculating the temperature of the unit by adopting a two-dimensional linear interpolation method, and judging the phase region of the unit according to the temperature of the unit.
Further, according to the finite element calculation method of the fillet square billet continuous casting solidification heat transfer, a Jacobian iteration method is adopted to solve a matrix equation
And calculating the temperature of each node.
Generally, the above technical solution conceived by the present invention has the following beneficial effects compared with the prior art: the finite element calculation method for the continuous casting, solidification and heat transfer of the fillet square billet fully considers the special condition that the square billet is usually provided with fillets in the actual production process, adopts the triangular units, can simulate and calculate any curve of the boundary of an area by using segmented straight lines when the grid is dense enough, and has certain guarantee on the calculation precision; the finite element method is adopted for calculation, and compared with a finite difference method and the like, the calculation precision is improved; and proper boundary conditions are selected according to different cold regions, so that the full-flow solidification heat transfer of the fillet square billet continuous casting production is simulated more accurately. In a word, the actual condition of fillet square billet continuous casting is fully considered, and the temperature field change of the fillet square billet continuous casting process is described, so that the fillet square billet is uniformly cooled, and the support and guidance are provided for improving the quality of a continuous casting billet.
Drawings
FIG. 1 is a schematic flow chart of a finite element calculation method for solidification heat transfer in continuous casting of a fillet square billet according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a two-dimensional finite element model of a rounded square billet according to an embodiment of the present invention;
FIG. 3 is a cloud graph of temperature distribution of a round-corner square billet at different positions of a continuous casting machine according to an embodiment of the present invention, wherein (a) is a cloud graph of temperature distribution of a casting slab at a mold outlet 0.66m away from a meniscus; FIG. (b) is a temperature cloud of the cast slab at roll No. 6 at a distance of 1.848m from the meniscus; FIG. (c) is a temperature cloud of the cast slab at roll number 11 from meniscus 2.948 m; FIG. d is a temperature cloud of the cast slab at roll 16 from meniscus 4.318 m; FIG. (e) is a temperature cloud of the cast slab at roll number 21 from meniscus 5.857 m; FIG. f is a temperature cloud of the cast slab at roll number 26 from meniscus 7.863 m;
FIG. 4 is a comparison graph of the calculated temperature and the measured temperature of the corner of the rounded square billet provided by the embodiment of the invention;
FIG. 5 is a comparison graph of the calculated temperature of the corner of the rounded square billet and the calculated temperature of the corner of the square billet provided by the embodiment of the invention.
Detailed Description
To facilitate an understanding of the present application, the present application will now be described more fully with reference to the accompanying drawings. Preferred embodiments of the present application are given in the accompanying drawings. This application may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete.
In this embodiment, a 425mm × 320mm round corner bloom continuous casting process in a certain steel mill in China is taken as an example, and the round corner bloom continuous casting solidification heat transfer finite element calculation method is adopted to calculate the temperature change condition at each moment in the bloom continuous casting process.
The finite element calculation method for the continuous casting, solidification and heat transfer of the fillet square billet adopted in the embodiment specifically comprises the following steps as shown in fig. 1:
step 1: establishing a two-dimensional geometric model of the fillet square billet by using finite element analysis software according to the section size of the fillet square billet;
according to the section size of the fillet square billet, determining end point coordinates on a fillet and guiding the end point coordinates as key points into ANSYS or other finite element analysis software, then connecting the key points in the finite element analysis software such as ANSYS, wherein the fillet is connected by adopting 1/4 circular arcs, the circular arc radius is the fillet radius, and finally generating a fillet square geometric surface by the connecting lines to establish a fillet square billet two-dimensional geometric model. The section size of the fillet square billet comprises a wide surface width, a narrow surface width and a fillet radius.
In this example, the width of the wide surface of the bloom is 0.425m, the width of the narrow surface is 0.320m, and the corner radius is 0.025 m. The keypoint coordinates are (0.025,0), (0.400,0), (0.425,0.025), (0.425,0.295), (0.400,0.32), (0.025,0.32), (0,0.295), and (0,0.025), respectively.
