CN114357789A - Method for setting taper angle of inner crystallizer of electroslag remelting hollow steel ingot and inner crystallizer - Google Patents
Method for setting taper angle of inner crystallizer of electroslag remelting hollow steel ingot and inner crystallizer Download PDFInfo
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Abstract
The invention relates to a method for setting a taper angle of an inner crystallizer of an electroslag remelting hollow steel ingot and the inner crystallizer, which comprise the following steps: establishing a first 1/4 symmetrical slag bath-hollow ingot system three-dimensional solid model; carrying out grid division on a first 1/4 symmetrical slag bath-hollow ingot system three-dimensional solid model to obtain a first grid model; setting the physical property of the slag pool, and setting the physical property of the hollow ingot to obtain a second grid model; the calculation domain of the hollow ingot is endowed with a first attribute, and the calculation domain of the slag pool is endowed with a second attribute, so that a third grid model is obtained; establishing a three-dimensional transient multi-physical field coupling analysis model based on the electromagnetic field boundary condition, the flow field boundary condition and the heat transfer boundary condition; obtaining a simulation result of the dynamic solidification heat transfer of the hollow ingot and the deformation behavior based on the density base; according to the simulation result, the inner crystallizer of the slag/gold interface distance is determinedIs a distance H from the bottom of the cylindrical partcylAir gap width, actual contact height H of inner wall of hollow ingot and inner crystallizerconAnd determining the cone angle range of the conical part of the final inner crystallizer.
Description
Technical Field
The invention relates to the technical field of metallurgy, in particular to a method for setting a taper angle of an inner crystallizer of an electroslag remelting hollow steel ingot and the inner crystallizer.
Background
The electroslag remelting hollow ingot process is used as a production technology in the field of high-quality, high-efficiency and energy-saving electroslag metallurgy, and provides a new way for preparing high-quality special steel and special alloy hollow ingots. In the process of electroslag remelting a hollow steel ingot, liquid slag is added into an annular space formed by an inner crystallizer, an outer crystallizer and a dummy ingot device, and the end part of a consumable electrode is inserted into the annular space. When a plurality of parallel consumable electrodes (arranged in a butterfly shape), slag and a bottom water tank form a power supply loop with a transformer through a short network, current is output from the transformer and passes through liquid slag, so that the end parts of the consumable electrodes are gradually heated and melted. The molten metal passes through the slag pool and enters the metal molten pool, and because the center of the crystallizer is provided with the water-cooling inner crystallizer, the liquid metal is gradually solidified to form a hollow cast ingot. And when the hollow ingot reaches a certain height, the dummy ingot device starts to pump ingots.
The crystallizer in the electroslag remelting hollow ingot comprises two parts: a cylindrical portion (for controlling bore formation size control and solidification) and a conical portion (for controlling solidification) wherein the slag/gold interface is at a distance (H) from the bottom of the cylindrical portioncylAnd the height of the slag/gold interface is controlled during actual production) and the reasonable design of the cone angle theta of the conical part are crucial to the smooth operation of the process.
When the hollow steel ingot is solidified, the outer wall is far away from the outer crystallizer unlike the inward radial shrinkage of the outer wall; the inner wall is contracted radially inwards to enable the inner wall to be close to the inner crystallizer. Distance H from oversize slag/gold interface to bottom of cylindrical partcylAnd an excessively small taper angle theta, which results in a hollow ingot having a radial directionThe inner crystallizer is tightly held during solidification and shrinkage, and the inner crystallizer is broken when the friction force is too large during blank drawing. While too small a slag/gold interface is at a distance H from the bottom of the cylindrical portioncylAnd the taper angle theta of the too large conical part can cause poor cooling effect of the hollow ingot, the solidification shrinkage can not compensate the retraction displacement of the conical part of the inner crystallizer far away, and further, the air gap of the ingot casting-inner crystallizer is too large, and the risk of slag leakage and steel leakage can be caused in serious cases.
In recent years, with the intensive research on the solidification shrinkage and deformation rules of continuous casting blank shells in the crystallizer by domestic and foreign researchers, a series of research results are obtained aiming at the taper design of the continuous casting crystallizer. Chinese patent publication No.: CN 103406505B discloses that the taper of slab crystallizer can fully compensate the shrinkage of the slab shell in the crystallizer, effectively inhibit the deformation of the slab shell in the crystallizer, and prevent the frequent occurrence of cracks on the surface and under the slab caused by excessive deformation of the initial solidified slab shell on the upper part of the crystallizer. Chinese patent publication No.: CN 108526421B discloses a continuous casting thin slab narrow surface Gaussian concave curved surface crystallizer and a design method thereof, wherein the inner surface working surface of the narrow surface copper plate of the continuous casting crystallizer is a continuous change curve structure which takes a transverse width central line as a symmetrical Gaussian curve distribution and takes the height direction as meeting the solidification shrinkage characteristic of the narrow surface of a billet shell from top to bottom. However, the above patents are all continuous casting external crystallizer internal taper design methods, and there is a great difference between the electroslag remelting hollow steel ingot technology and the continuous casting technology: the drawing speed of the electroslag remelting hollow steel ingot is very slow (almost a few percent of the drawing speed of continuous casting); the superheat degree of the molten steel is large; the temperature gradient in the crystallizer is large; the multi-physical field coupling (electro-magnetic-flow-thermal) is significantly different.
