CN107096900B - The determination method of the best radius of the radian of the curved channel of induction heating tundish - Google Patents
The determination method of the best radius of the radian of the curved channel of induction heating tundish Download PDFInfo
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Abstract
The determination method of the best radius of the radian of the curved channel of induction heating tundish belongs to continuous casting production induction heating technique field, and the method includes the casting duty parameters of collection site list stream curved channel induction heating tundish；The Flow and heat flux of single stream curved channel induction heating tundish is calculated according to the radius of the radian of casting duty parameter and curved channel for the Three-dimensional Flow heat transfer model for establishing single stream curved channel induction heating tundish；The field trash for establishing single stream curved channel induction heating tundish collides long large-sized model, and inclusion removal rate is calculated according to Flow and heat flux；Above step is executed respectively to single stream curved channel induction heating tundish of different radius of the radian, the corresponding flow field of single stream curved channel induction heating tundish, temperature field and the inclusion removal rate of obtained each radius of the radian are compared and analyzed, the range of the final best radius of the radian for determining single stream curved channel induction heating tundish.
Description
Technical Field
The invention relates to the technical field of continuous casting tundish induction heating, in particular to a method for determining the optimal radian radius of an arc-shaped channel of an induction heating tundish.
Background
In the early stages of continuous casting development, the tundish only served as a transition for the molten steel. With the continuous improvement of the demand of people on high-quality steel grades, the quality of molten steel has more and more important significance on the continuous casting process. In order to ensure the smooth proceeding of the continuous casting process, it is necessary to ensure sufficient purity and stable temperature of the molten steel. The tundish plays an important role as a turning point for turning from intermittent operation to continuous operation. In addition to the conventional effect of stabilizing molten steel, it should have an effect of controlling cleanliness and temperature of molten steel.
Constant temperature steady state pouring with low superheat has been sought after in continuous casting processes. However, due to ladle replacement, wall heat dissipation and the like, the temperature change of molten steel is large in the later period of pouring and the transition period. If the degree of superheat of molten steel is too high, non-equiaxed grains appear in the cast slab, thereby causing segregation. On the contrary, if the superheat degree of the molten steel is too low, the viscosity of the molten steel is increased, and the inclusion in the casting blank is increased. Therefore, in order to reduce defects such as segregation in a cast slab and inclusions, it is necessary to control the temperature of molten steel to a small range, that is, to perform stable casting with a low degree of superheat.
In the continuous casting process, the molten steel in the tundish is heated by an external means, so that the heat loss in the ladle casting process can be compensated, the temperature of the molten steel is stable and controllable, and the quality of a casting blank is improved. At present, the plasma heating technology and the induction heating technology are widely applied, and the plasma heating technology is rarely used by enterprises due to low heating efficiency, large field noise and the like. The channel type induction heating technology has the advantages of high heating efficiency and no pollution, and simultaneously has the function of removing inclusions. The channel type of the existing channel type induction heating tundish is a linear channel, and the length of the linear channel cannot be guaranteed due to the limitation of the distance between the tundish long nozzle and the submerged nozzle, so that the heating efficiency is influenced. In order to solve the problem, an idea is provided to change two channels of a single-flow arc-shaped channel induction heating tundish from a linear type to an arc shape, so that the length of the channel can be equivalently increased on the basis of not changing the distance between a tundish long nozzle and an immersion nozzle, the heating efficiency is improved, and the energy consumption is reduced. The circle center of each arc-shaped channel in the two arc-shaped channels is located on one side, facing the other arc-shaped channel, of the arc-shaped channel, the radian radiuses of the two arc-shaped channels are the same, but no clear rule exists for how large the optimal radian radius of the arc-shaped channel is designed so far, random design is often performed on the radian radius of the arc-shaped channel on site, and the inventor finds that the heating efficiency of the induction heating tundish is influenced to a certain extent by the radian radius of the arc-shaped channel.
