CN113505482B - Method and device for obtaining taper curve of copper pipe of square billet crystallizer and storage medium - Google Patents
Method and device for obtaining taper curve of copper pipe of square billet crystallizer and storage medium Download PDFInfo
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- RYGMFSIKBFXOCR-UHFFFAOYSA-N Copper Chemical compound [Cu] RYGMFSIKBFXOCR-UHFFFAOYSA-N 0.000 title claims abstract description 102
- 229910052802 copper Inorganic materials 0.000 title claims abstract description 102
- 239000010949 copper Substances 0.000 title claims abstract description 102
- 238000000034 method Methods 0.000 title claims abstract description 44
- 238000003860 storage Methods 0.000 title claims abstract description 14
- 238000005266 casting Methods 0.000 claims abstract description 141
- 239000007790 solid phase Substances 0.000 claims abstract description 86
- 239000007788 liquid Substances 0.000 claims abstract description 44
- 238000007711 solidification Methods 0.000 claims abstract description 27
- 230000008023 solidification Effects 0.000 claims abstract description 27
- 238000012546 transfer Methods 0.000 claims abstract description 18
- 238000013178 mathematical model Methods 0.000 claims description 51
- 239000007787 solid Substances 0.000 claims description 23
- 238000004590 computer program Methods 0.000 claims description 20
- 239000000498 cooling water Substances 0.000 claims description 13
- 239000012071 phase Substances 0.000 claims description 10
- 238000001816 cooling Methods 0.000 claims description 8
- 238000009749 continuous casting Methods 0.000 claims description 7
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 claims description 6
- 230000005499 meniscus Effects 0.000 claims description 3
- 238000006243 chemical reaction Methods 0.000 claims 2
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- 230000015572 biosynthetic process Effects 0.000 abstract description 3
- 238000004519 manufacturing process Methods 0.000 abstract description 3
- 238000005457 optimization Methods 0.000 abstract description 3
- 229910000831 Steel Inorganic materials 0.000 description 11
- 239000010959 steel Substances 0.000 description 11
- 238000004364 calculation method Methods 0.000 description 7
- 230000006870 function Effects 0.000 description 7
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- 238000005299 abrasion Methods 0.000 description 2
- 238000013473 artificial intelligence Methods 0.000 description 2
- 230000004907 flux Effects 0.000 description 2
- 239000007791 liquid phase Substances 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000017525 heat dissipation Effects 0.000 description 1
- 238000010801 machine learning Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
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- 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
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- G—PHYSICS
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Abstract
The application relates to a method and a device for solving a taper curve of a copper pipe of a square billet crystallizer and a storage medium, wherein the method comprises the following steps: determining a temperature field of a casting blank based on solidification heat transfer characteristics of casting liquid, and solving solid phase rate of each point of the casting blank in the square blank crystallizer according to the temperature field of the casting blank, the solidus temperature of the casting liquid and the liquidus temperature of the casting liquid; determining the total width of the air gap in the preset height according to the solid phase rate of the casting blank in the preset height; sequentially determining the width of the square billet crystallizer copper pipe in each height according to the total width of the air gap of each preset height; and determining the taper curve of the square billet crystallizer copper pipe according to the width of each height of the square billet crystallizer copper pipe. According to the scheme, the width of the air gap formed by solidifying casting liquid can be effectively calculated, the width of the square billet crystallizer copper pipe is further adjusted according to the width of the air gap, optimization of a taper curve of the crystallizer copper pipe is effectively realized, the shape of an inner cavity of the crystallizer and a formed billet shell is as close as possible, the formation of the air gap is reduced, the heat transfer effect of the crystallizer is better improved, and the production requirement is met.
Description
Technical Field
The application relates to a method and a device for solving a copper pipe taper curve of a square billet crystallizer and a storage medium, and belongs to the technical field of design of copper pipe taper curves of the crystallizer.
Background
The crystallizer is a key device in the continuous casting process, is a forced water-cooled bottomless ingot mould, and can promote the molten steel to solidify rapidly by providing uniform and rapid cooling for the molten steel, and can ensure that the blank shell after the copper pipe of the crystallizer is discharged can bear the static pressure of the molten steel which is not solidified in the interior. The cooling performance of the mould directly affects the quality of the cast strand, called the "heart" of the continuous casting machine.
The casting solution generates heat shrinkage when solidifying in the crystallizer, and an air gap is formed between the blank shell and the crystallizer, so that heat transfer is greatly hindered, the cooling effect of the crystallizer is reduced, the blank shell is thinned, and the grain size of the primary blank shell can be influenced. The higher the continuous casting pulling speed is, the higher the requirement on cooling and heat transfer effects of the crystallizer is.
In order to improve the cooling effect, the inner cavity of the crystallizer is designed to be of an inverted cone, so that the blank shell and the copper pipe of the crystallizer are in good contact. The taper is too small, a larger air gap is generated between the inner cavity of the crystallizer and the solidified blank shell, and the heat transfer of the casting blank is influenced and the blank pulling speed is limited; the overlarge taper can lead to the abrasion of the solidified shell to the inner cavity of the crystallizer, affect the service life of the copper pipe of the crystallizer, and even lead to the shell to be broken after exiting the crystallizer, thereby causing steel leakage accidents.
If the taper design of the crystallizer is based on the central solidification shrinkage, an air gap is formed at the corner, so that the temperature of the corner is overheated, and cracks and steel leakage are easy to form at the corner; if the taper design is based on the solidification shrinkage of the corner, the problem of overlarge taper at other positions is caused, so that the taper is extruded with the copper plate, the blank drawing resistance is increased, the abrasion of a crystallizer is serious, and even the blank shell is broken.