Chinese utility model patent publication No.: CN 201482972U discloses a crystallizer for electroslag remelting continuous stripping hollow steel ingot, the section of the core crystallizer presents an inverted trapezoid shape with wide upper edge and narrow lower edge, and the taper of the core crystallizer
The range is 3/100-3.5/100. However, this technique is characterized in that the inner mold (core) has no cylinderAnd in the section part, liquid metal is solidified and formed, an inner hole formed by the primary blank shell is inevitably large at the top and small at the bottom, and subsequent solidification cannot completely overcome the problems of slag leakage, steel leakage, locking of the inner crystallizer and the like between the inner hole of the hollow steel ingot and the inner crystallizer.
Therefore, the actual solidification shrinkage rule of the electroslag remelting hollow ingot under the combined action of the inner crystallizer and the outer crystallizer needs to be met sufficiently, the shrinkage of the hollow ingot in the inner crystallizer and the outer crystallizer is ensured to be uniform, the heat transfer and the growth of the hollow ingot are ensured to be uniform, the taper of the friction force applied to the inner crystallizer can be reduced to the maximum extent, and the problems of the solidification quality of the electroslag remelting hollow ingot, slag leakage, steel leakage, locking of the inner crystallizer and the like are solved.
Disclosure of Invention
Technical problem to be solved
In view of the above disadvantages and shortcomings of the prior art, the present invention provides a method for setting the taper angle of an inner crystallizer of an electroslag remelting hollow ingot and the inner crystallizer, which solves the problems of solidification quality of the electroslag remelting hollow ingot and easy generation of slag leakage, steel leakage and locking of the inner crystallizer under the traditional inner crystallizer.
(II) technical scheme
In order to achieve the purpose, the invention adopts the main technical scheme that:
in a first aspect, an embodiment of the present invention provides a method for setting a taper angle of a crystallizer in a hollow ingot with electroslag remelting, including:
s1, building a first 1/4 symmetrical slag pool-hollow ingot system three-dimensional solid model by adopting modeling software based on the pre-obtained electrode size, hollow ingot size and slag amount of the actual electroslag remelting hollow ingot;
s2, carrying out meshing on the first 1/4 symmetrical slag bath-hollow ingot system three-dimensional solid model to obtain a corresponding first mesh model;
s3, setting physical properties of the slag pool aiming at the calculation domain of the slag pool in the first grid model and setting physical properties of the hollow ingot aiming at the calculation domain of the hollow ingot to obtain a second grid model;
s4, giving a first attribute obtained in advance for the calculation domain of the hollow ingot in the second grid model, and giving a second attribute obtained in advance for the calculation domain of the slag bath to obtain a third grid model;
s5, based on the preset three-dimensional electromagnetic field boundary condition, the preset flow field boundary condition and the preset heat transfer boundary condition, establishing a three-dimensional transient multi-physical field coupling analysis model corresponding to the third grid model by adopting a multi-physical field coupling method;
s6, obtaining a simulation result of the dynamic solidification heat transfer of the hollow ingot and the deformation behavior based on the density base based on the three-dimensional transient multi-physical field coupling analysis model;
s7, determining the distance H between the slag/gold interface and the bottom of the cylindrical part of the inner crystallizer according to the simulation resultcylAir gap width, actual contact height H of inner wall and inner crystallizercon；
S8 based on HcylAir gap width, actual contact height H of inner wall and inner crystallizerconAnd a preset first conical part cone angle range, and determining the final conical part cone angle range of the inner crystallizer;
the first conical portion cone angle range includes a plurality of cone angle values.
Preferably, the first and second liquid crystal materials are,
the hollow ingot electrode size includes: electrode diameter;
the hollow ingot dimensions include: the inner diameter of the hollow ingot, the outer diameter of the hollow ingot and the wall thickness of the hollow ingot;
the height of the 1/4 symmetrical slag bath-hollow ingot system three-dimensional solid model is 5.5-6 times of the wall thickness of the hollow ingot;
in the step S3, fluent software is adopted to set the physical properties of the slag bath for the calculation domain of the slag bath in the first grid model and the physical properties of the hollow ingot for the calculation domain of the hollow ingot, so as to obtain a second grid model.
Preferably, in S3, the meshing is performed on the 1/4 symmetric slag bath-hollow ingot system three-dimensional solid model to obtain a first mesh model, which specifically includes:
aiming at the 1/4 symmetrical slag bath-hollow ingot system three-dimensional solid model, a non-uniform grid division method is adopted, the distance between grids of contact areas of the 1/4 symmetrical slag bath-hollow ingot system three-dimensional solid model is divided into 1-2 mm, and the distance between grids of non-contact areas is divided into 6-10 mm;
the contact area of the 1/4 symmetrical slag bath-hollow ingot system three-dimensional solid model is the contact area of the 1/4 symmetrical slag bath-hollow ingot system three-dimensional solid model, the area corresponding to the hollow ingot, the area corresponding to the inner crystallizer and the area corresponding to the outer crystallizer;
the non-contact area is an area corresponding to a hollow ingot in the 1/4 symmetrical slag bath-hollow ingot system three-dimensional solid model, an area corresponding to the inner crystallizer and an area corresponding to the outer crystallizer, which are not in contact with each other.
Preferably, the first and second liquid crystal materials are,
the pre-acquired first attribute comprises: the change relation of the electrical conductivity, viscosity, density, thermal conductivity and specific heat of the hollow ingot with the temperature;
the pre-acquired second attribute comprises: the change relation of the electrical conductivity, viscosity, density, thermal conductivity and specific heat of the slag system with the temperature.