Disclosure of Invention
In order to solve the problem that the radian radius of an arc-shaped channel of a single-flow arc-shaped channel induction heating tundish is not clearly specified in the prior art, the invention provides a method for determining the optimal radian radius of the arc-shaped channel of the induction heating tundish, which comprises the following steps:
step 1: collecting casting working condition parameters of an induction heating tundish of a field uniflow arc-shaped channel;
step 2: establishing a three-dimensional flow heat transfer model of the uniflow arc-shaped channel induction heating tundish, and calculating to obtain a flow field and a temperature field of the uniflow arc-shaped channel induction heating tundish according to the casting working condition parameters and the radian radius of the arc-shaped channel;
and step 3: establishing an inclusion collision growing model of the single-flow arc-shaped channel induction heating tundish, and calculating to obtain the inclusion removal rate of the single-flow arc-shaped channel induction heating tundish according to the flow field and the temperature field;
and 4, step 4: respectively executing the steps 1 to 3 to the single-flow arc-shaped channel induction heating tundish with different radian radiuses to obtain a flow field, a temperature field and an inclusion removal rate corresponding to the single-flow arc-shaped channel induction heating tundish with each radian radius;
and 5: and comparing and analyzing the flow field, the temperature field and the impurity removal rate corresponding to the single-flow arc-shaped channel induction heating tundish with each radian radius, and finally determining the range of the optimal radian radius of the single-flow arc-shaped channel induction heating tundish.
The step 2 comprises the following steps:
step 2.1: establishing a three-dimensional flow heat transfer model of the single-flow arc-shaped channel induction heating tundish;
step 2.2: establishing a water model experiment platform, simulating the flow of the molten steel in the single-flow arc-shaped channel induction heating tundish under a non-isothermal condition to obtain the average residence time distribution of the molten steel in the single-flow arc-shaped channel induction heating tundish, comparing the average residence time distribution with the actually measured average residence time distribution of the molten steel in the single-flow arc-shaped channel induction heating tundish, and verifying the accuracy of the three-dimensional flow heat transfer model;
step 2.3: calculating the three-dimensional flow heat transfer model according to the casting working condition parameters and the radian radius of the arc-shaped channel to obtain the electromagnetic force and the Joule heat of the single-flow arc-shaped channel induction heating tundish;
step 2.4: and calculating the three-dimensional flow heat transfer model according to the electromagnetic force and the Joule heat of the single-flow arc-shaped channel induction heating tundish to obtain the flow field and the temperature field of the single-flow arc-shaped channel induction heating tundish.
In step 3, the formula of the inclusion collision growth model is as follows:
Nij＝β(ri,rj)n(ri)n(rj) (2)；
wherein, the formula (1) is an inclusion motion equation rhoPIs the density of inclusions, dPIs the particle size of the inclusions, vPThe moving speed of the inclusions, t is time, FgGravity to which the inclusions are subjected, FfBuoyancy to which the inclusions are subjected, FdDrag force to which inclusions are subjected, FlIs Saffman lifting force, FPIs pressure, FtFor thermophoretic forces, FbIs Brown force; formula (2) is the inclusion collision growth equation, NijThe radius is r in unit time and unit volumeiAnd rjβ (r) of the particlesi,rj) Is the collision rate constant of the particles, n (r)i) Is a radius riNumber density of particles of (2), n (r)j) Is a radius rjThe number density of particles of (3) is a collision constant formula of Brownian collision, β1(ri,rj) Is the collision rate constant of Brownian collision, k is Boltzmann constant, T is the temperature of the molten steel, mu is the kinematic viscosity of the molten steel, formula (4) is the collision constant formula of Stokes collision, β2(ri,rj) Is the collision rate constant of Stokes collision, is the density difference between molten steel and inclusion, g is the gravitational acceleration, and equation (5) is the collision rate constant equation of turbulent collision, β3(ri,rj) Is a collision rate constant of turbulent collision, epsilon is a turbulent kinetic energy dissipation rate, and rho is the molten steel density;
and calculating the inclusion collision growing model by taking the flow field and the temperature field as source terms to obtain the number a of the inclusions at an inlet and the number b of the inclusions at an outlet of the single-flow arc-shaped channel induction heating tundish, and obtaining the removal rate W of the inclusions (a-b)/a.
The water model experiment platform comprises a tundish model, a hot water supply system, a cold water supply system and a temperature measuring system;
the water outlet of the hot water supply system is positioned in the arc-shaped channel of the tundish model, the water outlet of the cold water supply system is positioned in the pouring area of the tundish model, and the temperature measuring system is connected with the casting area of the tundish model.
The casting working condition parameters comprise the capacity of the single-flow arc-shaped channel induction heating tundish, the inlet flow of the ladle long nozzle and the heating power of an induction heating device of the single-flow arc-shaped channel induction heating tundish.