Step 2: performing mesh division on the two-dimensional geometric model of the fillet square billet obtained in the step (1), establishing a two-dimensional finite element model of the fillet square billet and storing mesh information;
selecting a cell type PLANE55 in finite element analysis software such as ANSYS, wherein the cell shape is a triangular cell, determining the cell size, and then performing meshing division on the two-dimensional geometric model of the fillet square billet obtained in the step 1 to establish the two-dimensional finite element model of the fillet square billet. And outputting the grid information as a DAT format file and saving the DAT format file. The mesh information includes cell information, node information, and boundary information. The unit information comprises a unit number and nodes contained in the unit; the node information comprises a node number and a node coordinate; the boundaries comprise an upper boundary, namely an inner arc, a lower boundary, namely an outer arc, a left boundary, namely a left side arc, a right boundary, namely a right side arc and a fillet boundary; the boundary information includes which cells and nodes are on the boundary.
In the embodiment, the unit size is selected to be smart size 2 and encrypted by 1 time, and the regional unit subdivision is automatically performed by ANSYS finite element software. The two-dimensional finite element model of the rounded square billet built in the embodiment is shown in fig. 2.
And step 3: aiming at the problem of fillet square billet continuous casting solidification heat transfer, a fillet square billet two-dimensional finite element solidification heat transfer model is established;
step 3.1: constructing a finite element heat transfer basic equation;
the primary variable in the heat transfer process is temperature, which is a function of geometric position in the object and time.
According to the Fourier heat transfer law and the energy conservation law, a control equation of the heat transfer problem can be established, namely the transient temperature field T (x, y, z, T) of the object satisfies the following equation (1);
wherein rho is the material density, kg/m3；cTThe specific heat of the material is J/(kg. K); kappax、κy、κzThermal conductivity in the x, y, z directions, W/(m.K), respectively; q (x, y, z, t) is the heat source intensity inside the object, W/kg.
The heat transfer boundary conditions are of three types, i.e.
Boundary condition S of the first kind1For Dirichlet conditions, i.e. Dirichlet conditions, temperature values are given on the boundaries:
boundary condition S of the second kind2Neumann condition for a given heat flow density:
boundary condition S of the third kind3Neumann conditions for a given convective heat transfer:
wherein n isx,ny,nzIs the square of the normal outside the boundaryCosine-wise;
to be at the boundary S1The above given temperature;
to be at the boundary S2Given solidification heat flux density, W/m2；
Is the convective heat transfer coefficient of an object and a surrounding medium, W/(m)2·K)；T∞Is ambient temperature; t is time, s; and the boundary of the object omega is
If the initial condition of the problem IC is
The corresponding variation extraction method is that when the boundary condition S is satisfied1、S2、S3And in the permissible temperature field of the initial condition IC, the real temperature field minimizes the following functional I, i.e.
In the process of the actual problem, the boundary condition S2And S3It is difficult to satisfy in advance, and therefore, the two conditions can be coupled into a functional, i.e.
Step 3.2: establishing a finite element calculation model of the transient heat transfer problem;
in transient heat transfer problems, the temperature field of the cell will change over time, i.e.
Where N (x, y, z) is a shape function, where the node temperature
Is time-varying, i.e.
Substituting formula (8) into formula (7), and
obtaining the variation extremum
Wherein
Wherein dA is the area integral; omegaeIs a cell boundary;
a second type of boundary condition for the cell;
a third type of boundary condition for a cell; equation (10) is the unit heat transfer equation;
in the case of a unit heat transfer matrix,
is a unit node temperature array;
is a unit heat capacity matrix;
is a unit node equivalent temperature load array.
Step 3.3: a plane three-node triangular heat transfer unit is constructed, and heat transfer analysis is carried out on the basis of the unit according to different heat transfer boundary conditions.
Encoding 3 nodes into i, j, m in a counterclockwise direction to construct a planar three-node triangular heat transfer unit, and deducing the following unit matrixes of three conditions by using the planar three-node triangular heat transfer unit consisting of the 3 nodes i, j, m:
(1) no heat transfer boundary, i.e. a complete internal unit;
(2) if a certain edge of the unit, e.g. the jm edge, is such as to meet the second type of heat transfer boundary condition S2The heat transfer boundary of (1): by
A constant number;
(3) if a certain edge of the unit, e.g. the jm edge, is such as to meet the third type of heat transfer boundary condition S3The heat transfer boundary of (1): by
A constant.