Preferably, the S5 includes:
s51, setting an electromagnetic field, a flow field and a heat transfer control equation of a slag pool-hollow ingot calculation domain and a third attribute;
the third attribute is that the inner and outer walls of the hollow ingot in the third 1/4 symmetrical slag bath-hollow ingot system three-dimensional solid model have uniform slag crust thickness in the circumferential direction;
s52, based on the set slag bath-hollow ingot calculation domain electromagnetic field, flow field and heat transfer control equation, the third attribute and the preset electromagnetic field boundary condition, flow field boundary condition and heat transfer boundary condition, adopting a multi-physical-field implementation coupling method to establish a three-dimensional transient multi-physical-field coupling analysis model corresponding to the third grid model.
Preferably, the first and second liquid crystal materials are,
the electromagnetic field boundary condition of the slag bath-hollow ingot calculation domain comprises the following steps:
the potential at the bottom of the hollow ingot is 0, and the current density of the hollow ingot electrode in the slag pool projection area is I/S;
i is a remelting stationary phase current value; s is the area of the projection area of the electrode (group) in the slag pool;
the hollow ingot electrode has continuous magnetic flux densities in the slag pool projection area, the bottom of the hollow ingot and the free surface of the slag pool, and the magnetic vector potential flux is 0;
the magnetic vector potential flux at the inner walls of the slag pool and the hollow ingot is 0;
the magnetic vector potential at the outer walls of the slag pool and the hollow ingot is 0;
the flow field boundary condition of the slag bath-hollow ingot calculation domain comprises the following steps:
the hollow ingot electrode is a speed inlet in the projection area of the slag pool;
the bottom of the hollow ingot is a free outlet;
the hollow ingot electrode is a non-slip wall surface in a slag pool projection area, the inner wall and the outer wall of the slag pool and the inner wall and the outer wall of the hollow ingot;
the free surface of the slag pool has zero shear stress;
the flow heat boundary condition of the slag bath-hollow ingot calculation domain comprises the following steps:
the projection area of the hollow ingot electrode in the slag pool is the superheat degree of metal liquid phase temperature of 30K, and the free surface of the slag pool is applied in a convection and radiation mode;
the heat transfer between the inner wall and the outer wall of the slag pool and the heat transfer between the inner wall and the outer wall of the hollow ingot are convection heat transfer, the heat transfer boundary of the inner wall is applied according to a formula (1), and the heat transfer boundary of the outer wall is applied according to a formula (2);
the formula (1) is:
the formula (2) is:
hmoldheat exchange coefficient of the crystallizer;
δslagis the thickness of the slag crust;
kslagthe heat conductivity coefficient of the solid slag;
kairis the thermal conductivity of air;
δin_gapthe width of the air gap at the inner wall;
δout_gapis the width of the air gap at the outer wall.
Preferably, the first and second liquid crystal materials are,
extracting the temperature of the inner wall node of the slag bath-hollow ingot system and the corresponding position coordinate thereof, and calculating the air gap width delta at the inner wall by using a formula (3)in_gapAnd the data are substituted into the formula (1), and iteration is carried out circularly until convergence is achieved;
wherein z isiIs the z coordinate of any point on the inner wall of the hollow ingot;
zs-mis the z coordinate of the slag-metal interface;
theta is a set conical part cone angle;
L0is the inner radius of the hollow ingot;
ρ(Tcoh) The metal density is 0.5 liquid phase fraction;
ρ(Tin_surf) The corresponding density of each node at the inner wall under the temperature;
extracting all node temperatures and corresponding position coordinates of the slag bath-hollow ingot system, and calculating the air gap width delta at the outer wall by using a formula (4)out_gapAnd the data are substituted into the formula (2), and iteration is carried out circularly until convergence is achieved;
Ti_avethe average temperature of the grid cells in the direction of the wall thickness, when Ti_ave>TcohThe metal is in liquid form and the displacement is 0.
Preferably, the S8 includes:
s81, judging whether the current state is the current stateThe actual contact height H of the inner wall and the inner crystallizer under the set cone angle of the conical partconAnd the distance H from the slag/gold interface in the radial direction of the inner wall and the outer wall of the hollow ingot to the bottom of the cylindrical partcylWhether the difference value meets a first preset range or not is judged, and a judgment result is obtained;
s82, taking any taper angle value in the preset range of the taper angle of the first conical part as a new set taper angle of the conical part, and repeating S5-S8 until obtaining the judgment result corresponding to each taper angle value in the preset range of the taper angle of the first conical part;
and S83, determining the final inner crystallizer conical part cone angle range based on the judgment result corresponding to each conical angle value in the preset first conical part cone angle range.
Preferably, the S83 specifically includes:
s831, acquiring a first taper angle value based on a judgment result corresponding to each taper angle value in a preset taper angle range of the first taper part;
the first cone angle value comprises a cone angle value of which the difference value meets a first preset range according to a judgment result;
s832, determining a final conical angle range of the conical part of the inner crystallizer based on the first conical angle value;
and the cone angle range of the final conical part of the inner crystallizer is greater than or equal to the minimum value of the first cone angle values and less than or equal to the maximum value of the first cone angle values.
On the other hand, the embodiment also provides an electroslag remelting hollow steel ingot inner crystallizer, and the taper angle of the electroslag remelting hollow steel ingot inner crystallizer is set by any one of the above methods for setting the taper angle of the electroslag remelting hollow steel ingot inner crystallizer.