According to the method for determining the optimal radian radius of the arc-shaped channel, the corresponding flow field, temperature field and inclusion removal rate of the induction heating tundish under the condition of different radian radii can be obtained, and the highest heating efficiency and the highest inclusion removal rate of the induction heating tundish when the radian radius of the arc-shaped channel is large are determined through comprehensive analysis of the flow field, the temperature field and the inclusion removal rate, so that the cleanliness of molten steel is improved to the maximum extent on the basis of energy conservation.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
FIG. 1 is a top view of a single flow arcuate channel induction heating tundish provided by the present invention;
FIG. 2 is a side view of a single flow arcuate channel induction heating tundish provided by the present invention;
FIG. 3 is a flow chart of a method of determining an optimal radius of curvature for an arcuate channel of an induction heating tundish provided by the present invention;
FIG. 4 is a flow chart of a flow field and a temperature field obtained by a three-dimensional flow heat transfer model according to the present invention;
FIG. 5 is a three-dimensional flow heat transfer geometric model of a single flow arcuate channel induction heating tundish provided by the present invention;
FIG. 6 is a schematic structural diagram of a water model experiment platform provided by the present invention;
FIG. 7 is a graph comparing an RTD curve obtained from a water model experiment with an actually measured mean residence time distribution curve of molten steel in a single flow arc channel induction heating tundish;
FIG. 8 is a schematic view of the flow field of a single flow arcuate channel induction heated tundish when the arcuate radius of the arcuate channel is 5 m;
FIG. 9 is a schematic temperature field of a single flow arcuate channel induction heated tundish when the arcuate radius of the arcuate channel is 5 m;
FIG. 10 is a schematic view of the flow field of a single flow arcuate channel induction heated tundish when the arcuate radius of the arcuate channel is 4 m;
FIG. 11 is a schematic temperature field of a single flow arcuate channel induction heated tundish at an arcuate radius of 4m of the arcuate channel;
FIG. 12 is a schematic view of the flow field of a single flow arcuate channel induction heated tundish when the radius of the arc of the arcuate channel is 3 m;
FIG. 13 is a schematic temperature field of a single flow arcuate channel induction heated tundish when the arcuate radius of the arcuate channel is 3 m.
Wherein,
the device comprises an induction heating device 1, a refractory material wall 2, an arc-shaped channel 3, a flow injection zone 4, a ladle long nozzle 5, a casting zone 6, a casting nozzle 7, a hot water supply system 8, a cold water supply system 9, a temperature measurement system 10, an image recording system 11, a conductivity meter 12 and a tracer injection device 13.
Detailed Description
As shown in fig. 1 and fig. 2, fig. 1 is a top view of a single flow arc channel induction heating tundish, fig. 2 is a side view of the single flow arc channel induction heating tundish, molten steel enters a pouring zone 4 through a ladle long nozzle 5, enters a casting zone 6 through two arc channels 3, and is cast through a casting nozzle 7, a refractory wall 2 plays a role in protection, and the induction heating device 1 can heat the molten steel in the arc channels 3, wherein the center of each arc channel 3 of the two arc channels 3 is at one side of the arc channel 3 facing the other arc channel 3, and the curvature radiuses r of the two arc channels 3 are the same, so as to solve the problem that the curvature radiuses of the single flow arc channel induction heating tundish arc channels in the prior art are not clearly specified, as shown in fig. 3, the invention provides a method for determining the optimal curvature radius of the arc channels of the induction heating tundish, the method comprises the following steps:
step 1: collecting casting working condition parameters of an induction heating tundish of a field uniflow arc-shaped channel;
the casting working condition parameters comprise the capacity of the single-flow arc-shaped channel induction heating tundish, the inlet flow of the ladle long nozzle and the heating power of an induction heating device of the single-flow arc-shaped channel induction heating tundish. The inlet flow is determined according to the pulling speed, and the heating power is set according to an induction heating device of the single-flow arc-shaped channel induction heating tundish. The accuracy of the acquisition of the casting working condition parameters directly influences the accuracy of the subsequent boundary condition application of the three-dimensional flow heat transfer model, and finally the accuracy of the simulation result and the rationality of the channel radius formulation are related.
