A method for determining the flow rate of molten steel at the solidification front in a crystallizer using the temperature of a copper plate

Abstract

The present invention relates to a method for determining the flow rate of molten steel at the solidification front in a crystallizer by using the temperature of a copper plate. The method comprises collecting the process parameters of the crystallizer and the physical properties of the copper plate, molten steel and solidified shell of the crystallizer, measuring the temperature of the copper plate of the crystallizer in real time by using a thermocouple, taking into account the energy conservation and heat transfer law in the thickness direction of the copper plate, calculating the sensible heat flux provided by the molten steel to the solidified shell, and then calculating the convection heat transfer coefficient of the molten steel flushing the solidification front, and calculating the flow rate of molten steel at the solidification front corresponding to the temperature measuring point of the thermocouple in the crystallizer based on the heat transfer characteristic number equation by using the relationship between the flow rate of molten steel at the solidification front and the convection heat transfer coefficient of the molten steel flushing the solidification front. The present invention can calculate the flow rate of molten steel at the solidification front of the crystallizer in real time, provide a reliable basis for the process control of the crystallizer, and then improve the quality of the ingot.

Description

Technical Field

[0001] The invention belongs to the technical field of parameter calculation methods in continuous casting production processes, and relates to a method for determining the flow rate of molten steel at the solidification front in a crystallizer by utilizing the temperature of a copper plate. Background Art

[0002] The crystallizer is the heart of the continuous casting machine. The flow behavior of molten steel in the crystallizer has a decisive influence on the quality of the continuous casting billet. When the flow rate of the molten steel flowing upward along the narrow surface of the crystallizer is too fast, it will cause large fluctuations in the slag-metal interface in the crystallizer, which is easy to cause local slag curling and lead to the formation of surface defects such as subcutaneous slag inclusions; when the flow rate of the molten steel is too low, the temperature of the molten steel in this area will be low, which is easy to cause local condensation to form deep vibration marks, and may cause the primary billet shell in the meniscus area to capture slag drops, inclusions and bubbles, causing billet defects. Therefore, real-time control of the flow rate of the molten steel in the crystallizer is of great significance to improving the quality of the billet.

[0003] In the actual production process, it is difficult to directly measure the flow rate of molten steel due to the "black box" operation mode of the crystallizer. Indirect measurement methods include deflection rod measurement method, steel nail sticking steel height measurement method, Von Karman vortex street method, thermocouple measurement method, electromagnetic induction method, etc. A protective slag layer is arranged on the upper layer of the molten steel in the crystallizer. Although the deflection method, Von Karman vortex street method and steel nail sticking steel height measurement method are easy to operate, they may introduce air or other impurities, form bubbles or inclusions, and destroy the originally formed slag layer during the speed measurement process, so that the ingot is in direct contact with the crystallizer wall, increasing friction and wear. At the same time, the participation of the measuring rod in the speed measurement flow field may cause changes in the flow field in the crystallizer, resulting in inaccurate measurement results. The electromagnetic induction method and thermocouple measurement method do not require direct contact with the molten steel surface, thereby reducing the interference with the crystallizer process, but additional measurement equipment is required.

[0004] Most continuous casting processes use a method of embedding thermocouples in the copper plate of the crystallizer to monitor the heat of the copper plate, which can effectively detect and predict bonding leakage. Therefore, if the thermocouple temperature measurement data can be used to calculate the flow rate of molten steel in the crystallizer, it can achieve the purpose of real-time measurement of the flow rate of molten steel in the continuous casting crystallizer without affecting the flow state of molten steel in the crystallizer and without adding new equipment. Summary of the invention

[0005] The purpose of the present invention is to provide a method for determining the flow rate of molten steel at the solidification front in a crystallizer by using the temperature of a copper plate, so as to solve the technical problem of measuring the flow rate of molten steel in a crystallizer in real time without affecting the flow field in the crystallizer during actual production.