(III) advantageous effects
The invention has the beneficial effects that: the method for setting the taper angle of the crystallizer in the electroslag remelting hollow steel ingot adopts a multi-physical-field coupling method based on the preset three-dimensional electric field, magnetic field, flow field and heat transfer boundary conditions to establish the three-dimensional transient multi-physical-field coupling corresponding to the third grid modelAn analysis model for simulating the electro-magnetic-flow-thermal coupling behavior in the solidification process of the electroslag remelting hollow ingot and the radial shrinkage and deformation behavior of the hollow ingot in the whole inner crystallizer and the whole outer crystallizer along the height thereof so as to obtain the simulation result of the dynamic solidification heat transfer of the hollow ingot and the deformation behavior based on the density base, and determining the distance H between the slag/gold interface and the bottom of the cylindrical part of the inner crystallizer according to the simulation result (which fully considers the shrinkage and uniform heat transfer and growth of the hollow ingot in the inner crystallizer and the outer crystallizer)cylAir gap width, actual contact height H of inner wall and inner crystallizercon(ii) a Compared with the prior art, the method can maximally reduce the taper of the friction force applied to the inner crystallizer, improve the solidification quality of the electroslag remelting hollow ingot, and solve the problems of slag leakage, steel leakage, locking of the inner crystallizer and the like.
Drawings
FIG. 1 provides a method for setting a taper angle of a crystallizer in a hollow ingot with electroslag remelting according to an embodiment of the present invention;
FIG. 2 is a schematic view of a crystallizer provided in the examples;
FIG. 3 is a diagram illustrating a first mesh model in an embodiment of the invention;
FIG. 4 is a graph showing the relationship between density of a phi 300 mm/phi 100mm electroslag remelting P900 hollow steel ingot and temperature variation in the embodiment of the invention;
FIG. 5 is a temperature chart of different inner mold tapers ((a) taper angle of 0.5 °, (b) taper angle of 1 °, (c) taper angle of 1.5 °, (d) taper angle of 2 °) of an electroslag remelting hollow ingot of Φ 300mm/Φ 100mm in an embodiment of the present invention;
FIG. 6 is a distribution diagram of air gaps at the inner mold wall of different inner mold tapers of a phi 300 mm/phi 100mm electroslag remelting hollow steel ingot in the embodiment of the invention;
FIG. 7 is a drawing of an electroslag remelted hollow ingot according to an embodiment of the present invention.
[ description of reference ]
1: an inner crystallizer;
2: an outer crystallizer;
3: a slag pool;
4: a slag-gold interface;
5: a molten pool;
6: casting a hollow ingot;
7: an air gap;
8: an inner wall initial position;
9: the position of the inner wall after solidification.
Detailed Description
For the purpose of better explaining the present invention and to facilitate understanding, the present invention will be described in detail by way of specific embodiments with reference to the accompanying drawings.
In order to better understand the above technical solutions, exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the invention are shown in the drawings, it should be understood that the invention can be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
In this embodiment, taking the process of electroslag remelting phi 300 mm/phi 100mm (outer diameter/inner diameter) P900 austenitic stainless steel hollow ingot as an example, the method for setting the taper angle of the crystallizer in the electroslag remelting hollow ingot is adopted to calculate the multi-field coupling in the process of electroslag remelting hollow ingot of the ingot type and steel type.
In the embodiment of the invention, the inner crystallizer is composed of a cylindrical section and a conical section (a cone angle theta):
as shown in fig. 2, the inner crystallizer 1 and the outer crystallizer 2 form an annular space, the consumable electrode is inserted into the slag bath 3, the current is switched on, the slag bath 3 generates a large amount of joule heat to melt the consumable electrode, the molten drop passes through the slag bath 3 and the slag/metal interface 4 to form a molten metal bath 4, and then the molten metal bath 4 is cooled by the inner crystallizer 1, the outer crystallizer 2 and the bottom water tank together to form a hollow steel ingot 6. Along with the solidification and cooling, the inner wall primary blank shell radially shrinks from an initial position 8 to a solidified position 9, and an air gap 7 is formed between the solidified position 9 of the inner wall and the inner crystallizer 1.
Further, the inner crystallizer 1 consists of a cylindrical section and a conical section, wherein the distance between the bottom of the cylindrical section and the slag/gold interface 4 is HcylEnsure to be hollowForming the size of an inner hole of the ingot; the taper angle of the conical section is theta, so that the friction force borne by the inner crystallizer can be maximally reduced when the heat transfer of the solidified shell of the hollow ingot is ensured.
Referring to fig. 1, the present embodiment provides a method of setting a taper angle of a mold in a hollow ingot of electroslag remelting, comprising:
s1, building a first 1/4 symmetrical slag pool-hollow ingot system three-dimensional solid model by adopting modeling software based on the pre-obtained electrode size, hollow ingot size and slag amount of the actual electroslag remelting hollow ingot; the first 1/4 symmetrical slag bath-hollow ingot system three-dimensional solid model in this embodiment.
In practical application, the commercial software of the finite volume method is selected, and a 1/4 slag bath-hollow ingot system three-dimensional solid model is established according to the actual electroslag remelting hollow ingot electrode size phi 55mm (eight electrodes), the hollow ingot size phi 300 mm/phi 100mm and the slag bath height 90mm, wherein the hollow ingot solid model height is 590 mm.
And S2, performing meshing division on the first 1/4 symmetrical slag bath-hollow ingot system three-dimensional solid model to obtain a corresponding first mesh model, as shown in FIG. 3.
S3, setting the physical property of the slag pool aiming at the calculation domain of the slag pool in the first grid model and setting the physical property of the hollow ingot aiming at the calculation domain of the hollow ingot to obtain a second grid model.
The slag pool and the hollow ingot calculation domain in the embodiment are both multiphase flows.
And S4, giving a first attribute obtained in advance to the calculation domain of the hollow ingot in the second grid model, and giving a second attribute obtained in advance to the calculation domain of the slag bath to obtain a third grid model.
And S5, based on the preset three-dimensional electromagnetic field boundary condition, the preset flow field boundary condition and the preset heat transfer boundary condition, adopting a multi-physical-field coupling method to establish a three-dimensional transient multi-physical-field coupling analysis model corresponding to the third grid model.