Step 2: establishing a three-dimensional flow heat transfer model of the uniflow arc-shaped channel induction heating tundish, and calculating a flow field and a temperature field of the uniflow arc-shaped channel induction heating tundish according to casting working condition parameters and the radian radius of the arc-shaped channel, as shown in fig. 4:
step 2.1: establishing a three-dimensional flow heat transfer model of the single-flow arc-shaped channel induction heating tundish;
in the invention, large commercial finite element software MAXWELL and FLUENT are adopted as a calculation tool to establish a three-dimensional flow heat transfer model of the single-flow arc-shaped channel induction heating tundish, as shown in figure 5, the three-dimensional flow heat transfer geometric model of the single-flow arc-shaped channel induction heating tundish is shown, a part marked as A represents a flow injection area of the induction heating tundish, and a part marked as B represents a casting area of the induction heating tundish;
step 2.2: establishing a water model experiment platform, simulating the flow of the molten steel in the single-flow arc-shaped channel induction heating tundish under a non-isothermal condition to obtain the average residence time distribution of the molten steel in the single-flow arc-shaped channel induction heating tundish, comparing the average residence time distribution with the actually measured average residence time distribution of the molten steel in the single-flow arc-shaped channel induction heating tundish, and verifying the accuracy of the three-dimensional flow heat transfer model;
in the invention, as shown in fig. 6, the water model experiment platform comprises a tundish model, a hot water supply system 8, a cold water supply system 9 and a temperature measuring system 10;
the water outlet of the hot water supply system 8 is positioned in the arc-shaped channel 3 of the tundish model, the water outlet of the cold water supply system 9 is positioned in the pouring area 4 of the tundish model, and the temperature measuring system 10 is connected with the casting area 6 of the tundish model.
According to the invention, the existing water model experiment platform is improved, and can only simulate the molten steel flow of the induction heating tundish under the isothermal condition, and in the invention, a hot water supply system 8 is established, and the water outlet of the hot water supply system 8 is positioned in the arc-shaped channel of the tundish model, so that the temperature of water in the arc-shaped channel can be different by adjusting the hot water supply system 8 and the cold water supply system 9 simultaneously, so as to simulate the heating process of the induction heating device on the molten steel in the arc-shaped channel, and thus the molten steel flow in the single-flow arc-shaped channel induction heating tundish under the non-isothermal condition is simulated.
An average residence time distribution curve (RTD curve) of the molten steel in the single-flow arc-shaped channel induction heating tundish is obtained through a water model experiment, as shown in fig. 7, a comparison graph of the RTD curve obtained through the water model experiment and an actually measured average residence time distribution curve of the molten steel in the single-flow arc-shaped channel induction heating tundish is shown, the coincidence trend of the two curves is good, and the accuracy of the three-dimensional flow heat transfer model is verified.
Step 2.3: calculating the three-dimensional flow heat transfer model according to the casting working condition parameters and the radian radius of the arc-shaped channel to obtain the electromagnetic force and the Joule heat of the single-flow arc-shaped channel induction heating tundish;
in the present invention, the three-dimensional flow heat transfer model comprises the following formula:
the equations (6) to (9) are Maxwell equations, an electromagnetic field of the single-flow arc-shaped channel induction heating tundish can be obtained through calculation, and a flow field and a temperature field are further obtained through calculation according to the calculated electromagnetic force and Joule heat of the electromagnetic field; in the formula, D is the electric displacement, rhoqFor free charge bulk density, E is the electric field strength, B is the magnetic flux density, t is the time, H is the magnetic field strength, and J is the conduction current density. In the calculation, the following assumptions are made:
(1) neglecting the effect of flow on the electromagnetic field.
(2) In the electromagnetic calculation process, the material is assumed to be isotropic, and the physical property parameter is a constant.
(3) In the electromagnetic field calculation process, the current frequency and current density of the alternating current are loaded to the coil.
According to the invention, MAXWELL software is adopted to compile formulas (6) to (9) to obtain calculation software, and casting condition parameters and radian radiuses of the arc-shaped channels are input into the software as known quantities to be calculated to obtain electromagnetic force and Joule heat of the single-flow arc-shaped channel induction heating tundish.
Step 2.4: and calculating the three-dimensional flow heat transfer model according to the electromagnetic force and the Joule heat of the single-flow arc-shaped channel induction heating tundish to obtain the flow field and the temperature field of the single-flow arc-shaped channel induction heating tundish.
In the present invention, the three-dimensional flow heat transfer model further comprises the following formula:
wherein, the continuity equation of the formula (10) is that rho is the molten steel density, kg/m3Nu is the flow velocity of molten steel, m/s, equation (11) is the Navier-Stokes equation, T is the temperature of molten steel, P is the static pressure, Pa, β are the thermal expansion coefficients of molten steel, mueffRepresents the effective viscosity, kg/(m.s), μeffIs determined by the following formula:
μeff＝μ+μt (15)
μ is dynamic viscosity, kg/(m · s); mu.stIs the turbulent viscosity, kg/(m.s); k is the turbulence energy; epsilon is the turbulent kinetic energy dissipation ratio; c. Cμ＝0.09。
Equations (12) to (13) are k-epsilon two-equation models, GkRepresenting the kinetic energy of turbulence at the average velocity gradient. Is determined by the following formula:
wherein, C1ε、C2ε、σkAnd σεAre all constants, formed by Launders B.E. and D.B.SpaThe ldng gives:
C1ε＝1.44，C2ε＝1.92，σκ＝1.0，σε＝1.3，vi、vjis the coefficient of turbulent viscosity, then ×)iRepresenting a coordinate system.