[0006] The present invention provides a method for determining the flow rate of molten steel at the solidification front in a crystallizer by using the temperature of a copper plate, comprising the following steps:

[0007] Step 1: multiple thermocouples are embedded in the copper plates in four directions of the continuous casting crystallizer. The thermocouples are arranged based on the principle of spatial symmetry, and the number of thermocouples is determined according to the width and height of the copper plates. The temperature of the crystallizer copper plates is measured in real time using the thermocouples;

[0008] Step 2: Collecting crystallizer process parameters;

[0009] Step 3: Collect the physical properties of the mold copper plate, molten steel and solidified shell;

[0010] Step 4: Calculate the heat flux taken away by the cooling water during the cooling of the crystallizer copper plate;

[0011] Step 5: Calculate the solidification latent heat flux of the solidified shell growth;

[0012] Step 6: According to the first law of thermodynamics, considering the energy conservation and heat transfer law in the thickness direction of the copper plate, calculate the sensible heat flux provided by the molten steel to the solidified shell;

[0013] Step 7: Calculate the convection heat transfer coefficient of the molten steel in the crystallizer flushing the solidification front using the sensible heat flux provided by the molten steel to the solidified shell;

[0014] Step 8: Calculate the molten steel flow rate at the solidification front corresponding to the thermocouple temperature measurement point in the crystallizer based on the convection heat transfer coefficient of the molten steel flushing the solidification front.

[0015] Furthermore, the crystallizer process parameters in step 2 include:

[0016] Cooling water temperature, heat transfer coefficient between cooling water and copper plate of crystallizer, temperature of copper plate measured by thermocouple, distance between thermocouple measuring point and cold side of copper plate, distance from embedded position of thermocouple to meniscus and continuous casting speed.

[0017] Furthermore, the physical properties of the crystallizer copper plate, molten steel and solidified shell in step 3 include:

[0018] Thermal conductivity of the copper plate, thermal conductivity of the molten steel, dynamic viscosity of the molten steel, specific heat of the molten steel, density of the molten steel, temperature of the molten steel, temperature of the solidified shell, density of the solidified shell, solidification enthalpy of the molten steel and solidification coefficient of the molten steel.

[0019] Furthermore, the step 4 specifically calculates the heat flux taken away by the cooling water during the cooling of the crystallizer copper plate according to the following formula:

[0020]

[0021] Among them, q c The heat flux taken away by cooling water in the process of cooling the copper plate of the crystallizer, in W / m2 ; T m is the copper plate temperature measured by the thermocouple, in K; T w is the cooling water temperature, unit K; h w is the convection heat transfer coefficient between cooling water and the copper plate of the crystallizer, in W·m -2 ·K -1 ; m is the thermal conductivity of the copper plate of the crystallizer, in W·m -1 ·K -1 ;d t It is the distance between the thermocouple measurement point and the cold side of the copper plate, in meters.

[0022] Furthermore, the step 5 is specifically as follows:

[0023] Step 5-1: Calculate the growth rate of the solidified shell according to the square root law of solidification time:

[0024]

[0025] in, is the growth rate of the solidified shell, in m / s; k s is the solidification coefficient of molten steel, in m·s -0.5 ;d s is the distance from the thermocouple embedding position to the meniscus, in m; V c is the continuous casting speed, in m / s;

[0026] Step 5-2: Calculate the mass of the solidified shell per unit time and per unit area according to the growth rate of the solidified shell:

[0027]

[0028] in, is the mass of solidified shell per unit time and unit area, in kg·m -2 ·s -1 ρ S is the density of the solidified shell, in kg / m 3 ;

[0029] Step 5-3: Calculate the latent heat flux of solidification shell growth:

[0030]

[0031] Where q1 is the solidification latent heat flux of the solidified shell growth, unit W / m 2 ; Δh is the solidification enthalpy of molten steel, unit is kJ / kg.

[0032] Furthermore, the step 6 is specifically as follows:

[0033] qs =q c -q1

[0034] Among them, q s The sensible heat flux provided by the molten steel to the solidified shell, in W / m 2 ;q c The heat flux taken away by cooling water in the process of cooling the copper plate of the crystallizer, in W / m 2 ; q1 is the solidification latent heat flux of solidification shell growth, unit W / m 2 .

[0035] Furthermore, in step 7, the convection heat transfer coefficient of the molten steel in the crystallizer flushing the solidification front is calculated according to the following formula:

[0036]

[0037] Among them, h L is the convection heat transfer coefficient of the molten steel flushing the solidification front, unit W·m -2 ·K -1 ; T L is the temperature of molten steel, unit K; T S is the temperature of the solidifying shell, in K.

[0038] Furthermore, the step 8 is specifically as follows:

[0039] Step 8-1: The relationship between the flow rate of the molten steel at the solidification front and the convective heat transfer coefficient of the molten steel flushing the solidification front is obtained from the heat transfer characteristic equation. The molten steel in the crystallizer is in a turbulent state, and the turbulent heat transfer characteristic equation is:

[0040] Nu=0.0296Re 4 / 5 Pr 1 / 3

[0041] Among them, Nu is the Nusselt number, Re is the Reynolds number, and Pr is the Prandtl number, which are calculated as follows:

[0042]

[0043]

[0044]

[0045] Among them, λ L is the thermal conductivity of molten steel, in W·m -1 ·K -1 ;d s is the distance from the embedded position of the thermocouple to the meniscus, in m; ρ L is the density of molten steel, in kg / m 3;u L is the velocity of the molten steel at the solidification front, in m / s; μ L is the dynamic viscosity of molten steel, in Pa·s; c p is the specific heat capacity of molten steel, in J·kg -1 ·K -1 .

[0046] Step 8-2: The relationship between the velocity of the molten steel at the solidification front and the convective heat transfer coefficient of the molten steel flushing the solidification front is derived from the turbulent heat transfer characteristic equation:

[0047]

[0048] Step 8-3: Based on the calculation formula of the heat flux taken away by the cooling water in the process of cooling the copper plate of the crystallizer, the solidification latent heat flux of the solidified shell growth, and the convection heat transfer coefficient of the molten steel scouring the solidification front, the flow rate of the molten steel at the solidification front is further expressed as follows:

[0049]

[0050] The method of the present invention for determining the flow rate of molten steel at the solidification front in a crystallizer by using the temperature of a copper plate has at least the following beneficial effects:

[0051] (1) The present invention proposes a method for calculating the flow rate of molten steel at the solidification front in a crystallizer based on the principle of conservation of energy using the temperature of a copper plate measured by a thermocouple. The method can monitor the flow state inside the crystallizer in real time. The method has no interference with the flow field of the crystallizer, and the calculation formula is simple and easy to apply.

[0052] (2) The present invention can be used for crystallizers of different specifications, continuous casting processes of different steel grades, etc. There is no need to change the existing calculation method, and only the crystallizer process parameters and the physical property parameters of the crystallizer copper plate, molten steel and solidified shell need to be collected according to the working conditions. Therefore, the present invention has wide applicability in the field of continuous casting. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 The present invention is a flow chart of a method for determining the flow rate of molten steel at the solidification front in a crystallizer by using the temperature of a copper plate. DETAILED DESCRIPTION

[0054] The present invention provides a method for determining the flow rate of molten steel at the solidification front in a crystallizer by utilizing the temperature of a copper plate. A plurality of thermocouples are installed on the copper plates in four directions of the crystallizer on a continuous casting machine to measure the temperature of the copper plates of the crystallizer, obtain the process parameters of the crystallizer and the physical properties of the copper plates, molten steel and solidified shell of the crystallizer, and calculate in real time the flow rate of the molten steel at the solidification front closest to the temperature measurement point of the thermocouples in the continuous casting crystallizer.

[0055] like Figure 1 As shown, a method of determining the flow rate of molten steel at the solidification front in a crystallizer by using the temperature of a copper plate of the present invention comprises the following steps:

[0056] Step 1: Multiple thermocouples are embedded in the copper plates in four directions of the continuous casting crystallizer. The thermocouples are arranged based on the principle of spatial symmetry, and their number is determined according to the width and height of the copper plate. In this embodiment, 3×5 thermocouples are installed along the width direction, and 3×1 thermocouples are installed along the narrow side copper plate direction. Thermocouples are used to measure the temperature of the crystallizer copper plate in real time.

[0057] Step 2: Collect the crystallizer process parameters, including: cooling water temperature, heat transfer coefficient between cooling water and crystallizer copper plate, copper plate temperature measured by thermocouple, distance from thermocouple measurement point to the cold side of copper plate, distance from thermocouple embedding position to meniscus, and continuous casting speed.

[0058] This embodiment takes a thin slab continuous casting crystallizer of a steel plant as an example, and the solidification coefficient of the steel slab is taken as a fixed value, and the specific values ​​are shown in Table 1 and Table 2.

[0059] Table 1 Process parameters of the crystallizer in this embodiment

[0060]

[0061] Step 3: Collect the physical properties of the copper plate of the crystallizer, the molten steel and the solidified shell, including: thermal conductivity of the copper plate, thermal conductivity of the molten steel, dynamic viscosity of the molten steel, specific heat of the molten steel, density of the molten steel, temperature of the molten steel, temperature of the solidified shell, density of the solidified shell, solidification enthalpy of the molten steel and solidification coefficient of the molten steel.

[0062] Table 2 Physical properties of the mold copper plate, molten steel and solidified shell in this embodiment

[0063] Parameter (unit) Numeric <![CDATA[Thermal conductivity λ of copper plate m (W·m -1 ·K -1 )]]> 370 <![CDATA[The temperature T of the molten steel L (K)]]> 1823 <![CDATA[The temperature T of the solidified shell S (K)]]> 1050 <![CDATA[The density ρ of the solidified shell S (kg / m 3 )]]> 7820 Solidification enthalpy of molten steel Δh (kJ / kg) 272 <![CDATA[Solidification coefficient k of molten steel S (m·s -0.5 )]]> 0.0034 <![CDATA[Dynamic viscosity μ of molten steel]] L (Pa·s)]]> 0.0062 <![CDATA[Thermal conductivity λ of molten steel]] L (W·m -1 ·K -1 )]]> 27 <![CDATA[Specific heat capacity c of molten steel]] p (J·kg -1 ·K -1 )]]> 720 <![CDATA[The density ρ of molten steel L (kg / m 3 )]]> 7020

[0064] Step 4: Calculate the heat flux taken away by cooling water during cooling of the crystallizer copper plate according to the following formula:

[0065]

[0066] Among them, q c The heat flux taken away by cooling water in the process of cooling the copper plate of the crystallizer, in W / m 2 ; T m is the copper plate temperature measured by the thermocouple, in K; T w is the cooling water temperature, unit K; h w is the convection heat transfer coefficient between cooling water and the copper plate of the crystallizer, in W·m -2 ·K -1 ; mis the thermal conductivity of the copper plate of the crystallizer, in W·m -1 ·K -1 ;d t It is the distance between the thermocouple measurement point and the cold side of the copper plate, in meters.

[0067] According to the specific crystallizer process parameters and related physical property parameters in this embodiment, the heat flux q taken away by the cooling water in the process of cooling the crystallizer copper plate is calculated by the above formula: c =2.814×10 6 W / m 2 .

[0068] Step 5: Calculate the solidification latent heat flux of the solidified shell growth, and the step 5 is specifically as follows:

[0069] Step 5-1: Calculate the growth rate of the solidified shell according to the square root law of solidification time:

[0070]

[0071] in, is the growth rate of the solidified shell, in m / s; k s is the solidification coefficient of molten steel, in m·s -0.5 ;d s is the distance from the thermocouple embedding position to the meniscus, in m; V c is the continuous casting speed, in m / s. According to the relevant parameters collected in this embodiment, the growth rate of the solidified shell is calculated by the above formula:

[0072] Step 5-2: Calculate the mass of the solidified shell per unit time and per unit area according to the growth rate of the solidified shell:

[0073]

[0074] in, is the mass of solidified shell per unit time and unit area, in kg·m -2 ·s -1 ρ S is the density of the solidified shell, in kg / m 3 In this embodiment, the mass of the solidified shell per unit time and per unit area is

[0075] Step 5-3: Calculate the latent heat flux of solidification shell growth:

[0076]

[0077] Where q1 is the solidification latent heat flux of the solidified shell growth, unit W / m 2; Δh is the solidification enthalpy of the molten steel, in kJ / kg. In this embodiment, the solidification latent heat flux of the solidified shell growth is q1=1.33×10 6 W / m 2 .

[0078] Step 6: According to the first law of thermodynamics, considering the energy conservation and heat transfer law in the thickness direction of the copper plate, the heat flux taken away by the cooling water in the process of cooling the copper plate of the crystallizer is equal to the sum of the sensible heat flux provided by the molten steel to the solidified shell and the solidification latent heat flux of the growth of the solidified shell. The sensible heat flux provided by the molten steel to the solidified shell is calculated as follows:

[0079] q s =q c -q1

[0080] Among them, q s The sensible heat flux provided by the molten steel to the solidified shell, in W / m 2 According to the heat flux taken away by the cooling water obtained in step 4-5 during the cooling of the copper plate of the crystallizer and the solidification latent heat flux of the growth of the solidified shell, the sensible heat flux q provided by the molten steel to the solidified shell in this embodiment is s =1.483×10 6 W / m 2 .

[0081] Step 7: The molten steel in the crystallizer continuously flushes the solidification front during the flow process, and transfers the heat of the high-temperature molten steel to the solidified shell. The convective heat transfer coefficient of the molten steel in the crystallizer flushing the solidification front is calculated using the transferred sensible heat flux;

[0082] In specific implementation, the convection heat transfer coefficient h of the molten steel in the crystallizer flushing the solidification front is calculated according to the following formula: L :

[0083]

[0084] Among them, h L is the convection heat transfer coefficient of the molten steel flushing the solidification front, unit W·m -2 ·K -1 ; T L is the temperature of molten steel, unit K; T S is the temperature of the solidified shell, in K. Based on the physical properties of the molten steel and the solidified shell collected in step 2 and the sensible heat flux provided by the molten steel obtained in step 6 to the solidified shell.

[0085] In this embodiment, h L =2.472×10 4 W·m -2 ·K -1 .

[0086] Step 8: Calculate the molten steel flow rate at the solidification front corresponding to the thermocouple temperature measuring point in the crystallizer according to the relationship between the molten steel flow rate at the solidification front and the convection heat transfer coefficient of the molten steel flushing the solidification front. The specific step 8 is:

[0087] Step 8-1: The relationship between the flow rate of the molten steel at the solidification front and the convective heat transfer coefficient of the molten steel flushing the solidification front is obtained from the heat transfer characteristic equation. The molten steel in the crystallizer is in a turbulent state, and the turbulent heat transfer characteristic equation is:

[0088] Nu=0.0296Re 4 / 5 Pr 1 / 3

[0089] Among them, Nu is the Nusselt number, Re is the Reynolds number, and Pr is the Prandtl number, which are calculated as follows:

[0090]

[0091]

[0092]

[0093] Among them, λ L is the thermal conductivity of molten steel, in W·m -1 ·K -1 ρ L is the density of molten steel, in kg / m 3 ;u L is the velocity of the molten steel at the solidification front, in m / s; μ L is the dynamic viscosity of molten steel, in Pa·s; c p is the specific heat capacity of molten steel, in J·kg -1 ·K -1 .

[0094] Step 8-2: The relationship between the turbulent heat transfer characteristic equation and the above three dimensionless expressions is derived as follows:

[0095]

[0096] Step 8-3: Based on the calculation formula of the heat flux taken away by the cooling water in the process of cooling the copper plate of the crystallizer, the solidification latent heat flux of the solidified shell growth, and the convection heat transfer coefficient of the molten steel scouring the solidification front, the flow rate of the molten steel at the solidification front is further expressed as follows:

[0097]

[0098] In this embodiment, the flow rate u of the molten steel at the solidification front is L =0.028m / s.

[0099] The method of using thermocouples to measure temperature and determine the flow rate of molten steel in a crystallizer and the above steps described in the above technical scheme and embodiments of the present invention can better achieve the purpose of real-time measurement of the flow rate of molten steel without affecting the flow field of molten steel in the crystallizer.

[0100] The above description is only a preferred embodiment of the present invention and is not intended to limit the concept of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for determining the flow rate of molten steel at the solidification front in a crystallizer by using the temperature of a copper plate, characterized in that: The following steps are involved: Step 1: multiple thermocouples are embedded in the copper plates in four directions of the continuous casting crystallizer. The thermocouples are arranged based on the principle of spatial symmetry, and the number of thermocouples is determined according to the width and height of the copper plates. The temperature of the crystallizer copper plates is measured in real time using the thermocouples; Step 2: Collecting crystallizer process parameters; Step 3: Collect the physical properties of the mold copper plate, molten steel and solidified shell; Step 4: Calculate the heat flux taken away by the cooling water during the cooling of the crystallizer copper plate; Step 5: Calculate the solidification latent heat flux of the solidified shell growth; Step 6: According to the first law of thermodynamics, considering the energy conservation and heat transfer law in the thickness direction of the copper plate, calculate the sensible heat flux provided by the molten steel to the solidified shell; Step 7: Calculate the convection heat transfer coefficient of the molten steel in the crystallizer flushing the solidification front using the sensible heat flux provided by the molten steel to the solidified shell; Step 8: Calculate the flow rate of the molten steel at the solidification front corresponding to the thermocouple temperature measurement point in the crystallizer according to the convection heat transfer coefficient of the molten steel flushing the solidification front; The step 4 specifically calculates the heat flux taken away by the cooling water during the cooling of the crystallizer copper plate according to the following formula: Among them, q c The heat flux taken away by cooling water in the process of cooling the copper plate of the crystallizer, in W / m 2 ; T m is the copper plate temperature measured by the thermocouple, in K; T w is the cooling water temperature, unit K; h w is the convection heat transfer coefficient between cooling water and the copper plate of the crystallizer, in W·m -2 ·K -1 ; m is the thermal conductivity of the copper plate of the crystallizer, in W·m -1 ·K -1 ;d t is the distance between the thermocouple measurement point and the cold side of the copper plate, in meters; The step 5 is specifically as follows: Step 5-1: Calculate the growth rate of the solidified shell according to the square root law of solidification time: in, is the growth rate of the solidified shell, in m / s; k S is the solidification coefficient of molten steel, in m·s -0.5 ;d S is the distance from the thermocouple embedding position to the meniscus, in m; V c is the continuous casting speed, in m / s; Step 5-2: Calculate the mass of the solidified shell per unit time and per unit area according to the growth rate of the solidified shell: in, is the mass of solidified shell per unit time and unit area, in kg·m -2 ·s -1 ρ S is the density of the solidified shell, in kg / m 3 ; Step 5-3: Calculate the latent heat flux of solidification shell growth: Where q1 is the solidification latent heat flux of the solidified shell growth, unit W / m 2 ; Δh is the solidification enthalpy of molten steel, unit is kJ / kg; The step 6 is specifically as follows: q s =q c -q1 Among them, q s The sensible heat flux provided by the molten steel to the solidified shell, in W / m 2 ;q c The heat flux taken away by cooling water in the process of cooling the copper plate of the crystallizer, in W / m 2 ; q1 is the solidification latent heat flux of solidification shell growth, unit W / m 2 ; In step 7, the convection heat transfer coefficient of the molten steel in the crystallizer flushing the solidification front is calculated according to the following formula: Among them, h L is the convection heat transfer coefficient of the molten steel flushing the solidification front, unit W·m -2 ·K -1 ; T L is the temperature of molten steel, in K; T S is the temperature of the solidifying shell, in K.

2. The method for determining the flow rate of molten steel at the solidification front in a crystallizer by using the copper plate temperature as claimed in claim 1, characterized in that: The crystallizer process parameters in step 2 include: Cooling water temperature, heat transfer coefficient between cooling water and copper plate of crystallizer, temperature of copper plate measured by thermocouple, distance between thermocouple measuring point and cold side of copper plate, distance from embedded position of thermocouple to meniscus and continuous casting speed.

3. The method for determining the flow rate of molten steel at the solidification front in a crystallizer by using the copper plate temperature as claimed in claim 1, characterized in that: The physical property parameters of the crystallizer copper plate, molten steel and solidified shell in step 3 include: Thermal conductivity of the copper plate, thermal conductivity of the molten steel, dynamic viscosity of the molten steel, specific heat of the molten steel, density of the molten steel, temperature of the molten steel, temperature of the solidified shell, density of the solidified shell, solidification enthalpy of the molten steel and solidification coefficient of the molten steel.

4. The method for determining the flow rate of molten steel at the solidification front in a crystallizer by using the copper plate temperature as claimed in claim 1, characterized in that: The step 8 is specifically as follows: Step 8-1: The relationship between the flow rate of the molten steel at the solidification front and the convective heat transfer coefficient of the molten steel flushing the solidification front is obtained from the heat transfer characteristic equation. The molten steel in the crystallizer is in a turbulent state, and the turbulent heat transfer characteristic equation is: Now=0.0296Re 4 / 5 Per 1 / 3 Among them, Nu is the Nusselt number, Re is the Reynolds number, and Pr is the Prandtl number, which are calculated as follows: Among them, λ L is the thermal conductivity of molten steel, in W·m -1 ·K -1 ;d S is the distance from the embedded position of the thermocouple to the meniscus, in m; ρ L is the density of molten steel, in kg / m 3 ;u L is the velocity of the molten steel at the solidification front, in m / s; μ L is the dynamic viscosity of molten steel, in Pa·s; c p is the specific heat capacity of molten steel, in J·kg -1 ·K -1 ; Step 8-2: The relationship between the velocity of the molten steel at the solidification front and the convective heat transfer coefficient of the molten steel flushing the solidification front is derived from the turbulent heat transfer characteristic equation: Step 8-3: Based on the calculation formula of the heat flux taken away by cooling water in the process of cooling the copper plate of the crystallizer, the solidification latent heat flux of the solidified shell growth, and the convection heat transfer coefficient of the molten steel scouring the solidification front, the flow rate of the molten steel at the solidification front is expressed as follows:

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