Specifically, the three-dimensional transient multi-physical field coupling analysis model in the embodiment is used for simulating electro-magnetic-flow-thermal coupling behavior in the solidification process of the electroslag remelting hollow ingot and contraction and deformation behaviors of the inner and outer billet shells of the hollow ingot on the whole inner and outer crystallizers along the height and the circumferential direction of the inner and outer crystallizers.
And S6, obtaining a simulation result of the dynamic solidification heat transfer of the hollow ingot and the deformation behavior based on the density base based on the three-dimensional transient multi-physical field coupling analysis model.
S7, determining the distance H between the slag/gold interface and the bottom of the cylindrical part of the inner crystallizer according to the simulation resultcylAir gap width, actual contact height H of inner wall and inner crystallizercon。
S8 based on HcylAir gap width, actual contact height H of inner wall and inner crystallizerconAnd a preset first conical part cone angle range, and determining the final inner crystallizer conical part cone angle range.
The first conical portion cone angle range includes a plurality of cone angle values.
In practical applications of this embodiment, the dimensions of the hollow ingot electrode include: the diameter of the electrode.
The hollow ingot dimensions include: the inner diameter of the hollow ingot, the outer diameter of the hollow ingot and the wall thickness of the hollow ingot.
1/4 the height of the symmetrical slag bath-hollow ingot system three-dimensional solid model is 5.5-6 times of the wall thickness of the hollow ingot.
In the step S3, fluent software is adopted to set the physical properties of the slag bath for the calculation domain of the slag bath in the first grid model and the physical properties of the hollow ingot for the calculation domain of the hollow ingot, so as to obtain a second grid model.
In practical application of this embodiment, in S3, performing mesh division on the 1/4 symmetric slag bath-hollow ingot system three-dimensional solid model to obtain a first mesh model specifically includes:
aiming at the 1/4 symmetrical slag bath-hollow ingot system three-dimensional solid model, a non-uniform grid division method is adopted, the distance between grids of a contact area of the 1/4 symmetrical slag bath-hollow ingot system three-dimensional solid model is divided into 1-2 mm, and the distance between grids of a non-contact area is divided into 6-10 mm.
The contact area of the 1/4 symmetrical slag bath-hollow ingot system three-dimensional solid model is the contact area of the 1/4 symmetrical slag bath-hollow ingot system three-dimensional solid model, the area corresponding to the hollow ingot, the area corresponding to the inner crystallizer and the area corresponding to the outer crystallizer.
The non-contact area is an area corresponding to a hollow ingot in the 1/4 symmetrical slag bath-hollow ingot system three-dimensional solid model, an area corresponding to the inner crystallizer and an area corresponding to the outer crystallizer, which are not in contact with each other.
In practical application of this embodiment, the first attribute obtained in advance includes: the change relationship of the electrical conductivity, viscosity, density, thermal conductivity and specific heat of the hollow ingot with temperature.
In specific application, determining the electrical conductivity, viscosity, density, thermal conductivity coefficient and specific heat of the steel grade along with temperature change according to the content of main chemical components in the electroslag remelting hollow ingot steel; according to CaF in remelting slag system2，Al2O3CaO and SiO2And determining the electrical conductivity, viscosity, density, thermal conductivity coefficient and specific heat of the slag system according to the contents of the main components, and correspondingly giving the electrical conductivity, viscosity, density, thermal conductivity coefficient and specific heat to the ingot and the slag bath respectively to obtain the calculated domain attributes.
In the present example, the selected P900 steel composition is shown in Table 1
TABLE 1P900 Steel composition
In this example, the density of the P900 austenitic stainless steel is shown in fig. 4 as a function of temperature.
The pre-acquired second attribute comprises: the change relation of the electrical conductivity, viscosity, density, thermal conductivity and specific heat of the slag system with the temperature.
In practical applications of this embodiment, the S5 includes:
s51, setting a slag bath-hollow ingot calculation domain electromagnetic field, a flow field and heat transfer control equation and a third attribute.
The electromagnetic field control equation in the present embodiment includes:
wherein the current density
Electric scalar potential phi and magnetic vector potential
Magnetic induction intensity
σ denotes the conductivity, QJouleIt is expressed as the joule heat,
representing an electromagnetic force.
The flow field control equation is:
where ρ represents density;
represents a speed; p represents pressure; mu represents viscosity; β represents a thermal expansion coefficient;
represents the acceleration of gravity;
representing mushy zone resistance, T representing temperature; t0 denotes the reference temperature.
The heat transfer control equation is:
h represents enthalpy, λeffRepresenting the effective thermal conductivity.
The third attribute is that the inner and outer walls of the hollow ingot in the third 1/4 symmetrical slag bath-hollow ingot system three-dimensional solid model have uniform slag crust thickness in the circumferential direction;
s52, based on the set slag bath-hollow ingot calculation domain electromagnetic field, flow field and heat transfer control equation, the third attribute and the preset electromagnetic field boundary condition, flow field boundary condition and heat transfer boundary condition, adopting a multi-physical-field implementation coupling method to establish a three-dimensional transient multi-physical-field coupling analysis model corresponding to the third grid model.
In practical application of this embodiment, the electromagnetic field boundary conditions of the slag bath-hollow ingot calculation domain include:
the potential at the bottom of the hollow ingot is 0, and the current density of the hollow ingot electrode in the slag pool projection area is I/S.
I is a remelting stationary phase current value; s is the area of the projection area of the electrode (group) in the slag bath.