Equation (14) is an energy equation, where λ is the heat conductivity of molten steel, and cPIs the specific heat capacity at constant pressure of molten steel, STIs the viscous dissipation factor. Q represents Joule heat generated by electromagnetic induction, and T represents the molten steel temperature.
The method comprises the steps of obtaining a flow field of a single-flow arc-shaped channel induction heating tundish by compiling formulas (10) to (17) by using FLUENT calculation software, and obtaining a flow field and a temperature field of the single-flow arc-shaped channel induction heating tundish by calculating by using electromagnetic force and Joule heat as source terms.
In the calculation of the flow field and the temperature field, a speed inlet and a pressure outlet are adopted, a wall surface adopts a standard wall surface function, the surface of the molten steel adopts a non-slip wall surface condition, and the heat exchange adopts a second type of boundary condition. In the flow field calculation process, the molten steel is regarded as incompressible Newtonian fluid. Since the convection phenomenon of molten steel needs to be considered herein, the density of molten steel is regarded as a function 8523-0.8358T/K of temperature and other parameters are regarded as constants, and the surface of molten steel is regarded as a horizontal liquid surface regardless of the influence of a slag layer on the surface of molten steel.
And step 3: establishing an inclusion collision growing model of the single-flow arc-shaped channel induction heating tundish, and calculating to obtain the inclusion removal rate of the single-flow arc-shaped channel induction heating tundish according to the flow field and the temperature field;
from the principle of force balance, the Euler-Lagrange method is adopted to analyze the movement behavior of impurities in the single-flow arc-shaped channel induction heating tundish, establish a collision growth model of the impurities under the induction heating condition, and examine the conditions of collision growth and removal rate of the impurities in the tundish under the radian radius of the arc-shaped channel.
When the impurities move in the induction heating tundish, the impurities are subjected to the action of gravity, buoyancy, drag force and Saffman lifting force. Since brownian motion of the inclusion is considered, brownian force also needs to be considered. Due to the induction heating, the electromagnetic pressure and thermophoretic force have great influence on the movement of the impurities.
The formula of the inclusion collision growth model is as follows:
Nij＝β(ri,rj)n(ri)n(rj) (2)；
wherein, the formula (1) is an inclusion motion equation rhoPIs the density of inclusions, dPIs the particle size of the inclusions, vPThe moving speed of the inclusions, t is time, FgGravity to which the inclusions are subjected, FfBuoyancy to which the inclusions are subjected, FdDrag force to which inclusions are subjected, FlIs Saffman lifting force, FPIs pressure, FtFor thermophoretic forces, FbIs Brown force; formula (2) is the inclusion collision growth equation, NijIs divided into unit time and unit volume inner radiusIs otherwise riAnd rjβ (r) of the particlesi,rj) Is the collision rate constant of the particles, n (r)i) Number density of particles of radius ri, n (r)j) Is a radius rjThe number density of particles of (3) is a collision constant formula of Brownian collision, β1(ri,rj) Is the collision rate constant of Brownian collision, k is Boltzmann constant, T is the molten steel temperature, mu is the kinematic viscosity of the molten steel, formula (4) is the collision constant formula of Stokes collision, β2(ri,rj) Is the collision rate constant of Stokes collision, is the density difference between molten steel and inclusion, g is the gravitational acceleration, and equation (5) is the collision rate constant equation of turbulent collision, β3(ri,rj) Is a collision rate constant of turbulent collision, epsilon is a turbulent kinetic energy dissipation rate, and rho is the molten steel density;
and (3) calculating the inclusion collision growing model by taking the flow field and the temperature field as source terms to obtain the number a of the inclusions at the inlet and the number b of the inclusions at the outlet of the single-flow arc-shaped channel induction heating tundish, and obtaining the removal rate W of the inclusions which is (a-b)/a.
In the invention, FLUENT calculation software can be adopted to compile the formulas (1) to (5) to obtain calculation software, and after the flow field and the temperature field are calculated in the step 2, the flow field and the temperature field are used as source terms to calculate the number a of the inclusions at the inlet and the number b of the inclusions at the outlet so as to obtain the removal rate of the inclusions.