The node temperature array of the unit is
The interpolation relation of the unit temperature field is taken as
Wherein the shape function matrix N is
N＝[Ni Nj Nm] (17)
Wherein
In the above formula, xi、yi、xj、yj、xm、ymThe abscissa and ordinate of i, j, m respectively;
next, the corresponding heat transfer matrix is calculated for several different heat transfer boundaries
And node equivalent temperature load array
(1) Being wholly internal units (without heat-transfer boundaries)
Substituting shape function expression (17)
And
in the calculation formulas (11) and (12) (note that only two-dimensional problems are considered here), there are
(2) For a certain edge of the unit, e.g. the jm edge, to comply with a second type of heat transfer boundary condition S2At the heat transfer boundary of
Form function expressions (17) and BC (S)2) Substitution of expression (3)
And
in the calculation formulas (11) and (12) (note that only two-dimensional problems are considered here), there are
Wherein l is the length of the jm side.
(3) For the cell a certain edge of the cell, e.g. the jm edge, is such as to meet a third type of heat transfer boundary condition S3At the heat transfer boundary of
Similarly, the shape function expressions (17) and BC (S)3) Substitution of expression (4)
And
in the calculation formulae (11) and (12), there are
And 4, step 4: calculating the temperature field change in the continuous casting process by utilizing a fillet square billet two-dimensional finite element solidification heat transfer model;
step 4.1: reading the information of the round-corner square billet steel type, the structural parameters of a continuous casting machine, the cold-state performance parameters of a nozzle and the continuous casting process parameters, and calculating the solidus temperature and the liquidus temperature;
the steel grade information comprises a steel grade and chemical components;
the structural parameters of the continuous casting machine comprise the height of a crystallizer, the structural parameters of a secondary cooling zone and the length of an air cooling zone; the secondary cooling area structural parameters comprise the number, the length, the inlet position and the outlet position of the secondary cooling areas;
the cold-state performance parameters of the nozzle comprise a nozzle number, a test mounting height, a spraying infinitesimal size, a spraying infinitesimal number, a spraying shape, a spraying water flow and a spraying characteristic; the spraying characteristic refers to the water flow percentage of spraying microelements in the original spraying network obtained by a cold-state performance test experiment of the nozzle under the conditions of testing the installation height and vertically installing the nozzle;
the continuous casting process parameters comprise casting temperature, casting speed, crystallizer water quantity and water temperature difference, secondary cooling water flow and water temperature of each zone, environment temperature and section size of a fillet square billet; the section size of the fillet square billet comprises a wide surface width, a narrow surface width and a fillet radius.
In this example, the chemical composition of the steel type is shown in table 1.
TABLE 1 chemical composition of 425mm × 320mm bloom in certain steel works in China
In this embodiment, the bloom caster comprises 4 secondary cooling zones, wherein the length of the secondary cooling zone 1 is 0.427m, and the inlet and outlet are respectively 0.66m and 1.087m from the meniscus; zone 2 has a length of 2.5526m, with the inlet and outlet spaced from the meniscus by 1.087m and 3.6396m, respectively; zone 3 has a length of 2.1256m, the inlet and outlet being spaced from the meniscus 3.6396m and 5.7652m respectively; zone 4 has a length of 2.028m and the inlet and outlet are 5.7652m and 7.7932m from the meniscus respectively. The liquidus temperature of the bloom is 1500 ℃, the solidus temperature is 1451 ℃, the casting temperature is 1538 ℃, the drawing speed is 0.65m/min, the cooling conditions of the crystallizer are shown in table 2, the secondary cooling specific water amount is 0.21L/kg, the secondary cooling water temperature is 20 ℃, the ambient temperature is 70 ℃, and the cooling conditions of the secondary cooling zone are shown in table 3.
