Method for determining inclination angle of single-flow arc-shaped channel induction heating tundish channel

Abstract

The invention discloses a method for determining a channel inclination angle of a uniflow arc-shaped channel induction heating tundish, and the method comprises the steps: carrying out the coupling calculation of a flow field, a temperature field, an inclusion removal rate and the like of induction heating tundishes with different channel inclination angles through a method for building a three-dimensional unsteady state mathematical model; and conditions of various aspects such as space and technical transformation (economical efficiency) of a steel mill are comprehensively considered, and the optimal channel inclination angle of the single-flow arc-shaped channel induction heating tundish is finally formulated. The method has the advantages that the channel inclination angle determining method can determine the flow field of the induction heating tundish when the channel inclination angle is large, the temperature field distribution is more reasonable, and the inclusion removal rate is the highest, so that the cleanliness of molten steel is improved to the maximum extent on the basis of optimization of the flow field.

Description

Technical Field

[0001] The invention belongs to the technical field of induction heating of a continuous casting tundish, and relates to a method for determining an inclination angle of a tundish channel for induction heating of a single-flow arc-shaped channel. Background Art

[0002] In the early stage of continuous casting, the tundish only played the role of transitional molten steel. With the increasing demand for high-quality steel grades, the continuous casting process has become increasingly important for the quality of molten steel. In order to ensure the smooth implementation of the continuous casting process, the molten steel must be of sufficient purity and stable temperature. As the turning point from intermittent operation to continuous operation, the tundish should not only have the traditional function of stabilizing the molten steel, but also control the cleanliness and temperature of the molten steel. The continuous casting process has always pursued low superheat constant temperature steady state pouring, but due to reasons such as changing tundishes and wall heat dissipation, the temperature of the molten steel changes greatly in the later stage of pouring and the transition stage. If the superheat of the molten steel is too high, non-equiaxed crystals will appear in the ingot, resulting in segregation; on the contrary, if the superheat of the molten steel is too low, the viscosity of the molten steel will increase, which will increase the inclusions in the ingot. Therefore, in order to reduce defects such as segregation and inclusions in the ingot, the temperature of the molten steel must be controlled within a very small range, that is, low superheat steady state pouring. Channel induction heating technology can compensate for heat loss during the pouring process, make the temperature of molten steel stable and controllable, and improve the quality of ingots. The channel type of the existing induction heating tundish is a linear channel. Due to the limitation of the distance between the long water nozzle and the submerged water nozzle of the ladle, the length of the channel cannot be guaranteed, which affects the heating efficiency. To solve this problem, an arc-shaped induction heating tundish channel is proposed, which can increase the length of the channel equivalently without changing the distance between the long water nozzle and the submerged water nozzle of the ladle, thereby improving the heating efficiency. However, the inclination angle of the arc-shaped channel has not been determined, and the change of the inclination angle of the channel will have a great influence on the flow field, temperature field and inclusion removal rate in the casting area. Summary of the invention

[0003] The present invention discloses a method for determining the channel inclination angle of a single-flow arc-shaped channel induction heating tundish. By establishing a three-dimensional non-steady-state mathematical model, a coupling calculation is performed on the flow field, temperature field and inclusion removal rate of the induction heating tundish with different channel inclination angles, and various aspects such as the space of the steel plant and technical transformation (economic efficiency) are comprehensively considered to finally determine the optimal channel inclination angle of the single-flow arc-shaped channel induction heating tundish.

[0004] The method comprises the following steps:

[0005] Step 1: Collect casting parameters of the single-stream arc-shaped channel induction heating tundish on site;

[0006] Step 2: Establish a three-dimensional flow and heat transfer model of the single-flow arc-shaped channel induction heating tundish, and calculate the flow field and temperature field of the single-flow arc-shaped channel induction heating tundish according to the casting working condition parameters and different channel inclination parameters;

[0007] Step 3: establishing an inclusion collision growth model for a single-flow arc-channel induction heating tundish, and calculating the inclusion removal rate of the arc-channel induction heating tundish according to the flow field and the temperature field;

[0008] Step 4: performing steps 1 to 3 respectively on the arc-shaped channel induction heating tundishes with different channel inclination angles, and obtaining the flow field, temperature field and inclusion removal rate corresponding to the single-flow arc-shaped channel induction heating tundish of each inclination angle;

[0009] Step 5: Compare and analyze the flow field, temperature field and inclusion removal rate corresponding to the arc-shaped channel induction heating tundish with each channel inclination angle, and finally determine the range of the optimal channel inclination angle of the single-flow arc-shaped channel induction heating tundish.