And 4, step 4: respectively executing the steps 1 to 3 to the single-flow arc-shaped channel induction heating tundish with different radian radiuses to obtain a flow field, a temperature field and an inclusion removal rate corresponding to the single-flow arc-shaped channel induction heating tundish with each radian radius;
and 5: and comparing and analyzing the flow field, the temperature field and the impurity removal rate corresponding to the single-flow arc-shaped channel induction heating tundish with each radian radius, and finally determining the range of the optimal radian radius of the single-flow arc-shaped channel induction heating tundish.
For example, if the casting condition parameters of the continuous casting tundish at the site are collected as follows: the capacity of the single-flow arc-shaped channel induction heating tundish is 36 tons, the inlet flow of the ladle long nozzle is 2.7t/min, and the heating power of the induction heating device is 800 kw; the radian radiuses of known arc-shaped channels are three, 3m, 4m and 5m respectively, the fact that the radian radiuses of a single-flow arc-shaped channel induction heating tundish are in the same casting working condition is obtained through experiments, the heating efficiency is high when the radian radiuses of the single-flow arc-shaped channel induction heating tundish are in the range, the content of impurities is minimum, then the steps 1 to 3 can be repeated on the single-flow arc-shaped channel induction heating tundish with the radian radiuses of 3m, 4m and 5m respectively, and the removal rate of the flow field, the temperature field and the impurities corresponding to the single-flow arc-shaped channel induction heating tundish with each radian radius is obtained:
the steps 1 to 3 are carried out on the single-flow arc-shaped channel induction heating tundish with the arc radius of 5m, a flow field obtained by solving the three-dimensional flow heat transfer model is shown in fig. 8, and a temperature field is shown in fig. 9: it can be seen from fig. 8 that the molten steel enters the arc-shaped passage 3 after staying for a short time in the pouring area 4, since the arc-shaped passage 3 is arc-shaped, the molten steel first meets together at a high speed after flowing out from the arc-shaped passage 3 to the casting area 6, and then since the density of the high-temperature molten steel flowing out from the arc-shaped passage 3 is less than that of the molten steel originally in the casting area 6, the molten steel flowing out from the arc-shaped passage 3 moves upward under the action of buoyancy after meeting together. The intersected streams enhance the stirring of the molten steel, are beneficial to uniform distribution of temperature and floating removal of impurities, and can relieve the upward impact force of the molten steel to a certain extent, so that slag entrapment is avoided, and the flow field distribution of the casting area 6 is symmetrical; the container marked a in fig. 9 represents the pouring zone 4 and the container marked B represents the pouring zone 6, connected by the arched channel 3. As can be seen from fig. 9, since the temperature of the high temperature molten steel flowing out of the arc-shaped passage 3 is higher than that of the molten steel in the casting zone 6, a temperature difference is generated in the casting zone 6, and the temperature difference promotes a natural convection in the casting zone 6, so that the temperature distribution in the casting zone 6 becomes more uniform, and the low temperature zone is mainly distributed at the lower part of the casting zone 6, and the maximum temperature is 1846K. The inclusion removal rate W1 was 55.21% when the arc radius of the arc-shaped passage 3 was 5m according to step 4.
The steps 1 to 3 are carried out on the single-flow arc-shaped channel induction heating tundish with the radian radius of 4m, a flow field obtained by solving a three-dimensional flow heat transfer model is shown in a graph 10, and a temperature field is shown in a graph 11: it can be seen from fig. 10 that the molten steel enters the arc-shaped channel 3 after staying in the pouring area 4 for a short time, and the arc radius of the arc-shaped channel 3 is reduced, so that the bending degree of the arc-shaped channel 3 is increased, the flowing speed of the molten steel in the arc-shaped channel 3 is increased, and the molten steel flows out of the arc-shaped channel 3 and then is converged together at a higher speed, so that the stirring of the molten steel is further enhanced, the uniform distribution of temperature and the floating removal of inclusions are facilitated, and meanwhile, the upward impact force of the molten steel is relieved, and slag entrapment is avoided. Meanwhile, it can be seen that the flow field distribution of the flow injection region 4 is also symmetrical. As can be seen from fig. 11, the temperature distribution of the casting zone 6 is more uniform and the range of the low temperature zone is smaller due to the enhancement of the convection, and the length of the arc-shaped channel 3 between the pouring zone 4 and the casting zone 6 is longer due to the smaller radius of the arc-shaped channel 3 and the larger bending degree of the arc-shaped channel 3, so that the residence time of the molten steel in the arc-shaped channel 3 is longer, the heating time of the molten steel by the induction heating device is also longer, and the maximum temperature of the molten steel in the casting zone 6 is 1848K. Obtaining the removal rate W of the impurities when the radian radius of the arc-shaped channel 3 is 4m according to the step 42＝68.75％。