Disclosure of Invention
The application provides a method, a device and a storage medium for solving the problem that in the prior art, when a crystallizer is designed by taking central solidification shrinkage as a standard, an air gap is formed at the corner, the temperature at the corner is overheated, cracks are easily formed at the corner, and steel leakage occurs; the angle part solidification shrinkage is used as a standard design crystallizer taper, so that the problem of overlarge taper at other positions can be caused, the mold is extruded with a copper plate, the blank pulling resistance is increased, the copper plate is seriously worn, and the blank shell can be broken.
In order to solve the technical problems, the application provides the following technical scheme:
according to a first aspect, an embodiment of the present application provides a method for obtaining a taper curve of a copper tube of a square billet crystallizer, including:
determining a temperature field of a casting blank based on solidification heat transfer characteristics of casting liquid, and solving solid phase rate of each point of the casting blank in the square blank crystallizer according to the temperature field of the casting blank, the solidus temperature of the casting liquid and the liquidus temperature of the casting liquid;
determining the total width of the air gap in the preset height according to the solid phase rate of the casting blank in the preset height;
sequentially determining the width of each height of the copper pipe inner cavity of the square billet crystallizer according to the total width of the air gap in each preset height;
and determining the taper curve of the square billet crystallizer copper pipe according to the width of each height of the square billet crystallizer copper pipe.
Preferably, the determining the total width of the air gap in the preset height according to the solid phase rate of the casting blank in the preset height comprises the following steps:
adopting a first mathematical model to obtain the width of an air gap formed in a region with the solid phase rate of more than or equal to 1 in a preset height;
according to the air gap width formed by the area with the solid phase rate larger than or equal to 1 in the preset height, adopting a second mathematical model to obtain the air gap width corresponding to each solid phase rate with the solid phase rate between 0 and 1;
and determining the total width of the air gaps formed in the preset height of the square billet crystallizer by adopting a third mathematical model according to the width of the air gaps formed in the area with the solid phase rate of more than or equal to 1 in the preset height and the width of the air gaps corresponding to the solid phase rates between 0 and 1.
Preferably, the method comprises the steps of,
the first mathematical model is:
σ 0 ＝(ρ av /ρ-1)*h 0 (1-1)
the second mathematical model is:
σ i+1 ＝(0+0.05*i)*(σ 0 /h 0 )*h i+1 (1-2)
the third mathematical model is:
wherein ρ is av Is the average density of the solid blank shell; ρ is the density of the casting solution, h 0 The thickness of the solid blank shell (i.e. the solid phase rate is more than or equal to 1); sigma (sigma) 0 The width of the air gap is equal to or larger than 1 when the casting solution is solidified into a solid blank shell (i.e. the solid phase rate is equal to or larger than 1); h is a i+1 For a two-phase zone shell thickness, sigma, of between i/10 and (i+1)/10 solids fraction i+1 The casting solution is converted into an air gap width caused by solidification shrinkage in a two-phase region between i/10 and (i+1)/10 of a solid phase rate; sigma is the total width of an air gap caused by solidification of the final casting solution in the preset height of the square billet crystallizer; wherein i is an integer from 0 to 9.
Preferably, the method comprises the steps of,
the method for determining the total width of the air gap in the preset height according to the solid phase rate of the casting blank in the preset height comprises the following steps:
determining the width of the air gap corresponding to the corner according to the solid phase ratio of the corner position;
determining the width of the air gap corresponding to the center of the broad face according to the solid phase rate of the center of the broad face;
the method for determining the width of the square billet crystallizer copper pipe in each height sequentially according to the total width of the air gap in each preset height comprises the following steps:
determining the width of the corner of the square billet crystallizer according to the width of the air gap corresponding to the corner;
determining the width of the wide surface center of the square billet crystallizer according to the width of the air gap corresponding to the wide surface center;
and step 153, linearly calculating the corner width and the wide surface center width of the square billet crystallizer, and determining the corresponding widths of the square billet crystallizer in other positions except the corner and the wide surface center positions.
Preferably, the determining the temperature field of the casting blank based on the solidification heat transfer characteristic of the casting liquid, and calculating the solid phase ratio of each point of the casting blank in the square blank crystallizer according to the temperature field of the casting blank, the solidus temperature of the casting liquid and the liquidus temperature of the casting liquid comprises:
determining a temperature field of a casting blank in the square billet crystallizer according to a preset fourth mathematical model and boundary conditions thereof;
and solving the solid phase rate of each point of the casting blank in the square blank crystallizer according to the temperature field of the casting blank, the solidus temperature of the casting liquid and the liquidus temperature of the casting liquid.
Preferably, the method comprises the steps of,
the fourth mathematical model is:
the boundary conditions are:
T(x,y)| t＝0 ＝T C (1-7)
wherein T is temperature, DEG C; t is the residence time of casting solution in the crystallizer, s; lambda (T) is the effective thermal conductivity, W/(m·deg.C); ρ (T) is the density of the casting solution, kg/m 3 The method comprises the steps of carrying out a first treatment on the surface of the C (T) is the specific heat of casting solution, J/(kg DEG C); q is instantaneous heat flux density in the height direction of the crystallizer, W/m 2 The method comprises the steps of carrying out a first treatment on the surface of the L is the distance between the casting liquid and the meniscus at the moment t, and m; v is the pulling speed of the continuous casting machine, m/s; c (C) w Specific heat for cooling water, namely 4200J/(kg. Deg.C); q (Q) w For cooling water flow, m 3 /s；ΔT w The temperature difference of water at the inlet and the outlet of cooling water is DEG C; ρ w For cooling water density, 1000kg/m 3 The method comprises the steps of carrying out a first treatment on the surface of the S is the effective area of the crystallizer, m 2 For billets, the value A is 2680000 and the value B is related to the water cooling parameters of the crystallizer.