In this example, the reflow current was 5000A; the total area of the electrode group is 0.018997m2。
The hollow ingot electrode has continuous magnetic flux density in the slag pool projection area, the bottom of the hollow ingot and the free surface of the slag pool, and the magnetic vector potential flux is 0.
The magnetic vector potential flux at the inner walls of the slag pool and the hollow ingot is 0.
The magnetic vector potential at the outer walls of the slag pool and the hollow ingot is 0.
The flow field boundary condition of the slag bath-hollow ingot calculation domain comprises the following steps:
the hollow ingot electrode is a speed inlet in the projection area of the slag pool.
The bottom of the hollow ingot is a free outlet.
The hollow ingot electrode is a non-slip wall surface in the projection area of the slag pool, the inner wall and the outer wall of the slag pool and the inner wall and the outer wall of the hollow ingot.
The free surface of the slag pool has zero shear stress.
In this example, the ingot-drawing speed is 5mm/min, and the corresponding entrance speed is 2.3X 10-3 m/s.
The flow heat boundary condition of the slag bath-hollow ingot calculation domain comprises the following steps:
the projection area of the hollow ingot electrode in the slag pool is the superheat degree of metal liquid phase temperature of 30K, and the free surface of the slag pool is applied in a convection and radiation mode.
The heat transfer between the inner wall and the outer wall of the slag pool and the heat transfer between the inner wall and the outer wall of the hollow ingot are convection heat transfer, the heat transfer boundary of the inner wall is applied according to a formula (1), and the heat transfer boundary of the outer wall is applied according to a formula (2).
The formula (1) is:
the formula (2) is:
hmoldheat exchange coefficient of the crystallizer.
In this example hmold＝2000W·m-2·K-1。
δslagIs the thickness of the slag crust.
kslagThe heat conductivity coefficient of the solid slag.
kairIs the thermal conductivity of air.
δin_gapIs the width of the air gap at the inner wall.
δout_gapIs at the outer wallThe width of the gap.
In the practical application of the embodiment, the temperature of the inner wall node of the slag pool-hollow ingot system and the corresponding position coordinate thereof are extracted, and the air gap width delta at the inner wall is calculated by using the formula (3)in_gapAnd substituting the two results into the formula (1), and circularly iterating until convergence (if the maximum value of the difference between the two adjacent iteration results is less than 10)-6The iteration stops).
Wherein z isiIs the z coordinate of any point on the inner wall of the hollow ingot.
zs-mIs the z coordinate of the slag-metal interface.
Theta is the set conical section cone angle.
L0Is the inner radius of the hollow ingot.
ρ(Tcoh) The metal density was 0.5 in terms of liquid fraction.
ρ(Tin_surf) The corresponding metal density at the temperature of each node at the inner wall.
Extracting all node temperatures and corresponding position coordinates of the slag bath-hollow ingot system, and calculating the air gap thickness delta at the outer wall by using a formula (4)out_gapAnd substituting the two results into the formula (2), and circularly iterating until convergence (if the maximum value of the difference between the two adjacent iteration results is less than 10)-6The iteration stops).
Ti_aveThe average temperature of the ith grid cell (n grid cells in total) in the wall thickness direction, when Ti_ave>TcohThe metal is in liquid form and the displacement is 0.
In practical applications of this embodiment, the S8 includes:
s81, judging the actual contact height H of the inner wall and the inner crystallizer under the current preset cone part angleconAnd the slag/gold boundaryDistance H of surface from bottom of cylindrical partcylWhether the difference value meets a first preset range or not is judged, and a judgment result is obtained;
the first predetermined range in this embodiment is 5 to 10 mm.
S82, setting any taper angle value within the preset range of the taper angle of the first conical portion as a new set taper angle of the conical portion, and repeating S5-S8 until obtaining the corresponding determination result for each taper angle value within the preset range of the taper angle of the first conical portion.
The preset ranges of the first conical portion taper angle in this embodiment include 0.5 °,1 °, 1.5 °, and 2 °. Corresponds to Hcyl13.2mm,16.4mm,20.0mm and 25.2mm, respectively; hcon112.1mm,32.6mm,25.4mm and 26.2mm, respectively.
In this embodiment, the temperature of the slag bath-hollow ingot system node and the corresponding position coordinates thereof are shown in fig. 5.
In this example, the width of the air gap and H on the inner wall of the hollow ingotconAs shown in fig. 6.
And S83, determining the final inner crystallizer conical part cone angle range based on the judgment result corresponding to each conical angle value in the preset first conical part cone angle range.
In practical application of this embodiment, the S83 specifically includes:
and S831, acquiring a first taper angle value based on a judgment result corresponding to each taper angle value in a preset taper angle range of the first taper part.
The first cone angle value comprises a cone angle value of which the difference value meets a first preset range according to a judgment result.
And S832, determining the final conical angle range of the conical part of the inner crystallizer based on the first conical angle value.
And the cone angle range of the final conical part of the inner crystallizer is greater than or equal to the minimum value of the first cone angle values and less than or equal to the maximum value of the first cone angle values.