TABLE 2 Cooling conditions for 425mm × 320mm bloom crystallizer in a certain steel mill in China
TABLE 3 Secondary cooling conditions for 425mm × 320mm bloom in a certain steel mill in China
In the embodiment, 3 circular full water nozzles are arranged on the wide surface of the secondary cooling 1 area at equal intervals, and 2 circular full water nozzles are arranged on the narrow surface at equal intervals. The models of the nozzles are all 30.12, and the installation height is 90 mm. The wide surface and the narrow surface of the secondary cooling 2 area are respectively provided with 1 elliptical air-water nozzle with the model number of 30.09, and the installation heights of the nozzles are respectively 180mm and 143.5 mm. The wide face and the narrow face of the secondary cooling 3 area are respectively provided with 1 elliptical air-water nozzle with the model number of 30.10, and the installation heights of the inner arc, the outer arc and the narrow face are respectively 170mm, 180mm and 120 mm. The wide face and the narrow face of the secondary cooling 4 area are respectively provided with 1 elliptical air-water nozzle with the model number of 30.41, and the installation heights of the inner arc, the outer arc and the narrow face are respectively 170mm, 180mm and 120 mm.
Step 4.2: importing the grid information of a fillet square billet two-dimensional finite element model;
and (3) importing the mesh information obtained after the two-dimensional geometric model of the fillet square billet in the step (2) is subjected to mesh division into a calculation program. The mesh information includes cell information, node information, and boundary information. The unit information comprises a unit number and nodes contained in the unit; the node information comprises a node number and a node coordinate; the boundaries comprise an upper boundary, namely an inner arc, a lower boundary, namely an outer arc, a left boundary, namely a left side arc, a right boundary, namely a right side arc and a fillet boundary; the boundary information includes which cells and nodes are on the boundary.
Step 4.3: determining a time step length;
the time step is the time each time the slice (called slice because the two-dimensional model has no thickness) is moved. The time step length multiplied by the pulling speed is the distance of each moving of the slice, and the accumulated moving distance is the position of the slice.
In this embodiment, the time step is 0.1s, and the pulling rate is 0.65 m/min.
Step 4.4: judging a unit phase region, and calculating physical property parameters of the unit;
and calculating the temperature of the unit by adopting a two-dimensional linear interpolation method, judging the phase region of the unit according to the temperature of the unit and calculating the physical property parameters.
The phase region comprises a liquid phase region, a solid phase region and a solid-liquid two-phase region; the temperature higher than the liquidus temperature is a liquid phase region, the temperature lower than the solidus temperature is a solid phase region, and the temperature between the liquidus temperature and the solidus temperature is a two-phase region. The physical parameters include unit density, unit specific heat, unit solid phase ratio and unit heat conduction coefficient.
In this embodiment, the liquid and solidus temperatures are 1500 ℃ and 1451 ℃ respectively, the cell phase region is determined according to the cell temperature, and the corresponding calculation formula is selected to calculate the physical property parameters of the cell.
Step 4.5: calculating a unit heat transfer matrix, a node load and a unit heat capacity matrix and integrating a total heat transfer matrix, a total temperature load and a total heat capacity matrix;
and (4) calculating a unit heat transfer matrix, a node load and a unit heat capacity matrix according to the calculation formula in the step (3.3). And (3) calculating boundary conditions of the inner arc, the outer arc and the side arc of the casting blank according to the difference of the positions of the continuous casting machines where the slices are positioned according to the water quantity and the water temperature difference of the crystallizer and the cold state performance of the nozzle read in the step 4.1, and calculating the boundary conditions at the round angle according to the boundary conditions of two adjacent boundaries.
The integrated total heat transfer matrix is that each unit matrix is decomposed into sub-matrixes, and then the block sub-matrixes determined by each node sequence are filled into the total heat transfer matrix according to the unit node numbers in a 'number matching' mode. The integrated total temperature load and the integrated total heat capacity matrix are the same.
Step 4.6: solving temperature fields, i.e. solving finite element two-dimensional unsteady heat-conduction control equations
Meanwhile, judging whether the slice position exceeds the calculation area, if so, finishing the calculation, otherwise, continuing to move the slice, and turning to the step 4.4;
solving matrix equations by adopting Jacobi iterative method
Calculating the temperature of each node, judging whether the position of the slice exceeds a calculation area after iteration is finished, if so, finishing the calculation of continuous casting and solidification heat transfer of the fillet square billet, and if not, moving to the lower partOne position, go to step 4.4.