Preferably, the method comprises the steps of,
the method for determining the width of the inner cavity corner of the square billet crystallizer according to the width of the air gap corresponding to the corner comprises the following steps:
based on the width alpha and angle of the upper opening of the inner cavity of the copper pipe by adopting a fifth mathematical modelWidth sigma of air gap corresponding to the portion (0,h) Obtaining the width z of the corner of the square billet crystallizer (0,h) The fifth mathematical model is:
z (0,h) ＝α-σ (0,h) (1-9)
adopting a sixth mathematical model, and based on the width alpha of the upper opening of the inner cavity of the copper pipe and the width sigma of the air gap corresponding to the center of the broad face (α/2,h) Solving the central width z of the wide surface of the square billet crystallizer (α/2,h) The sixth mathematical model is:
z (α/2,h) ＝α-σ (α/2,h) (1-10)
adopting a seventh mathematical model and based on the corner width z of the square billet crystallizer (0,h) Width z of wide face center of square billet crystallizer (α/2,h) Obtaining the width z of the inner cavity of the crystallizer at the position of xmm of the distance corner (x,h) The seventh mathematical model is:
z (x,h) ＝z (0,h) +2(z (α/2,h) -z (0,h) )/α*x (1-11)
wherein the width of the upper opening of the inner cavity of the copper pipe is alpha mm, the coordinates of the corner part are set to be (0, h) and the coordinates of the center of the wide surface are set to be (alpha/2,h) at the position which is far from the upper opening hmm of the copper pipe, the coordinates of the position which is between the corner part and the center of the wide surface and is far from the corner part xmm are set to be (x, h), and the width of the position which is at the corner part is z (0,h) The width of the center position of the broad face is z (α/2,h) 。
In a second aspect, according to an embodiment of the present application, there is provided a device for obtaining a taper curve of a copper tube of a square billet crystallizer, including:
the temperature field and solid phase rate obtaining module is used for determining the temperature field of the casting blank based on the solidification heat transfer characteristic of casting liquid, and obtaining the solid phase rate of each point of the casting blank in the square blank crystallizer according to the temperature field of the casting blank, the solidus temperature of the casting liquid and the liquidus temperature of the casting liquid;
the air gap total width obtaining module is used for determining the air gap total width in the preset height according to the solid phase rate of the casting blank in the preset height;
the copper pipe inner cavity width obtaining module is used for determining the width of the square billet crystallizer copper pipe in each height according to the total width of the air gap of each preset height in sequence;
and determining the taper curve of the square billet crystallizer copper pipe according to the width of the crystallizer copper pipe in each height.
In a third aspect, according to an embodiment of the present application, there is provided a device for obtaining a square billet crystallizer copper tube taper curve, where the device includes a processor, a memory, and a computer program stored in the memory and capable of running on the processor, where the computer program is loaded and executed by the processor, so as to implement the steps of the method for obtaining a square billet crystallizer copper tube taper curve according to any one of the foregoing steps.
In a fourth aspect, according to an embodiment of the present application, there is provided a computer readable storage medium storing a computer program, where the computer program is executed by a processor to implement the steps of the method for obtaining a taper curve of a copper tube of a bloom crystallizer.
The beneficial effects of this application lie in: and obtaining the solid phase rate of each point of the square billet based on the obtained temperature field, liquidus temperature and solidus temperature, and then determining the width of the air gap in each height of the square billet crystallizer copper pipe according to the solid phase rate of the casting billet in each preset height, and further determining the width of the square billet crystallizer copper pipe in each height according to the width of the air gap. According to the scheme, the width of the air gap formed by solidifying casting liquid can be effectively calculated, the width of the square billet crystallizer is adjusted according to the width of the air gap, optimization of the taper curve of the copper pipe of the crystallizer is effectively realized, the shape of the inner cavity of the crystallizer and the shape of the formed billet shell are as close as possible, the formation of the air gap is reduced, the heat transfer effect of the crystallizer is better improved, and the production requirement is met.
In addition, according to the scheme, the width of the corner and the width of the air gap in the center of the wide surface are obtained through a mathematical model, the width of the inner cavity of the crystallizer in the center of the corner and the wide surface is obtained, and the widths of the inner cavities of the crystallizer in other positions are obtained through linear calculation, so that a taper curve of the square billet crystallizer copper pipe is designed.
The foregoing description is only an overview of the technical solutions of the present application, and in order to make the technical means of the present application more clearly understood, it can be implemented according to the content of the specification, and the following detailed description of the preferred embodiments of the present application will be given with reference to the accompanying drawings.
Drawings
FIG. 1 is a flow chart of a method for obtaining a taper curve of a copper tube of a square billet crystallizer according to an embodiment of the present application;
FIG. 2 is a flow chart of the sub-steps involved in step S14 in one embodiment of the present application;
FIG. 3 is a flow chart of a method for determining a taper curve of a copper tube of a billet crystallizer according to still another embodiment of the present application;
FIG. 4 is a flow chart of sub-steps involved in step S12 in one embodiment of the present application;
FIGS. 5 and 6 are schematic diagrams of thickness curves of solid blank shells at different solid phases at the corner and the center of the broad face;
FIG. 7 is a schematic view of the taper curve of a copper tube at the center of the corner and the broad face designed according to the determined width;
FIG. 8 is a block diagram of a device for obtaining a taper curve of a copper tube of a billet crystallizer according to an embodiment of the present application;
fig. 9 is a block diagram of a device for obtaining a taper curve of a copper tube of a billet crystallizer according to an embodiment of the present application.