[0010] In step 1, the casting condition parameters include the capacity of the single-flow arc-shaped channel induction heating tundish, the inlet flow rate of the ladle long nozzle, and the heating power and frequency of the induction heating device of the single-flow arc-shaped channel induction heating tundish;

[0011] Step 2 includes the following 4 steps:

[0012] 2.1: Establish a three-dimensional flow and heat transfer model for the single-flow arc channel induction heating tundish;

[0013] 2.2: Establish a water model experimental platform to simulate the flow of molten steel in a single-flow arc-shaped channel induction heating tundish under non-isothermal conditions, obtain the average residence time distribution of molten steel in the single-flow arc-shaped channel induction heating tundish, and compare it with the measured average residence time to verify the accuracy of the model;

[0014] 2.3: The electromagnetic force and Joule heat of the single-stream arc-channel induction heating tundish are calculated based on the three-dimensional flow heat transfer model according to the casting condition parameters;

[0015] 2.4: Based on the three-dimensional flow heat transfer model of the electromagnetic force and Joule heat of the single-flow arc channel induction heating package, the flow field and temperature field of the single-flow arc channel induction heating package are calculated.

[0016] The 2.2 intermediate water model experimental platform includes a ladle model, a hot water supply system, a cold water supply system and a temperature measurement system; the outlet of the hot water supply system is located in the arc channel of the intermediate ladle model, the outlet of the cold water supply system is located in the injection area of ​​the intermediate ladle model, and the temperature measurement system is connected to the casting area of ​​the intermediate ladle model.

[0017] In step 3, the formula of the inclusion collision growth model is:

[0018]

[0019] N ij =β(r i ,r j )n(r i )n(r j ) (2)

[0020]

[0021] Where, formula (1) is the equation of motion of inclusions, ρ P is the density of inclusions, d P is the particle size of inclusions, ν P is the velocity of the inclusion, t is the time, F g is the gravity of the inclusion, F f is the buoyancy of the inclusion, F d is the drag force on the inclusion, F l For Saffman lift, F P is the pressure, F t is the thermophoretic force, F b for Brown Force;

[0022] Formula (2) is the inclusion collision growth equation, N ij The radius per unit time and per unit volume are r i and r j The collision coefficient of the particles, β(r i ,r j ) is the particle collision rate constant, n(r i ) is the radius r i The number density of particles, n(r j ) is the radius r j The number density of particles,

[0023] Formula (3) is the collision constant formula of Brownian collision, β1(r i ,r j ) is the collision rate constant of Brownian collision, k is the Boltzmann constant, T is the temperature of the molten steel, and μ is the kinematic viscosity of the molten steel;

[0024] Formula (4) is the collision constant formula of Stokes collision, β2(r i ,r j ) is the collision rate constant of Stokes collision, Δρ is the density difference between molten steel and inclusions, and g is the gravitational acceleration;

[0025] Formula (5) is the collision rate constant formula for turbulent collision, β3(ri ,r j ) is the collision rate constant of turbulent collision, ε is the turbulent kinetic energy dissipation rate, and ρ is the density of molten steel.

[0026] The flow field and temperature field are used as source items to calculate the inclusion collision growth model to obtain the number of inclusions a at the inlet and the number of inclusions b at the outlet of the single-flow arc channel induction heating tundish, and the inclusion removal rate W=(ab) / a.