The steps 1 to 3 are carried out on the single-flow arc-shaped channel induction heating tundish with the radian radius of 3m, a flow field obtained by solving a three-dimensional flow heat transfer model is shown in fig. 12, and a temperature field is shown in fig. 13: it can be seen from fig. 12 that the molten steel enters the arc-shaped channel 3 after the molten steel temporarily stays in the pouring area 4, the curvature of the arc-shaped channel 3 is further increased due to the further reduction of the arc radius of the arc-shaped channel 3, the speed of the molten steel flowing in the arc-shaped channel 3 is also increased, the speed of the molten steel flowing in the arc-shaped channel 3 near the coil of the induction heating device is increased more due to the skin effect and the proximity principle, so that the impact force of the molten steel flowing out from the side near the coil is larger than that of the molten steel flowing out from the side far from the coil when the two molten steel flows together after the molten steel flows out from the two arc-shaped channels 3, which indicates that a critical value exists in the influence of the arc radius of the arc-shaped channel 3 on the difference of the impact forces of the molten steel flowing out from the two arc-shaped channels 3, and the proximity principle does not have a, the impact force of the molten steel in the two arc-shaped channels 3 is basically the same, and when the radian radius of the arc-shaped channels 3 is larger than a critical value, the influence of the principle nearby becomes obvious, so that the flow field distribution of the flow injection zone 4 is asymmetric, the flow field of the single-flow arc-shaped channel induction heating tundish is deteriorated, and the realization of low-superheat-degree constant-temperature steady-state pouring is not facilitated. As can be seen from fig. 13, the distribution of the temperature field also becomes less uniform due to the deterioration of the flow field, and the range of the low temperature region increases with a maximum temperature of 1845K. However, the arc radius of the arc-shaped channel 3 is 3m, the bending degree of the arc-shaped channel 3 is larger, so that the length of the arc-shaped channel 3 between the pouring area 4 and the casting area 6 is longer, the residence time of the molten steel in the arc-shaped channel 3 is longer, the heating time of the molten steel by the induction heating device is longer, and the highest temperature of the casting area 6 is lower than that of the molten steel with the arc radii of 4m and 5 m.
The comparative analysis shows that the efficiency of induction heating is not increased along with the increase of the length of the arc-shaped channel 3, namely the efficiency of induction heating is not increased along with the decrease of the arc radius of the arc-shaped channel 3, the arc radius has a critical value, when the critical value is larger than the critical value, the heating efficiency is increased gradually along with the decrease of the arc radius, namely the increase of the length of the arc-shaped channel 3, when the critical value is smaller than the critical value, the arc-shaped channel 3 continues to increase along with the continuous decrease of the arc radius of the arc-shaped channel 3, the heating efficiency is not increased any more, even can be reduced, the heating efficiency is very low, and under the condition that the heating efficiency is very low, even if the removal rate of the impurities is very high, the realization. Therefore, for the uniflow arc-shaped channel 3 induction heating tundish with the capacity of 36 tons, the inlet flow of the ladle long nozzle of 2.7t/min and the heating power of the induction heating device of 800kw, the preferred range of the arc radius of the arc-shaped channel 3 is 4-5 m, wherein if the range is further narrowed, the comparison analysis can still be carried out by the method, and for the uniflow arc-shaped channel induction heating tundish with different casting working condition parameters, the preferred range of the arc radius can be determined by the method, or the optimal arc radius of the arc-shaped channel 3 can be determined in the preferred range.
According to the method for determining the optimal radian radius of the arc-shaped channel, the corresponding flow field, temperature field and inclusion removal rate of the induction heating tundish under the condition of different radian radii can be obtained, and the heating efficiency and inclusion removal rate of the induction heating tundish are determined to be the highest when the radian radius of the arc-shaped channel 3 is large through comprehensive analysis of the flow field, the temperature field and the inclusion removal rate, so that the cleanliness of molten steel is improved to the maximum extent on the basis of energy conservation.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (5)
1. A method of determining an optimum radius of curvature for an arcuate channel of an induction heating tundish, the method comprising:
step 1: collecting casting working condition parameters of an induction heating tundish of a field uniflow arc-shaped channel;
step 2: establishing a three-dimensional flow heat transfer model of the uniflow arc-shaped channel induction heating tundish, and calculating to obtain a flow field and a temperature field of the uniflow arc-shaped channel induction heating tundish according to the casting working condition parameters and the radian radius of the arc-shaped channel;
and step 3: establishing an inclusion collision growing model of the single-flow arc-shaped channel induction heating tundish, and calculating to obtain the inclusion removal rate of the single-flow arc-shaped channel induction heating tundish according to the flow field and the temperature field;
and 4, step 4: respectively executing the steps 1 to 3 to the single-flow arc-shaped channel induction heating tundish with different radian radiuses to obtain a flow field, a temperature field and an inclusion removal rate corresponding to the single-flow arc-shaped channel induction heating tundish with each radian radius;
and 5: and comparing and analyzing the flow field, the temperature field and the impurity removal rate corresponding to the single-flow arc-shaped channel induction heating tundish with each radian radius, and finally determining the range of the optimal radian radius of the single-flow arc-shaped channel induction heating tundish.