Detailed Description
The following examples are illustrative of the present application but are not intended to limit the scope of the present application.
Fig. 1 is a method for obtaining a taper curve of a copper tube of a square billet crystallizer according to an embodiment of the present application, including:
step S12, determining a temperature field of a casting blank based on solidification heat transfer characteristics of casting liquid, and solving solid phase rate of each point of the casting blank in the square blank crystallizer according to the temperature field of the casting blank, solidus temperature of the casting liquid and liquidus temperature of the casting liquid;
in the embodiment of the application, the space formed by the casting solution in the square billet crystallizer is regarded as a three-dimensional space, so that the temperature of each point of the casting solution in the square billet crystallizer can be determined through a preset fourth mathematical model and boundary conditions thereof, and a temperature field of a casting blank is formed.
In the examples herein, the solid fraction is denoted as f S ，f S Less than or equal to 0 and representing a liquid phase region of a casting blank, 0<f S <1 represents a two-phase region of a casting blank, and f is more than or equal to 1 S Representing the solid phase region of the cast strand.
In the examples of the present application, the solid fraction f S The following formula is adopted for the calculation of (a):
wherein f S Is solid phase rate; t (T) S And T L The solidus temperature and the liquidus temperature, respectively; f (f) S Less than or equal to 0, the solidification area is a liquid phase area, 0<f S <1 represents that the solidification zone is a two-phase zone, f is not less than 1 S The coagulated region is represented as a solid phase region.
S14, determining the total width of the air gap in the preset height according to the solid phase rate of the casting blank in the preset height;
in the embodiment of the application, for each height divided in advance, determining the total width of the air gap in each height according to the solid phase rate of the casting blank in the height;
when the total width of the air gap of each height is calculated, the heat dissipation is faster based on the area close to the crystallizer, the solid phase rate is generally the largest, the lower the solid phase rate is, the more likely is the liquid state, and the solid phase rate is sequentially increased from the central area to the edge area of the square billet; as an alternative embodiment, between 0-1, the solid fraction is divided by 10 equally, i.e. the corresponding air gap widths are calculated for 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 and 1, respectively, and then the total air gap widths for each height are summed up.
S16, determining the width of the air gap in each height of the copper pipe inner cavity of the square billet crystallizer according to the total width of the air gap of each preset height in sequence; and determining the taper curve of the inner cavity of the square billet crystallizer copper pipe according to the width of the square billet crystallizer copper pipe in each height.
In the embodiment of the application, the corner width and the broad face center width of the copper pipe are preferably determined first, and then the widths of the copper pipes of the square billet crystallizer in the heights of other positions are determined according to the corner width and the broad face center width. The width in each height of other positions can be linearly solved according to the width of the corner and the width of the center of the wide surface.
In one embodiment of the present application, referring to fig. 2, in step S14, the determining the total width of the air gap in the preset height according to the solid phase ratio of the casting blank in the preset height includes:
step S141, adopting a first mathematical model to obtain the width of an air gap formed in a region with the solid phase ratio of more than or equal to 1 in a preset height;
step S142, according to the air gap width formed by the area with the solid phase rate greater than or equal to 1 in the preset height, adopting a second mathematical model to obtain the air gap width corresponding to each solid phase rate with the solid phase rate between 0 and 1;
step S143, determining the total width of the air gaps formed in the preset height of the square billet crystallizer by adopting a third mathematical model according to the air gap width formed in the area with the solid phase rate larger than or equal to 1 in the preset height and the air gap width corresponding to each solid phase rate between 0 and 1.
Further, in the embodiments of the present application,
the first mathematical model is:
σ 0 ＝(ρ av /ρ-1)*h 0 (1-1)
the second mathematical model is:
σ i+1 ＝(0+0.05*i)*(σ 0 /h 0 )*h i+1 (1-2)
the third mathematical model is:
wherein ρ is av Is the average density of the solid blank shell; ρ is the density of the casting solution, h 0 The thickness of the solid blank shell (i.e. the solid phase rate is more than or equal to 1); sigma (sigma) 0 The width of the air gap is equal to or larger than 1 when the casting solution is solidified into a solid blank shell (i.e. the solid phase rate is equal to or larger than 1); h is a i+1 For a two-phase zone shell thickness, sigma, of between i/10 and (i+1)/10 solids fraction i+1 The casting solution is converted into an air gap width caused by solidification shrinkage in a two-phase region between i/10 and (i+1)/10 of a solid phase rate; sigma is the total width of an air gap caused by solidification of the final casting solution in the preset height of the square billet crystallizer; wherein i is an integer from 0 to 9.
In an embodiment of the present application, as shown in figure 3,
in step S14, determining the total width of the air gap in the preset height according to the solid phase ratio of the casting blank in the preset height includes:
step S144, determining the width of the air gap corresponding to the corner according to the solid phase ratio of the corner position;
step S145, determining the width of the air gap corresponding to the center position of the broad face according to the solid phase rate corresponding to the center position of the broad face;
in step S15, the determining the width of the copper tube of the square billet crystallizer in each height sequentially according to the total width of the air gap in each preset height includes:
step S151, determining the width of the corner of the square billet crystallizer according to the width of the air gap corresponding to the corner;
step S152, determining the width of the center of the wide surface of the square billet crystallizer according to the width of the air gap corresponding to the center of the wide surface;
and step 153, linearly calculating the corner width and the wide surface center width of the square billet crystallizer, and determining the corresponding widths of the square billet crystallizer in other positions except the corner and the wide surface center positions.