In the embodiment, the method for setting the taper angle of the crystallizer in the electroslag remelting hollow steel ingot is based on the preset three-dimensional electromagnetic field, the preset flow field and the preset heat transferEstablishing a three-dimensional transient multi-physical-field coupling analysis model corresponding to the third grid model by adopting a multi-physical-field implementation coupling method under the boundary condition, simulating the electro-magnetic-flow-thermal coupling behavior in the solidification process of the electroslag remelting hollow ingot and the radial contraction and deformation behaviors of the inner blank shell and the outer blank shell of the hollow ingot in the whole inner crystallizer and the outer crystallizer along the height of the inner crystallizer and the outer crystallizer, thereby obtaining the simulation result of the dynamic solidification heat transfer of the hollow ingot and the deformation behavior based on the density base, and determining the distance H between the slag/metal interface and the bottom of the cylindrical part of the inner crystallizer according to the simulation result (the simulation result fully considers the contraction and uniform heat transfer and growth of the hollow ingot in the inner crystallizer and the outer crystallizer)cylAir gap width, actual contact height H of inner wall and inner crystallizercon(ii) a Compared with the prior art, the method can maximally reduce the taper of the friction force applied to the inner crystallizer, improve the solidification quality of the electroslag remelting hollow ingot, and solve the problems of slag leakage, steel leakage, locking of the inner crystallizer and the like. A hollow ingot with good surface quality was obtained as shown in fig. 7.
Since the system described in the above embodiment of the present invention is a system used for implementing the method of the above embodiment of the present invention, a person skilled in the art can understand the specific structure and the modification of the system based on the method described in the above embodiment of the present invention, and thus the detailed description is omitted here. All systems adopted by the method of the above embodiments of the present invention are within the intended scope of the present invention.
As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions.
It should be noted that in the claims, any reference signs placed between parentheses shall not be construed as limiting the claim. The word "comprising" does not exclude the presence of elements or steps not listed in a claim. The word "a" or "an" preceding an element does not exclude the presence of a plurality of such elements. The invention may be implemented by means of hardware comprising several distinct elements, and by means of a suitably programmed computer. In the claims enumerating several means, several of these means may be embodied by one and the same item of hardware. The use of the terms first, second, third and the like are for convenience only and do not denote any order. These words are to be understood as part of the name of the component.
Furthermore, it should be noted that in the description of the present specification, the description of the term "one embodiment", "some embodiments", "examples", "specific examples" or "some examples", etc., means that a specific feature, structure, material or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, the claims should be construed to include preferred embodiments and all changes and modifications that fall within the scope of the invention.
It will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the spirit or scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention should also include such modifications and variations.
Claims (10)
1. A method for setting a taper angle of a crystallizer in a hollow steel ingot with electroslag remelting is characterized by comprising the following steps of:
s1, building a first 1/4 symmetrical slag pool-hollow ingot system three-dimensional solid model by adopting modeling software based on the pre-obtained electrode size, hollow ingot size and slag amount of the actual electroslag remelting hollow ingot;
s2, carrying out meshing on the first 1/4 symmetrical slag bath-hollow ingot system three-dimensional solid model to obtain a corresponding first mesh model;
s3, setting physical properties of the slag pool aiming at the calculation domain of the slag pool in the first grid model and setting physical properties of the hollow ingot aiming at the calculation domain of the hollow ingot to obtain a second grid model;
s4, giving a first attribute obtained in advance for the calculation domain of the hollow ingot in the second grid model, and giving a second attribute obtained in advance for the calculation domain of the slag bath to obtain a third grid model;
s5, based on the preset three-dimensional electromagnetic field boundary condition, the preset flow field boundary condition and the preset heat transfer boundary condition, establishing a three-dimensional transient multi-physical field coupling analysis model corresponding to the third grid model by adopting a multi-physical field coupling method;
s6, obtaining a simulation result of the dynamic solidification heat transfer of the hollow ingot and the deformation behavior based on the density base based on the three-dimensional transient multi-physical field coupling analysis model;
s7, determining the distance H between the slag/gold interface and the bottom of the cylindrical part of the inner crystallizer according to the simulation resultcylAir gap width, actual contact height H of inner wall and inner crystallizercon；
S8 based on HcylAir gap width, actual contact height H of inner wall and inner crystallizerconAnd in advanceSetting a first conical part cone angle range, and determining a final inner crystallizer conical part cone angle range;
the first conical portion cone angle range includes a plurality of cone angle values.
2. The method of claim 1,
the hollow ingot electrode size includes: electrode diameter;
the hollow ingot dimensions include: the inner diameter of the hollow ingot, the outer diameter of the hollow ingot and the wall thickness of the hollow ingot;
the height of the 1/4 symmetrical slag bath-hollow ingot system three-dimensional solid model is 5.5-6 times of the wall thickness of the hollow ingot;
in the step S3, fluent software is adopted to set the physical properties of the slag bath for the calculation domain of the slag bath in the first grid model and the physical properties of the hollow ingot for the calculation domain of the hollow ingot, so as to obtain a second grid model.
3. The method according to claim 2, wherein the gridding the 1/4 symmetrical slag bath-hollow ingot system three-dimensional solid model in S3 to obtain a first grid model specifically comprises:
aiming at the 1/4 symmetrical slag bath-hollow ingot system three-dimensional solid model, a non-uniform grid division method is adopted, the distance between grids of contact areas of the 1/4 symmetrical slag bath-hollow ingot system three-dimensional solid model is divided into 1-2 mm, and the distance between grids of non-contact areas is divided into 6-10 mm;
the contact area of the 1/4 symmetrical slag bath-hollow ingot system three-dimensional solid model is the contact area of the 1/4 symmetrical slag bath-hollow ingot system three-dimensional solid model, the area corresponding to the hollow ingot, the area corresponding to the inner crystallizer and the area corresponding to the outer crystallizer;
the non-contact area is an area corresponding to a hollow ingot in the 1/4 symmetrical slag bath-hollow ingot system three-dimensional solid model, an area corresponding to the inner crystallizer and an area corresponding to the outer crystallizer, which are not in contact with each other.