[0027] The advantages of the present invention are:

[0028] The channel inclination angle determination method can obtain the flow field, temperature field and inclusion removal rate corresponding to the induction heating ladle under different channel inclination angle conditions, and through a comprehensive analysis of the flow field, temperature field and inclusion removal rate, it is determined at what channel inclination angle the flow field and temperature field distribution of the induction heating ladle are more reasonable and the inclusion removal rate is the highest, thereby maximizing the cleanliness of the molten steel on the basis of flow field optimization. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is a top view of the single-flow arc-shaped channel induction heating tundish of the present invention;

[0030] Figure 2 It is a side view of the single-flow arc-shaped channel induction heating tundish of the present invention;

[0031] Figure 3 It is a three-dimensional finite element mesh schematic diagram of a single-flow arc-shaped channel induction heating tundish of the present invention;

[0032] Figure 4 It is a schematic diagram of the water model experimental platform of the present invention;

[0033] Figure 5 This is a comparison chart of the model calculation results and the measured values ​​of the average residence time distribution of molten steel in the induction heating tundish obtained through the water model experiment;

[0034] Figure 6 (1) is a schematic diagram of the flow field of the tundish when the channel inclination angle is 0°, 4°, and 8°, respectively (a, b, c), (d, e, f), and (g, h, i);

[0035] Figure 6 (2) is a schematic diagram of the temperature field of the tundish when the channel inclination angle is 0°, 4°, and 8°, respectively, as shown in Figure j, Figure k, and Figure l;

[0036] Figure 6(3) is a schematic diagram of the inclusion removal rate of the tundish when the channel inclination angle is 0°, 4°, and 8°.

[0037] Explanation of icons: induction heating device 1, refractory wall 2, arc channel 3, injection area 4, long nozzle 5, casting area 6, casting nozzle 7, hot water supply system 8, cold water supply system 9, temperature measurement system 10, image recording system 11, conductivity meter 12, tracer injection device 13. DETAILED DESCRIPTION

[0038] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0039] like Figure 1 and Figure 2 As shown, the molten steel enters the injection area 4 through the ladle long nozzle 5, enters the casting area 6 through the two arc-shaped channels 3, and is cast through the casting nozzle 7. The refractory wall 2 plays a protective role. The induction heating device 1 can heat the molten steel in the arc-shaped channels 3, wherein the center of each of the two arc-shaped channels 3 is on the side of the arc-shaped channel 3 facing the other arc-shaped channel 3, and the curvature radius of the two arc-shaped channels 3 is the same. Figure 3 A method for determining the optimal inclination angle of the channel of an induction heating tundish is shown below:

[0040] Step 1: Collect on-site pouring parameters

[0041] The casting condition parameters include the capacity of the single-stream arc-shaped channel induction heating tundish, the inlet flow rate of the ladle long nozzle, and the heating power and frequency of the tundish induction heating device. Among them, the inlet flow rate is determined according to the casting speed, and the heating power is set according to the induction heating device of the single-stream arc-shaped channel induction heating tundish, generally 800kw~1200kw, and the frequency is 50Hz. The accuracy of the casting condition parameter collection directly affects the accuracy of the subsequent three-dimensional flow heat transfer model boundary conditions, and ultimately affects the accuracy of the simulation results and the rationality of the channel inclination angle.

[0042] Step 2: Establish a three-dimensional flow and heat transfer model of the single-flow arc-shaped channel induction heating tundish. According to the casting condition parameters and the channel inclination angle, the flow field and temperature field of the single-flow arc-shaped channel induction heating tundish are calculated. The following four steps:

[0043] Step 2.1: Establish a three-dimensional flow and heat transfer model for the single-flow arc-channel induction heating tundish.

[0044] The large-scale commercial finite element software MAXWELL and FLUENT are used as calculation tools to establish a three-dimensional flow and heat transfer model of the single-flow arc channel induction heating tundish. Figure 3 As shown, it is a schematic diagram of the three-dimensional finite element mesh of the single-flow arc channel induction heating tundish;

[0045] Step 2.2: Establish a water model experimental platform to simulate the flow of molten steel in the single-flow arc channel induction heating tundish under non-isothermal conditions, obtain the average residence time distribution curve of the molten steel, and compare it with the measured average residence time curve of the molten steel in the tundish to verify the accuracy of the three-dimensional flow heat transfer model.