Further, in this embodiment of the present application, referring to fig. 4, in step S12, the determining a temperature field of the casting blank based on the solidification heat transfer characteristic of the casting solution, and calculating the solid phase ratio of each point of the casting blank in the bloom crystallizer according to the temperature field of the casting blank, the solidus temperature of the casting solution, and the liquidus temperature of the casting solution includes:
step S121, determining a temperature field of a casting blank in the square billet crystallizer according to a preset fourth mathematical model and boundary conditions thereof;
and step S122, obtaining the solid phase rate of each point of the casting blank in the square blank crystallizer according to the temperature field of the casting blank, the solidus temperature of the casting liquid and the liquidus temperature of the casting liquid.
Still further, the method comprises the steps of,
the fourth mathematical model is:
the boundary conditions are:
T(x,y)| t＝0 ＝T C (1-7)
wherein T is temperature, DEG C; t is the residence time of casting solution in the crystallizer, s; lambda (T) is the effective thermal conductivity, W/(m·deg.C); ρ (T) is the density of the casting solution, kg/m 3 The method comprises the steps of carrying out a first treatment on the surface of the C (T) is the specific heat of casting solution, J/(kg DEG C); q is instantaneous heat flux density in the height direction of the crystallizer, W/m 2 The method comprises the steps of carrying out a first treatment on the surface of the L is the distance between the casting liquid and the meniscus at the moment t, and m; v is the pulling speed of the continuous casting machine, m/s; c (C) w Specific heat for cooling water, namely 4200J/(kg. Deg.C); q (Q) w For cooling water flow, m 3 /s；ΔT w The temperature difference of water at the inlet and the outlet of cooling water is DEG C; ρ w For cooling water density, 1000kg/m 3 The method comprises the steps of carrying out a first treatment on the surface of the S is the effective area of the crystallizer, m 2 For billets, the value A is 2680000 and the value B is related to the water cooling parameters of the crystallizer.
In the embodiments of the present application,
the method for determining the corner width of the square billet crystallizer according to the air gap width corresponding to the corner comprises the following steps:
adopting a fifth mathematical model based on the upper opening width alpha of the inner cavity of the copper pipe and the air gap width sigma corresponding to the corner (0,h) Obtaining the width z of the corner of the square billet crystallizer (0,h) The fifth mathematical model is:
z (0,h) ＝α-σ (0，h) (1-9)
adopting a sixth mathematical model, and based on the width alpha of the upper opening of the inner cavity of the copper pipe and the width sigma of the air gap corresponding to the center of the broad face (α/2,h) Solving the central width z of the wide surface of the square billet crystallizer (α/2,h) The sixth mathematical model is:
z (α/2,h) ＝α-σ (α/2,h) (1-10)
seven mathematical models are adopted, and the width z of the corner of the square billet crystallizer is based (0,h) Width z of wide face center of square billet crystallizer (α/2,h) Obtaining the width z of the inner cavity of the crystallizer at the position of xmm of the distance corner (x,h) The seventh mathematical model is:
z (x,h) ＝z (0,h) +2(z (α/2,h) -z (0,h) )/α*x (1-11)
wherein the width of the upper opening of the inner cavity of the copper pipe is alpha mm, the coordinates of the corner part are set to be (0, h) and the coordinates of the center of the wide surface are set to be (alpha/2,h) at the position which is far from the upper opening hmm of the copper pipe, the coordinates of the position which is between the corner part and the center of the wide surface and is far from the corner part xmm are set to be (x, h), and the width of the position which is at the corner part is z (0,h) The width of the center position of the broad face is z (α/2,h) ，σ (x，h) The total width of the air gap resulting from solidification of the final casting solution.
In summary, according to the technical scheme provided by the application, the solid phase rate of each point of the square billet is obtained based on the obtained temperature field, liquidus temperature and solidus temperature, then, the air gap width in each height of the copper pipe of the square billet crystallizer is determined according to the total air gap width in each preset height, and then, the width in each height of the inner cavity of the copper pipe of the square billet crystallizer is determined according to the air gap width. According to the scheme, the width of the air gap formed by solidifying casting liquid can be effectively calculated, the width of the square billet crystallizer copper pipe is further adjusted according to the width of the air gap, optimization of a taper curve of the crystallizer copper pipe is effectively realized, the shape of an inner cavity of the crystallizer and a formed billet shell is as close as possible, the formation of the air gap is reduced, the heat transfer effect of the crystallizer is better improved, and the production requirement is met.
In addition, according to the scheme, the air gap width between the corner and the center of the wide surface is obtained through a mathematical model, the width of the inner cavity of the crystallizer at the center of the corner and the center of the wide surface is obtained, and the widths of the inner cavities of the crystallizer at other positions are obtained through linear calculation, so that the taper curve of the square billet crystallizer copper pipe is designed.