4. The method of claim 3,
the pre-acquired first attribute comprises: the change relation of the electrical conductivity, viscosity, density, thermal conductivity and specific heat of the hollow ingot with the temperature;
the pre-acquired second attribute comprises: the change relation of the electrical conductivity, viscosity, density, thermal conductivity and specific heat of the slag system with the temperature.
5. The method according to claim 4, wherein the S5 includes:
s51, setting an electromagnetic field, a flow field and a heat transfer control equation of a slag pool-hollow ingot calculation domain and a third attribute;
the third attribute is that the inner and outer walls of the hollow ingot in the third 1/4 symmetrical slag bath-hollow ingot system three-dimensional solid model have uniform slag crust thickness in the circumferential direction;
s52, based on the set slag bath-hollow ingot calculation domain electromagnetic field, flow field and heat transfer control equation, the third attribute and the preset electromagnetic field boundary condition, flow field boundary condition and heat transfer boundary condition, adopting a multi-physical-field implementation coupling method to establish a three-dimensional transient multi-physical-field coupling analysis model corresponding to the third grid model.
6. The method of claim 5,
the electromagnetic field boundary condition of the slag bath-hollow ingot calculation domain comprises the following steps:
the potential at the bottom of the hollow ingot is 0, and the current density of the hollow ingot electrode in the slag pool projection area is I/S;
i is a remelting stationary phase current value; s is the area of the projection area of the electrode (group) in the slag pool;
the hollow ingot electrode has continuous magnetic flux densities in the slag pool projection area, the bottom of the hollow ingot and the free surface of the slag pool, and the magnetic vector potential flux is 0;
the magnetic vector potential flux at the inner walls of the slag pool and the hollow ingot is 0;
the magnetic vector potential at the outer walls of the slag pool and the hollow ingot is 0;
the flow field boundary condition of the slag bath-hollow ingot calculation domain comprises the following steps:
the hollow ingot electrode is a speed inlet in the projection area of the slag pool;
the bottom of the hollow ingot is a free outlet;
the hollow ingot electrode is a non-slip wall surface in a slag pool projection area, the inner wall and the outer wall of the slag pool and the inner wall and the outer wall of the hollow ingot;
the free surface of the slag pool has zero shear stress;
the flow heat boundary condition of the slag bath-hollow ingot calculation domain comprises the following steps:
the projection area of the hollow ingot electrode in the slag pool is the superheat degree of metal liquid phase temperature of 30K, and the free surface of the slag pool is applied in a convection and radiation mode;
the heat transfer between the inner wall and the outer wall of the slag pool and the heat transfer between the inner wall and the outer wall of the hollow ingot are convection heat transfer, the heat transfer boundary of the inner wall is applied according to a formula (1), and the heat transfer boundary of the outer wall is applied according to a formula (2);
the formula (1) is:
the formula (2) is:
hmoldheat exchange coefficient of the crystallizer;
δslagis the thickness of the slag crust;
kslagthe heat conductivity coefficient of the solid slag;
kairis the thermal conductivity of air;
δin_gapthe width of the air gap at the inner wall;
δout_gapis the width of the air gap at the outer wall.
7. The method of claim 6,
extracting the temperature of the inner wall node of the slag bath-hollow ingot system and the corresponding position coordinate thereof, and calculating the air gap width delta at the inner wall by using a formula (3)in_gapAnd the data are substituted into the formula (1), and iteration is carried out circularly until convergence is achieved;
wherein z isiIs the z coordinate of any point on the inner wall of the hollow ingot;
zs-mis the z coordinate of the slag-metal interface;
theta is a set conical part cone angle;
L0is the inner radius of the hollow ingot;
ρ(Tcoh) The metal density is 0.5 liquid phase fraction;
ρ(Tin_surf) The corresponding metal density at the temperature of each node on the inner wall;
extracting all node temperatures and corresponding position coordinates of the slag bath-hollow ingot system, and calculating the air gap width delta at the outer wall by using a formula (4)out_gapAnd the data are substituted into the formula (2), and iteration is carried out circularly until convergence is achieved;
Ti_avethe average temperature of the grid cells in the direction of the wall thickness, when Ti_ave>TcohThe metal is in liquid form and the displacement is 0.
8. The method according to claim 7, wherein the S8 includes:
s81, judging the actual contact height H of the inner wall and the inner crystallizer under the current preset cone part angleconAnd the distance H from the slag/gold interface in the radial direction of the inner wall and the outer wall of the hollow ingot to the bottom of the cylindrical partcylWhether the difference value meets a first preset range or not is judged, and a judgment result is obtained;
s82, taking any taper angle value in the preset range of the taper angle of the first conical part as a new set taper angle of the conical part, and repeating S5-S8 until obtaining the judgment result corresponding to each taper angle value in the preset range of the taper angle of the first conical part;
and S83, determining the final inner crystallizer conical part cone angle range based on the judgment result corresponding to each conical angle value in the preset first conical part cone angle range.
9. The method according to claim 8, wherein the S83 specifically includes:
s831, acquiring a first taper angle value based on a judgment result corresponding to each taper angle value in a preset taper angle range of the first taper part;
the first cone angle value comprises a cone angle value of which the difference value meets a first preset range according to a judgment result;
s832, determining a final conical angle range of the conical part of the inner crystallizer based on the first conical angle value;
and the cone angle range of the final conical part of the inner crystallizer is greater than or equal to the minimum value of the first cone angle values and less than or equal to the maximum value of the first cone angle values.
10. An electroslag remelting hollow ingot inner crystallizer, characterized in that the taper angle of the electroslag remelting hollow ingot inner crystallizer is set by the method for setting the taper angle of the electroslag remelting hollow ingot inner crystallizer of any of claims 1 to 9.
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