Method for measuring interface thermal resistance in molten steel solidification process

Abstract

The invention relates to the technical field of thin-strip continuous casting, in particular to a method for measuring interface thermal resistance in the molten steel solidification process, which comprises the following steps: calculating temperature distribution in the molten steel cooling process by using a mathematical modeling method, and accurately calculating the change condition of the interface thermal resistance in the molten steel solidification process by combining experimental data of a molten drop solidification device. The method specifically comprises the following steps: controlling the dripping temperature of molten steel, obtaining temperature measurement data of two thermocouples according to a thermal simulation experiment, obtaining the height and room temperature of a steel drop, and obtaining a heat flow of a steel sample and a copper substrate interface and the surface temperature of a copper mold based on the temperature measurement data of the two thermocouples; establishing a one-dimensional heat transfer model, and calculating the overall temperature distribution of the molten steel by combining the density, specific heat capacity and other parameters of the steel sample; the interface thermal resistance of the molten steel in the copper mold surface heat transfer process is calculated by adopting the following formula based on the overall temperature distribution of the molten steel, so that the interface thermal resistance can serve as a thermal resistance parameter of a heat transfer interface to be applied to a numerical simulation calculation process, and production is guided.

Description

Technical Field

[0001] The invention relates to the technical field of thin strip continuous casting, and in particular to a method for measuring interfacial thermal resistance during the solidification process of molten steel. Background Art

[0002] Twin-roller thin strip continuous casting technology for steel has a history of a hundred years. With the development of science and technology, thin strip continuous casting technology has re-entered the vision of steel companies with its characteristics of short process, low cost, and excellent solidification structure.

[0003] The sub-rapid solidification process of thin strip continuous casting is very complex. There are currently three main research methods: (1) Small / pilot thin strip continuous casting test line. Although the small / pilot thin strip continuous casting test line can simulate industrial production well, its experimental cost is too high and it is difficult to conduct large-scale experiments.

[0004] (2) Numerical simulation: Numerical simulation can establish mathematical models to guide on-site production, but key data is still highly dependent on the production site.

[0005] (3) Laboratory thermal simulation: Laboratory thermal simulation simplifies the production site into a controllable physical model and simulates the sub-rapid solidification process in the laboratory. The experimental cost is low and the reference value is high, which greatly reduces the difficulty and cost of research.

[0006] Existing droplet solidification equipment, originally developed by Professor Cramb's team at Carnegie Mellon University and later improved by the Institute of Steel at Central South University, can rapidly measure interfacial heat flux and, through varying conditions, analyze heat transfer under varying conditions. However, existing technology fails to accurately capture changes in interfacial thermal resistance during the solidification process.

[0007] In summary, there is an urgent need for a method that can accurately obtain the change of the interfacial thermal resistance during the solidification process of molten steel to solve the problems existing in the existing technology. Summary of the Invention

[0008] The present invention aims to provide a method for accurately measuring the change in interfacial thermal resistance during the solidification process of molten steel. This method uses mathematical modeling to calculate the temperature distribution of the molten steel during cooling, and combines experimental data from a droplet solidification device to accurately calculate the change in interfacial thermal resistance during the solidification process. The technical solution is as follows: A method for measuring interfacial thermal resistance during molten steel solidification comprises the following steps: The first step is to obtain experimental data. Specifically, select the steel sample to be measured for thermal resistance and the copper mold with the corresponding surface state, use the molten drop solidification device to conduct the experiment, and control the steel drop temperature. and atmosphere, and ensure that the center of the sample drops above the thermocouple temperature measuring end; obtain the temperature measurement data of the two thermocouples, which are expressed as and ; Get the height of the steel drop and room temperature ; The second step is to preliminarily process the experimental data, specifically: based on and Get the heat flow at the interface between the steel sample and the copper substrate And the surface temperature of the copper mold ; The third step is to calculate the thermal resistance. Specifically, first establish a one-dimensional heat transfer model, and for each time node, perform calculations on a spatial scale to obtain the overall temperature distribution of the molten steel. Based on the overall temperature distribution of the molten steel, the following formula is used to calculate the interfacial thermal resistance of the heat transfer process of the molten steel on the copper mold surface: : ; in: for The temperature of the spatial node at the contact boundary between the molten steel and the copper mold at the moment; for The surface temperature of the copper mold at all times; for Heat flow at the interface between steel sample and copper substrate at each moment.

[0009] Preferably, the experiment using the droplet solidification device is specifically as follows: A steel sample is placed in a quartz tube with a small hole at the bottom and heated and melted by an induction coil. The temperature of the molten steel is measured by a thermometer, and a proportional-integral-differential controller receives the temperature signal and controls the temperature by adjusting the power of the induction coil. When the target temperature is reached, a pulse of nitrogen or argon, the same atmosphere used during the experiment, is introduced into the tube, ejecting the molten steel so that it falls onto the copper mold and the droplets land above the measuring ends of the thermocouples; the droplets cool on the surface of the copper mold, and the two thermocouples record the corresponding temperature measurement data.

[0010] Preferably, in the second step: input and , using 1D-IHCP to inversely calculate the heat flow at the interface between the steel sample and the copper substrate And the surface temperature of the copper mold .

[0011] Preferably, in the third step: For the spatial nodes, The temperature of the time node is Temperature at each time point is the following formula: ; For the boundary conditions of the heat transfer interface, its thickness is , then: ①, for the contact boundary between molten steel and copper mold Node temperature as follows: ; ② The spatial node is advanced to the boundary of the molten steel-atmosphere interface. Node temperature as follows: ; in: is the time difference; For the Time nodes and The total heat flow of each spatial node; for Specific heat capacity of steel sample under temperature conditions; for Density of steel sample under temperature conditions; , Indicates that the first spatial node is in The temperature at the time node is given by Temperature at each time point Calculated; subscript represents the corresponding spatial node and ; and are the node spatial scale and the total number of nodes, respectively; For the The total heat flow at the node at the contact boundary between liquid steel and copper mold at each time node; for Specific heat capacity of steel sample under temperature conditions; for Density of steel sample under temperature conditions; is the thermal conductivity of the steel sample.

[0012] Preferably, in the third step: in a one-dimensional heat transfer model, the conduction of heat in steel obeys Fourier's law of heat conduction: ; in: is the specific heat capacity of the steel sample; is the density of the steel sample; is temperature; For time; for location; 0 ~ One-dimensional computational domain within the range; The initial conditions for temperature are as follows: ; Because the interface between the steel droplet and the copper mold is very thin, the heat flux flowing out from the bottom of the steel droplet is considered to be equal to the heat flux flowing into the copper mold obtained by inverse calculation of the experimental data, as shown in the following formula: ; Considering the heat transfer of thermal radiation and natural convection of the atmosphere, the heat flux density on the top surface of the sample is expressed as follows: ; in: is the total emissivity of the steel sample; is the Boltzmann constant; is the natural convection heat transfer coefficient; is the temperature at the top of the steel drop; is the heat flux at the top of the steel drop; The finite difference method is used to calculate the internal heat transfer process of the molten steel. Total heat flow of spatial nodes Use the following formula to calculate: ; in: For the The spatial nodes flow into the Heat flux density of spatial nodes; For the The spatial nodes flow into the Heat flux density of spatial nodes; For the The temperature of each spatial node; Introducing the enthalpy change of the solidification process, according to the law of conservation of energy, spatial nodes and Enthalpy at each time point Use the following formula to calculate: ; in: is the cross-sectional area perpendicular to the direction of heat transfer; Let the enthalpy per unit volume be , applying a one-dimensional control volume , then the heat conduction equation becomes the following: ; in: For the spatial nodes and Enthalpy per unit volume at each time point; The relationship between enthalpy and temperature It is expressed in the following formula: ; in: Indicates the reference temperature; express Location The temperature of the moment; The specific heat capacity is expressed by the equivalent specific heat capacity value corresponding to each temperature during the solidification process, and considering the density change, the following expression is obtained: ; ; like Small enough so that The value of is small enough so that and , then we have the following expressions: ; Then we get: ; Based on the above formula, we get The temperature of the time node is The temperature at each time point is described as follows: .

[0013] In addition to the above-described objects, features and advantages, the present invention has other objects, features and advantages. The present invention will be further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are intended to explain the present invention and do not constitute an undue limitation of the present invention. In the accompanying drawings: Figure 1 This is a schematic diagram of a method for measuring interfacial thermal resistance during the solidification process of molten steel in a preferred embodiment of the present invention; Figure 2 Schematic diagram of a droplet solidification device for conducting an experiment in a preferred embodiment of the present invention, wherein: (a) is a schematic diagram of the structure of the droplet solidification device; (b) is a schematic diagram of the interface between the molten steel and the copper mold in (a); Figure 3 It is a diagram of the principle of differential node division in a preferred embodiment of the present invention; Figure 4 : is a temperature-position-time distribution diagram of molten steel in a preferred embodiment of the present invention; Figure 5 Schematic diagram of the change of interfacial thermal resistance over time during the heat transfer process of molten steel on the copper mold surface in a preferred embodiment of the present invention; Among them, 1. CCD camera, 2. Observation window, 3. Air inlet, 4. Vacuum pump, 5. Infrared temperature probe, 6. Equipment cavity, 7. Exhaust port, 8. Thermocouple, 9. Cooling water channel, 10. Water-cooled copper mold, 11. Induction coil, 12. Quartz tube, 13. Steel drop, 14. Thermocouple hole. DETAILED DESCRIPTION

[0015] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0016] Example: See also Figure 1 , a method for measuring the interfacial thermal resistance during the solidification process of molten steel, controlling the drop temperature of molten steel , obtain the temperature measurement data of two thermocouples according to the thermal simulation experiment and , and obtain the steel drop height and room temperature , and based on and Get the heat flow at the interface between the steel sample and the copper substrate And the surface temperature of the copper mold , in combination with the density of steel samples Specific heat capacity , thermal conductivity , total emissivity σ and natural convection heat transfer coefficient , calculate the temperature distribution of the entire molten steel Based on the overall temperature distribution of the molten steel, the following formula is used to calculate the interfacial thermal resistance of the heat transfer process of the molten steel on the copper mold surface: The specific steps include: The first step is to obtain experimental data. Specifically, select the steel sample to be measured for thermal resistance and the copper mold with the corresponding surface state, use the molten drop solidification device to conduct the experiment, and control the steel drop temperature. (unit is ℃) and atmosphere, and ensure that the center of the sample drops above the thermocouple temperature measuring end; obtain the temperature measurement data of the two thermocouples, which are expressed as and ; Get the height of the steel drop (unit: mm) and room temperature .

[0017] The experiment was carried out using a droplet solidification device, see Figure 2 Specifically, the steel sample is placed in a quartz tube with a small hole at the bottom and heated and melted by an induction coil. Figure 2 As shown in (a), the temperature of the molten steel is measured by a thermometer, and a proportional-integral-differential controller receives the temperature signal and controls the temperature by adjusting the power of the induction coil. Other details not described herein may be referred to in the prior art.

[0018] When the target temperature is reached, a nitrogen or argon pulse, the same as the atmosphere controlled during the experiment, is introduced into the tube to eject the molten steel, causing it to fall onto the copper mold and droplets to fall onto the measuring end of the thermocouples; the droplets cool on the surface of the copper mold, and the two thermocouples record the corresponding temperature data. Figure 2 As shown in (b), two thermocouples were inserted horizontally below the hot surface of the copper mold, with their distances to the surface being 1 mm and 3 mm respectively.

[0019] The second step is to preliminarily process the experimental data, specifically: based on and Get the heat flow at the interface between the steel sample and the copper substrate And the surface temperature of the copper mold .

[0020] In this embodiment, preferably, in the second step, input and , using 1D-IHCP to inversely calculate the heat flow at the interface between the steel sample and the copper substrate And the surface temperature of the copper mold The inverse calculation using 1D-IHCP can refer to the existing technology.

[0021] The third step is to calculate the thermal resistance. Specifically, first establish a one-dimensional heat transfer model, and for each time node, perform calculations on a spatial scale to obtain the overall temperature distribution of the molten steel. Based on the overall temperature distribution of the molten steel, the following formula is used to calculate the interfacial thermal resistance of the heat transfer process of the molten steel on the copper mold surface: : ; in: for The temperature of the spatial node at the contact boundary between the molten steel and the copper mold at the moment; for The surface temperature of the copper mold at all times; for Heat flow at the interface between steel sample and copper substrate at each moment.

[0022] Details are as follows: In the one-dimensional heat transfer model, heat conduction in steel obeys Fourier's law of heat conduction: ; in: is the specific heat capacity of the steel sample, and its unit is J / K kg; is the density of the steel sample, in kg / m 3 ; is temperature; is the time in seconds; is the position, the unit is m; 0 ~ One-dimensional computational domain within the range; The initial conditions for temperature are as follows: ; Since the interface between the steel droplet and the copper mold is very thin, the heat flux flowing out from the bottom of the steel droplet can be considered to be equal to the heat flux flowing into the copper mold obtained by inverse calculation of the experimental data, as shown in the following formula: ; is the value of heat flow changing with time obtained from the experiment.

[0023] In order to simulate the effect of heat dissipation from the top surface of the sample to the atmosphere, considering the thermal radiation and natural convection heat transfer of the atmosphere, the heat flux density on the top surface of the sample is expressed as follows: ; in: is the total emissivity of the steel sample; is the Boltzmann constant; is the natural convection heat transfer coefficient; is the temperature at the top of the steel drop; is the heat flux at the top of the steel drop; The finite difference method is used to calculate the internal heat transfer process of molten steel. Figure 3 , Indicates the nodes, For the The temperature of the node. Total heat flow of spatial nodes Use the following formula to calculate: ; in: For the The spatial nodes flow into the Heat flux density of spatial nodes; For the The spatial nodes flow into the Heat flux density of spatial nodes; For the The temperature of a spatial node, such as Figure 3 shown.

[0024] In order to consider the solidification phase change stage, the enthalpy change of the solidification process is introduced. According to the law of conservation of energy, spatial nodes and Enthalpy at each time point Use the following formula to calculate: ; in: is the cross-sectional area perpendicular to the direction of heat transfer; Let the enthalpy per unit volume be , applying a one-dimensional control volume , then the heat conduction equation becomes the following: ; in: For the spatial nodes and Enthalpy per unit volume at each time point; The relationship between enthalpy and temperature It is expressed in the following formula: ; in: Indicates the reference temperature; express Location The temperature of the moment; The enthalpy method can well represent the solidification process, but the equivalent specific heat method can better reflect the temperature change during the solidification process. The specific heat capacity is expressed by the equivalent specific heat value corresponding to each temperature during the solidification process, and the density change is taken into account. The following expression is obtained: ; ; Heat capacity and density are both functions of temperature, expressed as and express, Indicates that the node is at the time step The temperature change within. Small enough so that The value of is small enough so that and , then we have the following expressions: ; Then we get: ; Based on the above formula, for the spatial nodes, and get the The temperature of the time node is Temperature at each time point Described as follows: ; When considering boundary conditions, the thickness of the control volume has a slightly different expression, such as Figure 3 As shown, for the boundary conditions of the heat transfer interface, its thickness is , then: ①, for the contact boundary between molten steel and copper mold Node temperature as follows: ; ② The spatial node is advanced to the boundary of the molten steel-atmosphere interface. Node temperature as follows: ; in: is the time difference; For the Time nodes and The total heat flow of each spatial node; for Specific heat capacity of steel sample under temperature conditions; for Density of steel sample under temperature conditions; , Indicates that the first spatial node is in The temperature at the time node is given by Temperature at each time point Calculate, and so on, calculate the The temperature of the spatial node until the N Nodes arrive at the top of the steel drop; represents the corresponding spatial node and ; and are the node spatial scale and the total number of nodes, respectively; For the The total heat flow at the node at the contact boundary between liquid steel and copper mold at each time node; for Specific heat capacity of steel sample under temperature conditions; for Density of steel sample under temperature conditions; is the thermal conductivity of the steel sample, and its unit is W / mK.

[0025] Using the technical solution of this embodiment, the calculated overall temperature distribution of the molten steel is as follows: Figure 4 As shown in the figure, the calculated curve of interface thermal resistance changing with time is as follows Figure 5 shown.

[0026] The droplet solidification device can well measure the interface heat flow of molten steel solidification heat transfer, but the heat flow results obtained are still difficult to quantitatively apply directly to the actual production process or directly use as parameters of the heat transfer interface in numerical simulation calculations. This embodiment establishes a one-dimensional heat transfer model based on experiments using the droplet solidification device, combining relevant parameters (including the steel droplet temperature , two thermocouple temperature measurement data and , heat flow at the interface between steel sample and copper substrate , the surface temperature of the copper mold , density of steel samples Specific heat capacity , thermal conductivity , total emissivity σ and natural convection heat transfer coefficient ), calculate the temperature distribution of the entire molten steel Based on the overall temperature distribution of the molten steel, the following formula is used to calculate the interfacial thermal resistance of the heat transfer process of the molten steel on the copper mold surface: , so that it can be used as the thermal resistance parameter of the heat transfer interface in the numerical simulation calculation process, thereby guiding production.

[0027] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A method for measuring interfacial thermal resistance during molten steel solidification, characterized in that: The following steps are involved: The first step is to obtain experimental data. Specifically, select the steel sample to be measured for thermal resistance and the copper mold with the corresponding surface state, use the molten drop solidification device to conduct the experiment, and control the steel drop temperature. and atmosphere, and ensure that the center of the sample drops above the thermocouple temperature measuring end; obtain the temperature measurement data of the two thermocouples, which are expressed as and ; Get the height of the steel drop and room temperature ; The second step is to preliminarily process the experimental data, specifically: based on and Get the heat flow at the interface between the steel sample and the copper substrate And the surface temperature of the copper mold ; The third step is to calculate the thermal resistance. Specifically, first establish a one-dimensional heat transfer model, and for each time node, perform calculations on a spatial scale to obtain the overall temperature distribution of the molten steel. Based on the overall temperature distribution of the molten steel, the following formula is used to calculate the interfacial thermal resistance of the heat transfer process of the molten steel on the copper mold surface: : ； in: for The temperature of the spatial node at the contact boundary between the molten steel and the copper mold at the moment; for The surface temperature of the copper mold at all times; for Heat flow at the interface between steel sample and copper substrate at each moment.

2. The method for measuring interfacial thermal resistance during molten steel solidification according to claim 1, wherein: The specific steps of the experiment using the molten drop solidification device are: A steel sample is placed in a quartz tube with a small hole at the bottom and heated and melted by an induction coil. The temperature of the molten steel is measured by a thermometer, and a proportional-integral-differential controller receives the temperature signal and controls the temperature by adjusting the power of the induction coil. When the target temperature is reached, a pulse of nitrogen or argon, the same atmosphere used during the experiment, is introduced into the tube, ejecting the molten steel so that it falls onto the copper mold and the droplets land above the measuring ends of the thermocouples; the droplets cool on the surface of the copper mold, and the two thermocouples record the corresponding temperature measurement data.

3. The method for measuring interfacial thermal resistance during molten steel solidification according to claim 1, wherein: In the second step: input and , using 1D-IHCP to inversely calculate the heat flow at the interface between the steel sample and the copper substrate And the surface temperature of the copper mold .

4. The method for measuring interfacial thermal resistance during solidification of molten steel according to any one of claims 1 to 3, wherein: In the third step: For the spatial nodes, The temperature of the time node is Temperature at each time point is the following formula: ； For the boundary conditions of the heat transfer interface, its thickness is , then: ①, for the contact boundary between molten steel and copper mold Node temperature as follows: ； ② The spatial node is advanced to the boundary of the molten steel-atmosphere interface. Node temperature as follows: ； in: is the time difference; For the Time nodes and The total heat flow of each spatial node; for Specific heat capacity of steel sample under temperature conditions; for Density of steel sample under temperature conditions; , Indicates that the first spatial node is in The temperature at the time node is given by Temperature at each time point Calculated; subscript represents the corresponding spatial node and ; and are the node spatial scale and the total number of nodes, respectively; For the The total heat flow at the node at the contact boundary between liquid steel and copper mold at each time node; for Specific heat capacity of steel sample under temperature conditions; for Density of steel sample under temperature conditions; is the thermal conductivity of the steel sample.

5. The method for measuring interfacial thermal resistance during molten steel solidification according to claim 4, wherein: In the third step: In the one-dimensional heat transfer model, heat conduction in steel obeys Fourier's law of heat conduction: ； in: is the specific heat capacity of the steel sample; is the density of the steel sample; is temperature; For time; for location; 0 ~ One-dimensional computational domain within the range; The initial conditions for temperature are as follows: ； The heat flux flowing out from the bottom of the steel droplet is equal to the heat flux flowing into the copper mold obtained by back-calculation of experimental data, as shown in the following formula: ； Considering the heat transfer of thermal radiation and natural convection of the atmosphere, the heat flux density on the top surface of the sample is expressed as follows: ； in: is the total emissivity of the steel sample; is the Boltzmann constant; is the natural convection heat transfer coefficient; is the temperature at the top of the steel drop; is the heat flux at the top of the steel drop; The finite difference method is used to calculate the internal heat transfer process of the molten steel. Total heat flow of spatial nodes Use the following formula to calculate: ； in: For the The spatial nodes flow into the Heat flux density of spatial nodes; For the The spatial nodes flow into the Heat flux density of spatial nodes; For the The temperature of each spatial node; Introducing the enthalpy change of the solidification process, according to the law of conservation of energy, spatial nodes and Enthalpy at each time point Use the following formula to calculate: ； in: is the cross-sectional area perpendicular to the direction of heat transfer; Let the enthalpy per unit volume be , applying a one-dimensional control volume , then the heat conduction equation becomes the following: ； in: For the spatial nodes and Enthalpy per unit volume at each time point; The relationship between enthalpy and temperature It is expressed in the following formula: ； in: Indicates the reference temperature; express Location The temperature of the moment; The specific heat capacity is expressed by the equivalent specific heat capacity value corresponding to each temperature during the solidification process, and considering the density change, the following expression is obtained: ； ； like and , then we have the following expressions: ； Then we get: ； Based on the above formula, we get The temperature of the time node is The temperature at each time point is described as follows: 。

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