The following is an illustration of one specific embodiment:
for a small-sized billet continuous casting machine, the casting steel grade is C70DA, the section size is 140X 140mm, the casting temperature is 1500 ℃, the cooling water quantity of a crystallizer is 1750L/min, and the pulling speed is 2.6m/min. And adjusting initial and boundary conditions, and solving a heat transfer control equation to obtain a temperature field of the casting blank in the crystallizer. The solidus and liquidus temperatures of the combined components, C70DA steel grade are 1387 ℃ and 1476 ℃, respectively, and the thickness curves of the solid blank shell at the corner and the center position of the broad face under different solid phases can be obtained, as shown in figures 5 and 6 respectively.
Counting the temperature field of the solid blank in the crystallizer to obtain the average temperature of the broad-face center blank of about 1200 ℃, the average temperature of the corner blank of about 1100 ℃, and combining the C70DA steel grade components to obtain the broad-face center average density of the solid blank of about 7480kg/m 3 The average density of the corner blank shell is about 7530kg/m 3 The density of the molten steel at the casting temperature was about 7020kg/m 3 . And solving the width of the air gap caused by solidification of molten steel into a solid blank shell by combining thickness curves of the crystallizer at different solid phases, and further designing taper curves of the copper pipe at the central positions of the corners and the wide faces, as shown in fig. 7, wherein the upper curve is the central width of the wide faces, and the lower curve is the width of the corners.
According to the method for obtaining the taper curve of the square billet crystallizer copper pipe, the angle part width of the square billet crystallizer and the air gap width of the wide surface center are obtained based on the mathematical model, then the angle part width and the air gap width of the wide surface center are obtained, and the widths of other positions are obtained by linear calculation based on the angle part width and the wide surface center width, so that the purpose of taper design of the square billet crystallizer copper pipe is achieved.
Example 2
The embodiment of the application also provides a device for obtaining the taper curve of the copper pipe of the square billet crystallizer, which is shown in fig. 8 and comprises:
a temperature field and solid phase ratio obtaining module 81, configured to determine a temperature field of a casting blank based on solidification heat transfer characteristics of casting liquid, and obtain solid phase ratios of each point of the casting blank in the square blank crystallizer according to the temperature field of the casting blank, the solidus temperature of the casting liquid, and the liquidus temperature of the casting liquid;
the air gap total width obtaining module 82 is configured to determine an air gap total width in a preset height according to a solid phase rate of the casting solution in the preset height;
the copper pipe inner cavity width obtaining module 83 is used for determining the width of the square billet crystallizer copper pipe in each height according to the total width of the air gap of each preset height in sequence;
and determining the taper curve of the square billet crystallizer copper pipe according to the width of the crystallizer copper pipe in each height.
Fig. 9 is a block diagram of a device for obtaining a taper curve of a copper tube of a square billet crystallizer according to an embodiment of the present application, where the device for obtaining a taper curve of a copper tube of a square billet crystallizer according to the embodiment may be a computing device such as a desktop computer, a notebook computer, a palm computer, a cloud server, etc., and the device may include, but is not limited to, a processor and a memory. The device for obtaining the taper curve of the copper tube of the square billet crystallizer in this embodiment at least includes a processor and a memory, where the memory stores a computer program, the computer program can run on the processor, and when the processor executes the computer program, the steps in the embodiment of the method for obtaining the taper curve of the copper tube of the square billet crystallizer are implemented, for example, the steps in the method for obtaining the taper curve of the copper tube of the square billet crystallizer shown in fig. 1. Or when the processor executes the computer program, the functions of the modules in the embodiment of the device for obtaining the taper curve of the copper pipe of the square billet crystallizer are realized.
The computer program may be divided into one or more modules, which are stored in the memory and executed by a processor to accomplish the present invention, for example. The one or more modules may be a series of computer program instruction segments capable of performing a specific function, the instruction segments being used to describe the execution of the computer program in the apparatus for determining the taper curve of the copper tube of the bloom crystallizer. For example, the computer program may be divided into a temperature field calculation module, a solid fraction calculation module, an air gap width calculation module, and a width determination module, each of which has the following specific functions:
the temperature field and solid phase rate obtaining module is used for determining the temperature field of the casting blank based on the solidification heat transfer characteristic of casting liquid, and obtaining the solid phase rate of each point of the casting blank in the square blank crystallizer according to the temperature field of the casting blank, the solidus temperature of the casting liquid and the liquidus temperature of the casting liquid;
the air gap total width obtaining module is used for determining the air gap total width in the preset height according to the solid phase rate of the casting blank in the preset height;
the square billet width obtaining module is used for determining the width of the square billet crystallizer copper pipe in each height according to the total width of the air gap in each preset height in sequence;
and determining the taper curve of the square billet crystallizer copper pipe according to the width of the crystallizer copper pipe in each height.
The processor may include one or more processing cores, such as: 4 core processor, 6 core processor, etc. The processor may be implemented in at least one hardware form of DSP (Digital Signal Processing ), FPGA (Field-Programmable Gate Array, field programmable gate array), PLA (Programmable Logic Array ). The processor may also include a main processor, which is a processor for processing data in an awake state, also called a CPU (Central Processing Unit ), and a coprocessor; a coprocessor is a low-power processor for processing data in a standby state. In some embodiments, the processor may also include an AI (Artificial Intelligence ) processor for processing computing operations related to machine learning. The processor is a control center of the square billet crystallizer copper pipe taper curve calculating device, and various interfaces and circuits are utilized to connect all parts of the whole square billet crystallizer copper pipe taper curve calculating device.