[0046] like Figure 4 As shown, the outlet of the hot water supply system 8 of the water model experimental platform is located in the arc channel 3 of the ladle model, the outlet of the cold water supply system 9 is located in the injection area 4 of the ladle model, the temperature measurement system 10 is connected to the casting area 6 of the ladle model, and the water model experimental platform also includes an image recording system 11, a conductivity meter 12, a tracer injection device 13, a drainage system, a flow meter and a thermocouple, etc.

[0047] The average residence time distribution curve (RTD curve) of molten steel in the single-flow arc channel induction heating tundish was obtained through water model experiments, such as Figure 5 The figure shows a comparison between the RTD curve obtained from the water model experiment and the measured average residence time curve of molten steel in the single-flow arc-shaped channel induction heating tundish. The two curves have a good trend of agreement, which verifies the accuracy of the three-dimensional flow heat transfer model.

[0048] Step 2.3: The electromagnetic force and Joule heat of the single-stream arc-channel induction heating tundish are calculated based on the three-dimensional flow heat transfer model according to the casting condition parameters.

[0049] The three-dimensional flow heat transfer model includes the following formulas:

[0050]

[0051] Among them, formula (6) to formula (9) are Maxwell equations, which can be used to calculate the electromagnetic field of the single-flow arc channel induction heating tundish. The flow field and temperature field are further calculated based on the calculated electromagnetic force and Joule heat of the electromagnetic field; where D is the electric displacement, ρ q is the free charge density, E is the electric field intensity, B is the magnetic flux density, t is the time, H is the magnetic field intensity, and J is the conduction current density. In the calculation process, the following assumptions are made:

[0052] ① Ignore the effect of flow on the electromagnetic field;

[0053] ② During electromagnetic calculations, it is assumed that the material is isotropic and the physical parameters are constants;

[0054] ③ During the electromagnetic field calculation process, the coil is loaded with the alternating current frequency and current density.

[0055] The MAXWELL software is used to compile formula (6) to formula (9) to obtain the calculation software. The casting condition parameters and the different inclination angles of the arc channel are input into the software as known quantities to calculate the electromagnetic force and Joule heat of the single-stream arc channel induction heating tundish.

[0056] Step 2.4: The flow field and temperature field of the single-flow arc-channel induction heating tundish are calculated based on the three-dimensional flow heat transfer model of the electromagnetic force and Joule heat of the single-flow arc-channel induction heating tundish.

[0057] The 3D flow heat transfer model also includes the following formulas:

[0058]

[0059]

[0060] Wherein, formula (10) is the continuity equation, ρ is the density of molten steel, kg / m 3 , ν is the flow rate of molten steel, m / s,

[0061] Formula (11) is the Navier-Stokes equation, where T is the temperature of the molten steel, P is the static pressure, Pa, β is the thermal expansion coefficient of the molten steel, ρg; μ eff Represents effective viscosity, kg / (m·s), μ eff Determined by the following formula:

[0062] μ eff =μ+μ t (15)

[0063]

[0064] μ is the dynamic viscosity, kg / (m·s); μ t is the turbulent viscosity, kg / (m·s); k is the turbulent kinetic energy; ε is the turbulent kinetic energy dissipation rate; c μ =0.09.

[0065] Formula (12) to Formula (13) are k-ε two-equation models, G k represents the turbulent kinetic energy under the mean velocity gradient and is determined by:

[0066]

[0067] Among them, C 1ε , C 2ε , σ k and σ ε are constants given by Launder BE and DBSpalding:

[0068] C 1ε =1.44, C2ε =1.92,σ κ =1.0,σ ε =1.3, v i 、v j is the turbulent viscosity coefficient, χ i Represents the coordinate system.

[0069] Formula (14) is the energy equation, where λ is the thermal conductivity of molten steel, c Ρ is the specific heat capacity of molten steel at constant pressure, S Τ is the viscous dissipation coefficient; Q represents the Joule heat generated by electromagnetic induction, and T is the molten steel temperature.