In the embodiment, a Jacobian iteration method is adopted to solve a matrix equation, the error is the square sum and the reopening of the difference between two iterations of all nodes, the error tolerance is 0.001, and in order to improve the calculation efficiency, a parallel calculation function parallel _ for in OpenCV is adopted to perform CPU parallel calculation.
And 5: carrying out visualization and result post-processing on the calculation result of the continuous casting, solidification and heat transfer of the fillet square billet;
extracting calculation results at different positions of the continuous casting machine, and importing the calculation results into Tecplot software for visualization processing; and extracting the temperature change condition at the round corner, and introducing the temperature change condition into Origin software to form a temperature change curve.
The embodiment provides a temperature distribution cloud chart of 425mm × 320mm round-corner large square billets in a certain domestic steel mill at different rollers of a continuous casting machine, as shown in fig. 3, wherein the chart (a) is the temperature distribution cloud chart of casting blanks at the outlet of a crystallizer, and the distance between the diagram (a) and the meniscus is 0.66 m; FIG. (b) is a cloud of temperature distributions of the cast slab at roll No. 6, here 1.848m from the meniscus; FIG. (c) is a cloud of temperature distributions of the cast slab at roll # 11, here from meniscus 2.948 m; FIG. d is a cloud of temperature distributions of the cast slab at roll 16, here spaced 4.318m from the meniscus; FIG. (e) is a cloud of temperature distributions of the cast slab at roll # 21, here spaced 5.857m from the meniscus; FIG. f is a cloud of temperature distributions of the cast slab at roll number 26, here spaced 7.863m from the meniscus; the corner calculated temperature is compared to the measured temperature as shown in figure 4. The round corner square billet corner calculated temperature was compared with the square corner square billet corner calculated temperature as shown in fig. 5. As can be seen from FIG. 3, the heat is gradually dissipated by the crystallizer and secondary cooling, and the heat is gradually transferred from the inner part of the billet to the surface. The corner temperature is significantly lower than the temperature at other locations on the surface, subject to two-dimensional heat transfer. In the crystallizer, the temperature field has better symmetry. Along with the solidification, the high-temperature liquid phase area in the square billet is gradually reduced, and meanwhile, the influence of the secondary cooling uneven cooling on the solidification heat transfer is gradually shown. It can be seen from fig. 4 that the simulation calculation result substantially corresponds to the actual temperature, and the temperature curve shows oscillation under the influence of the alternate change of the heat transfer conditions. It can be seen from figure 5 that there is obvious difference between fillet square billet and square angle square billet corner temperature, and fillet square billet corner temperature curve shows that the oscillation is obviously weaker than square angle square billet, this is because square angle square billet corner has three kinds of heat transfer conditions of rolling contact, anhydrous radiation, and water convection in two cold areas, and fillet square billet corner only has two kinds of heat transfer boundaries of anhydrous radiation, water convection, consequently can not ignore the fillet when calculating fillet square billet continuous casting solidification heat transfer, needs to be with its special treatment.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present 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 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 (9)
1. A finite element calculation method for fillet square billet continuous casting solidification heat transfer is characterized by comprising the following steps:
step 1: establishing a two-dimensional geometric model of the fillet square billet by using finite element analysis software according to the section size of the fillet square billet;
step 2: performing mesh division on the two-dimensional geometric model of the fillet square billet obtained in the step (1), establishing a two-dimensional finite element model of the fillet square billet and storing mesh information;
step 3, aiming at the problem of continuous casting, solidification and heat transfer of the fillet square billet, establishing a two-dimensional finite element solidification and heat transfer model of the fillet square billet;
and 4, step 4: and calculating the temperature field change in the continuous casting process by using a fillet square billet two-dimensional finite element solidification heat transfer model.
2. A finite element method of solidification heat transfer in round corner billet casting according to claim 1, wherein the mesh information includes element information, node information, boundary information; the unit information includes a unit number and a node included in the unit; the node information comprises a node number and a node coordinate; the boundaries comprise an upper boundary, namely an inner arc, a lower boundary, namely an outer arc, a left boundary, namely a left side arc, a right boundary, namely a right side arc and a fillet boundary; the boundary information includes cell information and node information existing on the boundary.