The memory can be used for storing the computer program and/or the module, and the processor can realize various functions of the device for solving the copper pipe taper curve of the square billet crystallizer by running or executing the computer program and/or the module stored in the memory and calling the data stored in the memory. The memory may mainly include a storage program area and a storage data area, wherein the storage program area may store an operating system, an application program (such as a sound playing function, an image playing function) required for at least one function, and the like; the storage data area may store data (such as audio data, phonebook, etc.) created according to the use of the handset, etc. In addition, the memory may include high-speed random access memory, and may also include non-volatile memory, such as a hard disk, memory, plug-in hard disk, smart Media Card (SMC), secure Digital (SD) Card, flash Card (Flash Card), at least one disk storage device, memory device, or other volatile solid-state storage device.
It will be understood by those skilled in the art that the apparatus described in this embodiment is merely an example of the apparatus for obtaining the taper curve of the copper tube of the square billet crystallizer, and does not limit the apparatus for obtaining the taper curve of the copper tube of the square billet crystallizer, and in other embodiments, the apparatus may further include more or fewer components, or may combine some components, or different components, for example, the apparatus for obtaining the taper curve of the copper tube of the square billet crystallizer may further include an input/output device, a network access device, a bus, and so on. The processor, memory, and peripheral interfaces may be connected by buses or signal lines. The individual peripheral devices may be connected to the peripheral device interface via buses, signal lines or circuit boards. Illustratively, peripheral devices include, but are not limited to: radio frequency circuitry, touch display screens, audio circuitry, and power supplies, among others.
Of course, the device for obtaining the taper curve of the copper tube of the square billet crystallizer can also comprise fewer or more components, which is not limited in this embodiment.
Optionally, the present application further provides a computer readable storage medium, where a computer program is stored, where the computer program is executed by a processor to implement the steps of the method for obtaining the taper curve of the copper tube of the billet crystallizer.
Optionally, the present application further provides a computer product, where the computer product includes a computer readable storage medium, where a program is stored in the computer readable storage medium, and the program is loaded and executed by a processor to implement the steps of the method embodiment for determining a taper curve of a copper tube of a bloom crystallizer.
The technical features of the above-described embodiments may be arbitrarily combined, and all possible combinations of the technical features in the above-described embodiments are not described for brevity of description, however, as long as there is no contradiction between the combinations of the technical features, they should be considered as the scope of the description.
The above examples merely represent a few embodiments of the present application, which are described in more detail and are not to be construed as limiting the scope of the invention. It should be noted that it would be apparent to those skilled in the art that various modifications and improvements could be made without departing from the spirit of the present application, which would be within the scope of the present application. Accordingly, the scope of protection of the present application is to be determined by the claims appended hereto.
Claims (7)
1. The method for obtaining the taper curve of the copper pipe of the square billet crystallizer is characterized by comprising the following steps of:
determining a temperature field of a casting blank based on solidification heat transfer characteristics of casting liquid, and solving solid phase rate of each point of the casting blank in the square blank crystallizer according to the temperature field of the casting blank, the solidus temperature of the casting liquid and the liquidus temperature of the casting liquid;
determining the total width of the air gap in the preset height according to the solid phase rate of the casting blank in the preset height;
sequentially determining the width of each height of the copper pipe inner cavity of the square billet crystallizer according to the total width of the air gap of each preset height;
the taper curve of the inner cavity of the square billet crystallizer copper pipe is determined according to the width of each height of the square billet crystallizer copper pipe;
the method for determining the total width of the air gap in the preset height according to the solid phase rate of the casting blank in the preset height comprises the following steps:
adopting a first mathematical model to obtain the width of an air gap formed in a region with the solid phase rate of more than or equal to 1 in a preset height;
according to the air gap width formed by the area with the solid phase rate larger than or equal to 1 in the preset height, adopting a second mathematical model to obtain the air gap width corresponding to each solid phase rate with the solid phase rate between 0 and 1;
according to the air gap width formed in the area with the solid phase rate being more than or equal to 1 in the preset height and the air gap width corresponding to each solid phase rate between 0 and 1, determining the total air gap width formed in the preset height of the square billet crystallizer by adopting a third mathematical model;
the first mathematical model is:
（1-1）
the second mathematical model is:
（1-2）
the third mathematical model is:
（1-3）
wherein,is the average density of the solid blank shell; />For the density of the casting solution,/->The thickness of the solid blank shell is equal to or more than 1; />The width of the air gap caused by solidifying casting solution into a solid blank shell; />For the solid phase rate of->To->Thickness of the blank shell in the two-phase region between +.>For the conversion of the casting solution to a solid phase fraction +.>To->The width of the air gap caused by solidification shrinkage in the two-phase region; />Presetting the total width of an air gap caused by solidification of final casting liquid in the height of a square billet crystallizer; wherein->Is an integer of 0 to 9.
2. The method according to claim 1, wherein,
the method for determining the total width of the air gap in the preset height according to the solid phase rate of the casting blank in the preset height comprises the following steps:
determining the width of the air gap corresponding to the corner according to the solid phase ratio of the corner position;
determining the width of the air gap corresponding to the center of the broad face according to the solid phase rate of the center of the broad face;
the method for determining the width of the copper pipe inner cavity of the square billet crystallizer in each height sequentially according to the total width of the air gap in each preset height comprises the following steps:
determining the width of the corner of the square billet crystallizer according to the width of the air gap corresponding to the corner;
determining the width of the wide surface center of the square billet crystallizer according to the width of the air gap corresponding to the wide surface center;
and linearly calculating the corner width and the wide surface center width of the square billet crystallizer, and determining the corresponding widths of the square billet crystallizer in other positions except the corner and the wide surface center positions.