[0070] Among them, the continuity equation (10), the Navier-Stokes equation (11) and the k-ε two-equation model (12), (13) are used to calculate the flow field of the single-flow arc channel induction heating tundish, and the energy equation (14) is used to calculate the temperature field of the single-flow arc channel induction heating tundish. The FLUENT calculation software is used to compile formulas (10) to (17) to obtain the calculation software, and the electromagnetic force and Joule heat are used as source terms to calculate the flow field and temperature field of the single-flow arc channel induction heating tundish.

[0071] In the calculation of flow field and temperature field, velocity inlet and pressure outlet are used, standard wall function is used for the wall, no-slip wall condition is used for the molten steel surface, and the second type boundary condition is used for heat transfer. In the process of flow field calculation, molten steel is regarded as an incompressible Newtonian fluid. Since the convection phenomenon of molten steel needs to be considered, the density of molten steel is regarded as a function of temperature 8523-0.8358T / K, and other parameters are regarded as constants. The influence of slag layer on the surface of molten steel is not considered, and the surface of molten steel is regarded as a horizontal liquid surface.

[0072] Step 3: Establish an inclusion collision growth model for the single-flow arc channel induction heating tundish, and calculate the inclusion removal rate of the single-flow arc channel induction heating tundish based on the flow field and temperature field.

[0073] Based on the force balance principle, the Euler-Lagrangian method was used to analyze the movement behavior of inclusions in the tundish under single-stream arc channel induction heating. A collision growth model of inclusions under induction heating was established, and the collision growth and removal rate of inclusions in the tundish under different blowing parameters were investigated.

[0074] When inclusions move in the induction heating tundish, they will be affected by gravity, buoyancy, drag, and Saffman lift. Since the Brownian motion of inclusions is considered, the Brownian force also needs to be considered. Due to the existence of induction heating, electromagnetic pressure and thermophoretic force will also have a great influence on the movement of inclusions.

[0075] The formula of the inclusion collision growth model is:

[0076]

[0077] N ij =β(r i ,r j )n(r i )n(r j ) (19)

[0078]

[0079] Where, formula (18) is the equation of motion of inclusions, ρ P is the density of inclusions, d P is the particle size of inclusions, ν P is the velocity of the inclusion, t is, F g is the gravity of the inclusion, F f is the buoyancy of the inclusion, F d is the drag force on the inclusion, F l For Saffman lift, F P is the pressure, F t is the thermophoretic force, F b for Brown Force;

[0080] Formula (19) is the inclusion collision growth equation, N ij The radius per unit time and per unit volume are r i and r j The collision coefficient of the particles, β(r i ,r j ) is the particle collision rate constant, n(r i ) is the radius r i The number density of particles, n(r j ) is the radius r j The number density of particles,

[0081] Formula (20) is the collision constant formula of Brownian collision, β1(r i ,r j ) is the collision rate constant of Brownian collision, k is the Boltzmann constant, T is the temperature of molten steel, and μ is the kinematic viscosity of molten steel;

[0082] Formula (21) is the collision constant formula of Stokes collision, β2(r i ,r j ) is the collision rate constant of Stokes collision, Δρ is the density difference between molten steel and inclusions, and g is the gravitational acceleration;

[0083] Formula (22) is the collision rate constant formula for turbulent collision, β3(r i ,r j) is the collision rate constant of turbulent collision, ε is the turbulent kinetic energy dissipation rate;

[0084] The inclusion collision growth model is calculated using the flow field and temperature field as source items to obtain the number of inclusions a at the inlet and b at the outlet of the single-flow arc channel induction heating tundish, and the inclusion removal rate W = (ab) / a.

[0085] The calculation software FLUENT is used to compile formula (18) to formula (22) to obtain the calculation software. After the flow field and temperature field are calculated in step 2, the flow field and temperature field are used as source items to calculate the number of inclusions a at the inlet and the number of inclusions b at the outlet, and then the inclusion removal rate is obtained.

[0086] Step 4: Perform steps 1 to 3 on the arc-shaped channel induction heating tundishes with different channel inclination angles to obtain the corresponding flow field, temperature field and inclusion removal rate.

[0087] Step 5: Compare and analyze the flow field, temperature field and inclusion removal rate corresponding to the arc-shaped channel induction heating tundish with different channel inclination angles, and finally determine the optimal channel inclination angle range of the single-flow arc-shaped channel induction heating tundish.