2. The method for determining an optimum radius of curvature of an arcuate channel of an induction heating tundish as claimed in claim 1, wherein step 2 comprises the steps of:
step 2.1: establishing a three-dimensional flow heat transfer model of the single-flow arc-shaped channel induction heating tundish;
step 2.2: establishing a water model experiment platform, simulating the flow of the molten steel in the single-flow arc-shaped channel induction heating tundish under a non-isothermal condition to obtain the average residence time distribution of the molten steel in the single-flow arc-shaped channel induction heating tundish, comparing the average residence time distribution with the actually measured average residence time distribution of the molten steel in the single-flow arc-shaped channel induction heating tundish, and verifying the accuracy of the three-dimensional flow heat transfer model;
step 2.3: calculating the three-dimensional flow heat transfer model according to the casting working condition parameters and the radian radius of the arc-shaped channel to obtain the electromagnetic force and the Joule heat of the single-flow arc-shaped channel induction heating tundish;
step 2.4: and calculating the three-dimensional flow heat transfer model according to the electromagnetic force and the Joule heat of the single-flow arc-shaped channel induction heating tundish to obtain the flow field and the temperature field of the single-flow arc-shaped channel induction heating tundish.
3. The method of claim 1, wherein in step 3, the formula of the inclusion collision growth model is as follows:
Nij＝β(ri,rj)n(ri)n(rj) (2)；
wherein, the formula (1) is an inclusion motion equation rhoPIs the density of inclusions, dPIs the particle size of the inclusions, vPThe moving speed of the inclusions, t is time, FgGravity to which the inclusions are subjected, FfBuoyancy to which the inclusions are subjected, FdDrag force to which inclusions are subjected, FlIs Saffman lifting force, FPIs pressure, FtFor thermophoretic forces, FbIs Brown force; formula (2) is the inclusion collision growth equation, NijThe radius is r in unit time and unit volumeiAnd rjβ (r) of the particlesi,rj) Is the collision rate constant of the particles, n (r)i) Is a radius riNumber density of particles of (2), n (r)j) Is a radius rjThe number density of particles of (3) is a collision constant formula of Brownian collision, β1(ri,rj) Is the collision rate constant of Brownian collision, k is Boltzmann constant, T is the temperature of the molten steel, and mu is the kinematic viscosity of the molten steelDegree, formula (4) is the collision constant formula for stokes collision, β2(ri,rj) Is the collision rate constant of Stokes collision, is the density difference between molten steel and inclusion, g is the gravitational acceleration, and equation (5) is the collision rate constant equation of turbulent collision, β3(ri,rj) Is a collision rate constant of turbulent collision, epsilon is a turbulent kinetic energy dissipation rate, and rho is the molten steel density;
and calculating the inclusion collision growing model by taking the flow field and the temperature field as source terms to obtain the number a of the inclusions at an inlet and the number b of the inclusions at an outlet of the single-flow arc-shaped channel induction heating tundish, and obtaining the removal rate W of the inclusions (a-b)/a.
4. The method for determining the optimal radius of curvature of an arc-shaped channel of an induction heating tundish according to claim 2, wherein the water model experiment platform comprises a tundish model, a hot water supply system, a cold water supply system and a temperature measuring system;
the water outlet of the hot water supply system is positioned in the arc-shaped channel of the tundish model, the water outlet of the cold water supply system is positioned in the pouring area of the tundish model, and the temperature measuring system is connected with the casting area of the tundish model.
5. The method for determining the optimal radius of curvature of an arcuate channel of an induction heating tundish according to claim 1, wherein the casting condition parameters include the capacity of the single flow arcuate channel induction heating tundish, the inlet flow rate of the ladle shroud, and the heating power of an induction heating device of the single flow arcuate channel induction heating tundish.
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| CN116213692A (en) * | 2023-02-27 | 2023-06-06 | 鞍钢股份有限公司 | Single-flow arc-shaped channel air curtain retaining wall induction heating tundish and pouring method |
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