3. A finite element method of solidification heat transfer in round-corner billet casting according to claim 1, wherein the step 3 comprises the steps of:
step 3.1: constructing a finite element heat transfer basic equation;
step 3.2: constructing a finite element calculation model of the transient heat transfer problem;
step 3.3: and constructing a plane three-node triangular unit, and performing heat transfer analysis aiming at different heat transfer boundary conditions based on the unit.
4. A finite element method of solidification heat transfer in round corner billet casting according to claim 3, wherein the method of planar three-node triangular unit is: and 3 nodes are coded into i, j and m in the anticlockwise direction to construct the plane three-node triangular heat transfer unit.
5. A finite element method of solidification heat transfer in fillet billet casting according to claim 4, wherein the step 4 comprises the steps of:
step 4.1: reading the information of the round-corner square billet steel type, the structural parameters of a continuous casting machine, the cold-state performance parameters of a nozzle and the continuous casting process parameters, and calculating the solidus temperature and the liquidus temperature;
step 4.2: importing the grid information of a fillet square billet two-dimensional finite element model;
step 4.3: determining a time step length; the time step is the time of each slice movement; the slice represents the fillet square billet two-dimensional finite element model;
step 4.4: judging a unit phase region, and calculating physical property parameters of the unit;
step 4.5: calculating a unit heat transfer matrix, a node load and a unit heat capacity matrix and integrating a total heat transfer matrix, a total temperature load and a total heat capacity matrix; the integrated total heat transfer matrix is that each unit heat transfer matrix is decomposed into sub-matrixes, and then the sub-matrixes of the blocks determined by each node sequence are filled into the total heat transfer matrix according to the unit node numbers in a 'number matching' mode; the integrated total temperature load and the integrated total heat capacity matrix are the same as the integrated total heat transfer matrix;
step 4.6: solving temperature fields, i.e. finite element two-dimensional unsteady heat-conduction control equations
And meanwhile, judging whether the slice position exceeds an air cooling area, if so, finishing the calculation, otherwise, continuing to move the slice, and turning to the step 4.4.
6. The finite element method for the solidification heat transfer of the rounded square billet casting according to claim 5, wherein the steel grade information comprises a steel grade, a chemical composition; the structural parameters of the continuous casting machine comprise the height of a crystallizer, the structural parameters of a secondary cooling zone and the length of an air cooling zone; the secondary cooling area structural parameters comprise the number, the length, the inlet position and the outlet position of the secondary cooling areas; the cold-state performance parameters of the nozzle comprise a nozzle number, a test mounting height, a spraying infinitesimal size, a spraying infinitesimal number, a spraying shape, a spraying water flow and a spraying characteristic; the spraying characteristic refers to the water flow percentage of spraying microelements in the original spraying network obtained by a cold-state performance test experiment of the nozzle under the conditions of testing the installation height and vertically installing the nozzle; the continuous casting process parameters comprise casting temperature, casting speed, crystallizer water quantity and water temperature difference, secondary cooling water flow and water temperature of each zone, environment temperature and section size of a fillet square billet; the section size of the fillet square billet comprises a wide surface width, a narrow surface width and a fillet radius.
7. A finite element method of rounded square billet casting solidification heat transfer according to claim 5, wherein the phase regions are a liquid phase region, a solid phase region and a solid-liquid two-phase region; the physical parameters include unit density, unit specific heat, unit solid phase ratio and unit heat conduction coefficient.
8. A finite element method of radius square billet casting solidification heat transfer according to claim 7, wherein the method of judging the unit phase region is: and calculating the temperature of the unit by adopting a two-dimensional linear interpolation method, and judging the phase region of the unit according to the temperature of the unit.