3. The method according to claim 2, wherein the determining the temperature field of the casting blank based on the solidification heat transfer characteristics of the casting liquid, and the calculating the solid phase ratio of each point of the casting blank in the square blank crystallizer based on the temperature field of the casting blank, the solidus temperature of the casting liquid and the liquidus temperature of the casting liquid comprises:
determining a temperature field of a casting blank in the square billet crystallizer according to a preset fourth mathematical model and boundary conditions thereof;
according to the temperature field of the casting blank, the solidus temperature of casting liquid and the liquidus temperature of casting liquid, the solid phase rate of each point of the casting blank in the square blank crystallizer is obtained;
the fourth mathematical model is:
（1-4）
the boundary conditions are:
（1-5）
（1-6）
（1-7）
（1-8）
wherein,temperature, DEG C; />S is the residence time of the casting solution in the crystallizer; />W/(m.DEG C) is the effective thermal conductivity; />For density of casting solution, kg/m 3 ；/>J/(kg. DEG C.) is the specific heat of the casting solution; />Is the instantaneous heat flow density in the height direction of the crystallizer, W/m 2 ；/>For casting fluids->The distance between the moment and the meniscus, m; />The drawing speed of the continuous casting machine is m/s; />Specific heat for cooling water, namely 4200J/(kg. Deg.C); />For cooling water flow, m 3 /s；/>The temperature difference of water at the inlet and the outlet of cooling water is DEG C; />For cooling water density, 1000kg/m 3 ；/>For the effective area of the crystallizer, m 2 For square billets, the following is added>Value 2680000, < >>The values are related to the crystallizer water cooling parameters.
4. The method according to claim 2, wherein,
the method for determining the corner width of the square billet crystallizer according to the air gap width corresponding to the corner comprises the following steps:
based on the width of the upper opening of the inner cavity of the copper pipe by adopting a fifth mathematical modelAir gap width corresponding to corner>Obtaining the corner width of square billet crystallizer as +.>The fifth mathematical model is:
（1-9）
based on the width of the upper opening of the inner cavity of the copper pipe by adopting a sixth mathematical modelAir gap width corresponding to broad face center>Solving the central width of the wide surface of the square billet crystallizer as +.>The sixth mathematical model is:
（1-10）
adopting a seventh mathematical model based on the corner width of the square billet crystallizerWide surface center width of square billet crystallizer>Find distance corner->Crystallizer cavity width at mm +.>The seventh mathematical model is:
（1-11）
wherein the width of the upper opening of the inner cavity of the copper pipe ismm, in the distance from the upper opening of the copper pipe +.>mm position, the corner coordinates are set to (0, ">) The broadside center coordinates are (++>,/>) Between the corner and the centre of the broad face and at a distance from the corner +.>Coordinates at mm (">,/>) The width of the corner part is ∈>The width of the center position of the broad face is +.>。
5. The utility model provides a square billet crystallizer copper pipe taper curve's device of solving which characterized in that includes:
the temperature field and solid phase rate obtaining module is used for determining the temperature field of the casting blank based on the solidification heat transfer characteristic of casting liquid, and obtaining the solid phase rate of each point of the casting blank in the square blank crystallizer according to the temperature field of the casting blank, the solidus temperature of the casting liquid and the liquidus temperature of the casting liquid;
the air gap total width obtaining module is used for determining the air gap total width in the preset height according to the solid phase rate of the casting blank in the preset height;
the copper pipe inner cavity width obtaining module is used for determining the width of the square billet crystallizer copper pipe in each height according to the total width of the air gap of each preset height in sequence;
determining a taper curve of the square billet crystallizer copper pipe according to the width of the crystallizer copper pipe in each height;
the method for determining the total width of the air gap in the preset height according to the solid phase rate of the casting blank in the preset height comprises the following steps:
adopting a first mathematical model to obtain the width of an air gap formed in a region with the solid phase rate of more than or equal to 1 in a preset height;
according to the air gap width formed by the area with the solid phase rate larger than or equal to 1 in the preset height, adopting a second mathematical model to obtain the air gap width corresponding to each solid phase rate with the solid phase rate between 0 and 1;
according to the air gap width formed in the area with the solid phase rate being more than or equal to 1 in the preset height and the air gap width corresponding to each solid phase rate between 0 and 1, determining the total air gap width formed in the preset height of the square billet crystallizer by adopting a third mathematical model;
the first mathematical model is:
（1-1）
the second mathematical model is:
（1-2）
the third mathematical model is:
（1-3）
wherein,is the average density of the solid blank shell; />For the density of the casting solution,/->The thickness of the solid blank shell is equal to or more than 1; />The width of the air gap caused by solidifying casting solution into a solid blank shell; />For the solid phase rate of->To->Thickness of the blank shell in the two-phase region between +.>For the conversion of the casting solution to a solid phase fraction +.>To->The width of the air gap caused by solidification shrinkage in the two-phase region; />Presetting the total width of an air gap caused by solidification of final casting liquid in the height of a square billet crystallizer; wherein->Is an integer of 0 to 9.
6. A device for determining the taper curve of copper tubes of a bloom crystallizer, the device comprising a processor, a memory and a computer program stored in the memory and executable on the processor, characterized in that the computer program is loaded and executed by the processor to implement the steps of the method for determining the taper curve of copper tubes of a bloom crystallizer according to any one of claims 1 to 4.
7. A computer-readable storage medium storing a computer program, wherein the computer program is executed by a processor to implement the steps of the method for determining a square billet crystallizer copper tube taper curve according to any one of claims 1 to 4.
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