[0088] Embodiment 1:

[0089] A single-flow arc-shaped channel induction heating tundish, such as Figure 3 As shown, taking a 46t single-stream tundish as an example, the channel inclination angles are 0°, 4°, and 8°, respectively. First, the electromagnetic force and Joule heat of the arc channel tundish under this working condition are calculated by step 2.3, and then the result of step 2.3 is imported into step 2.4, and the flow field and temperature field of the tundish are obtained by calculation. The electromagnetic force and Joule heat are directly brought into the subsequent formulas for calculation as source terms through the software, and this method is to bring each formula into the calculation by means of simulation software to finally obtain the flow field and temperature field and other results. The final specific calculation results are also presented in the form of physical fields such as flow field and temperature field.

[0090] Figure 6(1) is a schematic diagram of the flow field of the tundish when the channel inclination angles are 0°, 4°, and 8°, which are the injection area (a, d, g), arc channel (b, e, h), and pouring area (c, f, l), respectively. When the mass flow rate is 2.7 t / min and the heating power is 800 kW, it can be seen from Figure 6(1) that the flow law of the molten steel in the pouring area of ​​the tundish induction heating at different channel inclination angles is similar. The main difference is that different channel angles make the intersection position of the molten steel after flowing out of the channel different, and as the inclination angle increases, the intersection position gradually decreases. When the channel inclination angle is 0°, due to the high intersection position and being too close to the surface slag layer, slag rolling may occur; when the channel inclination angle is 4°, the flow of molten steel in the casting area is better, which alleviates the impact of the molten steel on the surface slag layer; when the channel inclination angle is 8°, due to the low intersection position of the molten steel, the upward flow path of the molten steel after the intersection is extended, which may slow down the flow speed of the molten steel in the casting area, resulting in problems such as lower temperature and increased dead zone volume.

[0091] Figure 6 (2) shows the schematic diagrams of the temperature field of the tundish when the channel inclination angle is 0°, 4°, and 8°, respectively. It can be seen from Figure J that when the channel inclination angle is 0°

[0092] , the temperature distribution in the pouring zone is relatively uniform, and the temperature difference does not exceed 2K; from the k figure, it can be seen that when the channel inclination angle is 4°, the average temperature in the pouring zone is higher than when the channel angle is 0°, indicating that when the channel inclination angle is 4°, the heating efficiency of the tundish is higher than when the channel inclination angle is 0°. This is mainly because when the inclination angle is 0°, the channel length is shorter than when the inclination angle is 4°, so the time for the molten steel to be heated is also reduced accordingly; from the l figure, it can be seen that when the channel inclination angle is 8°, the average temperature in the pouring zone is lower than the previous two cases, and a large range of low temperature zones appears. This is mainly because the larger inclination angle makes the intersection point of the molten steel after flowing out of the channel also lower accordingly, the upward flow path of the streams after the intersection is extended, the average residence time is extended, and the temperature loss is large, so the temperature in the pouring zone is relatively low.

[0093] Figure 6 (3) shows the removal rate of the induction heating tundish. The program we wrote is loaded in step 4. Based on step 2, the software automatically calls formulas (12) to (17) for calculation, and finally obtains the removal rate of the induction heating tundish when the channel inclination angle is 0°, 4°, and 8°. The inclusion removal rate when the channel inclination angle is 0° is lower than that when the channel inclination angle is 4°. This is mainly because the latter has a longer channel length, which is more conducive to the collision and growth of inclusions; while the inclusion removal rate when the channel inclination angle is 8° is lower than the former two. This is mainly because the large channel inclination angle makes the flow speed of the molten steel in the casting area too slow, and the dead zone volume increases, which is not conducive to the removal of inclusions.

[0094] In summary, the above embodiments are repeated for different channel inclination angles, and it is concluded that the optimal channel inclination angle of the arc channel induction heating tundish based on a steel plant of the present invention is about 3° to 5°, and the specific angle will be adjusted according to the on-site conditions.

Claims

1. A method for determining the inclination angle of a single-flow arc-shaped channel induction heating tundish channel, characterized in that: The method comprises the following steps: Step 1: Collect casting parameters of the single-stream arc-shaped channel induction heating tundish on site; Step 2: Establish a three-dimensional flow and heat transfer model of the single-flow arc-shaped channel induction heating tundish, and calculate the flow field and temperature field of the single-flow arc-shaped channel induction heating tundish according to the casting working condition parameters and different channel inclination parameters; Step 3: establishing an inclusion collision growth model for a single-flow arc-channel induction heating tundish, and calculating the inclusion removal rate of the arc-channel induction heating tundish according to the flow field and the temperature field; Step 4: performing steps 1 to 3 respectively on the arc-shaped channel induction heating tundishes with different channel inclination angles, and obtaining the flow field, temperature field and inclusion removal rate corresponding to the single-flow arc-shaped channel induction heating tundish of each inclination angle; Step 5: Compare and analyze the flow field, temperature field and inclusion removal rate corresponding to the arc-shaped channel induction heating tundish with each channel inclination angle, and finally determine the range of the optimal channel inclination angle of the single-flow arc-shaped channel induction heating tundish.

2. The method for determining the inclination angle of the single-flow arc-shaped channel induction heating tundish channel according to claim 1 is characterized in that: In the step 1, the casting condition parameters include the capacity of the single-flow arc-shaped channel induction heating tundish, the inlet flow rate of the ladle long nozzle, and the heating power and frequency of the induction heating device of the single-flow arc-shaped channel induction heating tundish; The step 2 includes the following 4 steps: 2.1: Establish a three-dimensional flow and heat transfer model for the induction heating tundish in a single-flow arc channel; 2.2: Establish a water model experimental platform to simulate the flow of molten steel in a single-flow arc-shaped channel induction heating tundish under non-isothermal conditions, obtain the average residence time distribution of molten steel in the single-flow arc-shaped channel induction heating tundish, and compare it with the measured average residence time to verify the accuracy of the model; 2.3: The electromagnetic force and Joule heat of the single-stream arc-channel induction heating tundish are calculated based on the three-dimensional flow heat transfer model according to the casting condition parameters; 2.4: The flow field and temperature field of the single-flow arc-channel induction heating tundish are calculated based on the electromagnetic force and Joule heat of the single-flow arc-channel induction heating tundish in the three-dimensional flow heat transfer model; In step 3, the formula of the inclusion collision growth model is: N ij =β(r i ,r j )n(r i )n(r j ) (2) Where, formula (1) is the equation of motion of inclusions, ρ P is the density of inclusions, d P is the particle size of inclusions, ν P is the velocity of the inclusion, t is the time, F g is the gravity of the inclusion, F f is the buoyancy of the inclusion, F d is the drag force on the inclusion, F l For Saffman lift, F P is the pressure, F t is the thermophoretic force, F b for Brown Force; Formula (2) is the inclusion collision growth equation, N ij The radius per unit time and per unit volume are r i and r j The collision coefficient of the particles, β(r i ,r j ) is the particle collision rate constant, n(r i ) is the radius r i The number density of particles, n(r j ) is the radius r j The number density of particles, Formula (3) is the collision constant formula of Brownian collision, β1(r i ,r j ) is the collision rate constant of Brownian collision, k is the Boltzmann constant, T is the temperature of the molten steel, and μ is the kinematic viscosity of the molten steel; Formula (4) is the collision constant formula of Stokes collision, β2(r i ,r j ) is the collision rate constant of Stokes collision, Δρ is the density difference between molten steel and inclusions, and g is the gravitational acceleration; Formula (5) is the collision rate constant formula for turbulent collision, β3(r i ,r j ) is the collision rate constant of turbulent collision, ε is the turbulent kinetic energy dissipation rate, and ρ is the density of molten steel. The flow field and temperature field are used as source items to calculate the inclusion collision growth model to obtain the number of inclusions a at the inlet and the number of inclusions b at the outlet of the single-flow arc channel induction heating tundish, and the inclusion removal rate W=(ab) / a.

3. The method for determining the inclination angle of the single-flow arc-shaped channel induction heating tundish channel according to claim 2 is characterized in that: The 2.2 intermediate water model experimental platform includes a ladle model, a hot water supply system, a cold water supply system and a temperature measurement system; the outlet of the hot water supply system is located in the arc channel of the intermediate ladle model, the outlet of the cold water supply system is located in the injection area of ​​the intermediate ladle model, and the temperature measurement system is connected to the casting area of ​​the intermediate ladle model.

4. The method for determining the inclination angle of the single-flow arc-shaped channel induction heating tundish channel according to claim 1, 2 or 3, characterized in that: A 46t single-flow arc-shaped channel induction heating tundish, with channel inclination angles of 0°, 4°, and 8°. First, the electromagnetic force and Joule heat of the arc-shaped channel tundish under this working condition are calculated by step 2.3, and then the result of step 2.3 is imported into step 2.4, and the flow field and temperature field of the tundish are calculated; the electromagnetic force and Joule heat are directly taken as source terms and brought into various formulas through simulation software to calculate and finally obtain the flow field and temperature field results. The final specific calculation results are also presented in the form of physical fields such as flow field and temperature field; FIG6 (1) is a schematic diagram of the flow field of the tundish when the channel inclination angle is 0°, 4°, and 8°, which are the injection areas a, d, g, arc channels b, e, h, and pouring areas c, f, and l, respectively. When the mass flow rate is 2.7 t / min and the heating power is 800 kW, the flow law of the molten steel in the pouring area of ​​the induction heating tundish with different channel inclination angles is similar. The main difference is that different channel angles make the intersection positions of the molten steel different after flowing out of the channel. As the inclination angle increases, the intersection position gradually decreases. When the channel inclination angle is 0°, due to the high intersection position and the position too close to the surface slag layer, there is a possibility of slag rolling. When the channel inclination angle is 4°, the flow of the molten steel in the pouring area is good, which alleviates the impact of the molten steel on the surface slag layer. When the channel inclination angle is 8°, due to the low intersection position of the molten steel, the upward flow path of the molten steel after the intersection is extended, which may slow down the flow speed of the molten steel in the pouring area, resulting in problems such as temperature reduction and increased dead zone volume. FIG6 (2) is a schematic diagram of the temperature field of the tundish when the channel inclination angle is 0°, 4°, and 8°, which are respectively J, K, and L. As can be seen from J, when the channel inclination angle is 0°, the temperature distribution in the pouring zone is relatively uniform, and the temperature difference does not exceed 2K. As can be seen from K, when the channel inclination angle is 4°, the average temperature in the pouring zone is higher than when the channel inclination angle is 0°, indicating that the heating efficiency of the tundish when the channel inclination angle is 4° is higher than when the channel inclination angle is 0°. This is mainly because when the inclination angle is 0°, its channel length is shorter than when the inclination angle is 4°, so the time for the molten steel to be heated is also reduced accordingly. As can be seen from L, when the channel inclination angle is 8°, the average temperature in the pouring zone is lower than the previous two cases, and a large range of low temperature zones appears. This is mainly because the larger inclination angle reduces the intersection point of the molten steel after it flows out of the channel, and the upward flow path of the streams after the intersection is extended, the average residence time is extended, and the temperature loss is large, so the temperature in the pouring zone is relatively low. Figure 6 (3) shows the removal rate of the induction heating tundish. The calculation is based on step 2, and finally the removal rate of the induction heating tundish when the channel inclination angle is 0°, 4°, and 8° is obtained; the inclusion removal rate when the channel inclination angle is 0° is less than that when the channel inclination angle is 4°. This is mainly because the latter has a longer channel length, which is more conducive to the collision and growth of inclusions; and the inclusion removal rate when the channel inclination angle is 8° is less than the former two. This is mainly because the channel inclination angle is too large, which makes the flow speed of the molten steel in the casting area too slow, and the dead zone volume increases, which is not conducive to the removal of inclusions. In summary, the above process is repeated for different channel inclination angles, and it is concluded that the optimal channel inclination angle of the present invention is about 3° to 5°, which is adjusted according to the site conditions.

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