9. A finite element method of radius square billet continuous casting solidification heat transfer as set forth in claim 5, wherein the Jacobi iteration method is used to solve the matrix equation
And calculating the temperature of each node.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210092697.4A CN114417674A (en) | 2022-01-26 | 2022-01-26 | Finite element calculation method for fillet square billet continuous casting solidification heat transfer |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210092697.4A CN114417674A (en) | 2022-01-26 | 2022-01-26 | Finite element calculation method for fillet square billet continuous casting solidification heat transfer |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN114417674A true CN114417674A (en) | 2022-04-29 |
Family
ID=81277335
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202210092697.4A Pending CN114417674A (en) | 2022-01-26 | 2022-01-26 | Finite element calculation method for fillet square billet continuous casting solidification heat transfer |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN114417674A (en) |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114833320A (en) * | 2022-05-19 | 2022-08-02 | 中冶南方工程技术有限公司 | Continuous casting three-dimensional temperature field visualization system supporting multiple billets |
| CN117745974A (en) * | 2024-02-19 | 2024-03-22 | 潍坊幻视软件科技有限公司 | Method for dynamically generating rounded rectangular grid |
-
2022
- 2022-01-26 CN CN202210092697.4A patent/CN114417674A/en active Pending
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114833320A (en) * | 2022-05-19 | 2022-08-02 | 中冶南方工程技术有限公司 | Continuous casting three-dimensional temperature field visualization system supporting multiple billets |
| CN114833320B (en) * | 2022-05-19 | 2023-10-27 | 中冶南方工程技术有限公司 | Continuous casting three-dimensional temperature field visualization system supporting multiple blank types |
| CN117745974A (en) * | 2024-02-19 | 2024-03-22 | 潍坊幻视软件科技有限公司 | Method for dynamically generating rounded rectangular grid |
| CN117745974B (en) * | 2024-02-19 | 2024-05-10 | 潍坊幻视软件科技有限公司 | Method for dynamically generating rounded rectangular grid |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN114417674A (en) | Finite element calculation method for fillet square billet continuous casting solidification heat transfer | |
| Feng et al. | Generalized constructal optimization for solidification heat transfer process of slab continuous casting based on heat loss rate | |
| CN105033214B (en) | Basic roll gap making method for wide and thick slab casting machine | |
| CN101767185B (en) | Quantitative reverse deformation arrangement based method for designing cast model | |
| CN109446748B (en) | Method for simulating solidification process of continuous casting round billet | |
| CN108959749B (en) | Design method of round billet continuous casting rotational flow water gap | |
| Du et al. | Analysis of the non-uniform thermal behavior in slab continuous casting mold based on the inverse finite-element model | |
| CN104493121A (en) | Online detection method for solidified bottom end position in bloom continuous casting production process | |
| CN115828571A (en) | Continuous casting billet online temperature field prediction method based on CPU + GPU heterogeneous parallel | |
| Long et al. | A mathematical model for mitigating centerline macro segregation in continuous casting slab | |
| Long et al. | Effect of uneven solidification on the quality of continuous casting slab | |
| CN116776668B (en) | Method for calculating solidification shrinkage of billet shell in billet continuous casting crystallizer | |
| CN102847901B (en) | Method for controlling width of ferrite stainless steel plate blank in continuous casting production | |
| Ren et al. | Control of dimensional accuracy of hollow turbine blades during investment casting | |
| CN116738518B (en) | Numerical simulation verification method for crack position under continuous casting light reduction and internal quality control method | |
| CN116052806A (en) | Finite volume calculation method for solidification heat transfer of irregular section continuous casting billet | |
| CN114491855A (en) | Finite element calculation method for circular billet continuous casting solidification heat transfer | |
| CN114417675A (en) | Finite element calculation method for continuous casting, solidification and heat transfer of special-shaped blank | |
| CN104399917A (en) | Gradual cambered chamfered mold with enhanced water cooling structure and design method | |
| CN109522677A (en) | A method of for the temperature controlled strip cross section layered method of hot-strip | |
| CN116652143A (en) | Online cooperative control method for light pressing and heavy pressing of bloom continuous casting | |
| Tkadleckova et al. | Study of Solidification of Continuously Cast Steel Round Billets Using Numerical Modellin | |
| El‐Bealy | Air‐water mist and homogeneity degree of spray cooling zones for improving quality in continuous casting of steel | |
| CN115455760A (en) | Casting blank on-line thermal state tracking method | |
| CN115026136A (en) | Method for predicting plate shape of endless rolling wedge-shaped transition process |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |