A method for measuring interface heat resistance in a molten steel solidification process

Abstract

This invention relates to the field of thin strip continuous casting technology, specifically to a method for measuring the interfacial thermal resistance during the solidification process of molten steel. This method uses mathematical modeling to calculate the temperature distribution during the cooling process of molten steel, and combines experimental data from a droplet solidification device to accurately calculate the changes in interfacial thermal resistance during the solidification process. Specifically, it includes: controlling the molten steel droplet temperature; obtaining temperature data from two thermocouples based on a thermal simulation experiment, acquiring the steel droplet height and room temperature; and obtaining the heat flow at the interface between the steel sample and the copper substrate, as well as the surface temperature of the copper mold, based on the two thermocouple temperature data; establishing a one-dimensional heat transfer model, and calculating the overall temperature distribution of the molten steel by combining parameters such as the density and specific heat capacity of the steel sample; and calculating the interfacial thermal resistance of the molten steel on the copper mold surface using the following formula based on the overall temperature distribution of the molten steel, so that it can be used as a thermal resistance parameter of the heat transfer interface in the numerical simulation calculation process, thereby guiding production.

Description

Technical Field

[0001] This invention relates to the field of thin strip continuous casting technology, specifically to a method for measuring the interfacial thermal resistance during the solidification process of molten steel. Background Technology

[0002] Twin-roll strip casting technology for steel has a history of over a century. With the development of science and technology, strip casting technology, with its short process, low cost, and excellent solidification structure, has re-entered the field of vision of steel enterprises. The sub-rapid solidification process of strip casting is very complex, and there are currently three main research methods:

[0003] (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 still depends heavily 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 experiment has low cost and high reference value, which greatly reduces the research difficulty and research cost.

[0006] In existing technologies, droplet solidification equipment was initially developed by Professor Cramb's team at Carnegie Mellon University and later improved by the Iron and Steel Research Institute of Central South University. It can quickly measure interfacial heat flow and obtain heat transfer information under different conditions. However, existing technologies cannot accurately obtain the changes in interfacial thermal resistance during the solidification process of molten steel.

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

[0008] The purpose of this invention is to provide a method for accurately measuring the changes in interfacial thermal resistance during the solidification process of molten steel. This method uses mathematical modeling to calculate the temperature distribution during the cooling process of molten steel and combines experimental data from a droplet solidification device to accurately calculate the changes in interfacial thermal resistance during the solidification process. The technical solution is as follows:

[0009] A method for determining the interfacial thermal resistance during the solidification process of molten steel includes the following steps:

[0010] The first step is to obtain experimental data. Specifically, this involves selecting a steel sample of the grade whose thermal resistance is to be measured and a copper mold with the corresponding surface condition, and conducting the experiment using a molten drop solidification apparatus to control the temperature of the molten steel drop. A suitable atmosphere was established, ensuring the sample center fell above the thermocouple measuring end; temperature data from two thermocouples were acquired and expressed as follows: and ; Obtain the height of the steel droplet and room temperature ;

[0011] The second step involves preliminary processing of the experimental data, specifically: based on... and Heat flow at the interface between the steel sample and the copper substrate was obtained. and the surface temperature of the copper mold ;

[0012] The third step is thermal resistance calculation, which involves: first, establishing a one-dimensional heat transfer model; then, for each time point, performing 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, calculating the interfacial thermal resistance of the molten steel during the heat transfer process on the copper mold surface using the following formula. :

[0013] ;

[0014] in: for Temperature of the spatial node at the contact boundary between molten steel and copper mold at any given moment; for The surface temperature of the copper mold at any given time; for Heat flow at the interface between the steel sample and the copper substrate.

[0015] Preferably, the experiment is conducted using a droplet solidification apparatus, specifically:

[0016] The steel sample is placed in a quartz tube with a small hole at the bottom and heated to melt by an induction coil; the temperature of the molten steel is measured by a thermometer, and a proportional-integral-derivative controller receives the temperature signal and controls the temperature by adjusting the power of the induction coil.

[0017] When the target temperature is reached, molten steel is sprayed out by introducing a pulse of nitrogen or argon gas, the same atmosphere controlled during the experiment, into the tube. The molten steel falls onto the copper mold and the droplets fall 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 data.

[0018] Preferably, in the second step: input and The heat flow at the interface between the steel sample and the copper substrate was calculated using 1D-IHCP. and the surface temperature of the copper mold .

[0019] Preferably, in the third step:

[0020] Regarding the first The spatial node, the first The temperature at the time point is used as the _ ... Temperature at each time point It is the following formula:

[0021] ;

[0022] For the boundary conditions of the heat transfer interface, its thickness is Then we have:

[0023] ① For the contact boundary between molten steel and copper mold node temperature as follows:

[0024] ;

[0025] ② The spatial node advances to the boundary of the molten steel-atmosphere interface. Regarding the boundary of the molten steel-atmosphere interface... node temperature as follows:

[0026] ;

[0027] in: For time difference; For the first The first time point and the first Total heat flow at each spatial node; for Specific heat capacity of steel samples under temperature conditions; for Density of steel samples under temperature conditions; , This indicates that the first spatial node is in the [location missing]. The temperature at the time point is determined by the _ ... Temperature at each time point Calculated; Subscript Represents the corresponding spatial node and ; and These represent the node spatial scale and the total number of nodes, respectively. For the first Total heat flow at the steel-copper mold contact boundary at each time point; for Specific heat capacity of steel samples under temperature conditions; for Density of steel samples under temperature conditions; The value is the thermal conductivity of the steel sample.

[0028] Preferably, in the third step: in the one-dimensional heat transfer model, the conduction of heat in steel follows Fourier's law of thermal conductivity:

[0029] ;

[0030] in: This represents the specific heat capacity of the steel sample. The density of the steel sample; For temperature; For time; For location; 0 ~ A one-dimensional computational domain within the range;

[0031] The initial temperature conditions are as follows:

[0032] ;

[0033] Because the interface between the steel droplet and the copper mold is very thin, it is assumed that the heat flow from the bottom of the steel droplet is equal to the heat flow into the copper mold calculated from the experimental data, as shown in the following equation:

[0034] ;

[0035] Considering thermal radiation and natural convection heat transfer from the atmosphere, the heat flux density at the top surface of the sample is expressed as follows:

[0036] ;

[0037] in: It is the total emissivity of the steel sample; It is the Boltzmann constant; It is the natural convection heat transfer coefficient; The temperature at the top of the steel droplet; It is the heat flow at the top of the steel droplet;

[0038] The heat transfer process inside molten steel is calculated using the finite difference method, with the flow into the first... Total heat flow at each spatial node Calculate using the following formula:

[0039] ;

[0040] in: For the first The spatial node flows into the first Heat flux density of each spatial node; For the first The spatial node flows into the first Heat flux density of each spatial node; For the first Temperature of each spatial node;

[0041] Introducing the enthalpy change during solidification, according to the law of conservation of energy, the first... The spatial node and the first enthalpy at each time point Calculate using the following formula:

[0042] ;

[0043] in: It is the cross-sectional area perpendicular to the heat transfer direction;

[0044] Enthalpy per unit volume Applying one-dimensional control volume Then the heat conduction equation becomes the following:

[0045] ;

[0046] in: For the first The spatial node and the first Enthalpy per unit volume at a given time point;

[0047] Expression for the relationship between enthalpy and temperature It can be expressed as follows:

[0048] ;

[0049] in: Indicates reference temperature; express Location at Temperature at any moment;

[0050] Expressing the specific heat capacity using the equivalent specific heat capacity at each temperature during the solidification process, and considering the density change, we have the following expression:

[0051] ;

[0052] ;

[0053] like Small enough to make The value of is small enough that and Then we have the following expression:

[0054] ;

[0055] Then we get:

[0056] ;

[0057] Based on the above formula, we obtain the... The temperature at the time point is used as the _ ... The temperature at each time point is described by the following formula:

[0058] .

[0059] In addition to the objectives, features, and advantages described above, the present invention has other objectives, features, and advantages. The invention will now be described in further detail with reference to the figures. Attached Figure Description

[0060] The accompanying drawings, which form part of this application, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0061] Figure 1 This is a schematic diagram of the method for determining the interfacial thermal resistance during the solidification process of molten steel in a preferred embodiment of the present invention.

[0062] Figure 2 This is a schematic diagram of an experiment conducted by the droplet solidification device 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);

[0063] Figure 3 This is a schematic diagram of the differential node partitioning principle in a preferred embodiment of the present invention;

[0064] Figure 4 This is a temperature-position-time distribution diagram of molten steel in a preferred embodiment of the present invention;

[0065] Figure 5 This is a schematic diagram showing the change of interfacial thermal resistance over time during the heat transfer process of molten steel on the surface of a copper mold in a preferred embodiment of the present invention.

[0066] 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 Implementation

[0067] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0068] Example:

[0069] See Figure 1 A method for determining the interfacial thermal resistance during the solidification process of molten steel, controlling the dripping temperature of molten steel. Temperature data from two thermocouples were obtained based on thermal simulation experiments. and And obtain the height of the steel droplet. and room temperature And based on and Heat flow at the interface between the steel sample and the copper substrate was obtained. and the surface temperature of the copper mold In the density of the combined steel sample Specific heat capacity thermal conductivity Total emissivity σ and natural convection heat transfer coefficient The overall temperature distribution of the molten steel was calculated. The interfacial thermal resistance of the molten steel on the copper mold surface is calculated using the following formula based on the overall temperature distribution of the molten steel. Specifically, it includes the following steps:

[0070] The first step is to obtain experimental data. Specifically, this involves selecting a steel sample of the grade whose thermal resistance is to be measured and a copper mold with the corresponding surface condition, and conducting the experiment using a molten drop solidification apparatus to control the temperature of the molten steel drop. (Unit: °C) and atmosphere, ensuring the sample center falls above the thermocouple measuring end; acquire the temperature data from two thermocouples, expressed as follows: and ; Obtain the height of the steel droplet (Unit: mm) and room temperature .

[0071] Experiments were conducted using a molten droplet solidification apparatus; see details below. Figure 2 Specifically, the steel sample is placed in a quartz tube with a small hole at the bottom and melted by heating with an induction coil. See details... Figure 2 As shown in (a); the temperature of the molten steel is measured by a thermometer, and a proportional-integral-derivative controller receives the temperature signal and controls the temperature by adjusting the power of the induction coil. Other details not described are available in the prior art.

[0072] When the target temperature is reached, molten steel is ejected by pulses of nitrogen or argon gas, the same atmosphere controlled during the experiment, which are then introduced into the tube. The molten steel falls onto the copper mold, with the droplets landing 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 data. The interface between the molten steel and the copper mold is as follows: Figure 2 As shown in (b), two thermocouples were horizontally inserted below the hot surface of the copper mold, with distances of 1 mm and 3 mm from the surface, respectively.

[0073] The second step involves preliminary processing of the experimental data, specifically: based on... and Heat flow at the interface between the steel sample and the copper substrate was obtained. and the surface temperature of the copper mold .

[0074] In this preferred embodiment, the input in the second step is preferred. and The heat flow at the interface between the steel sample and the copper substrate was calculated using 1D-IHCP. and the surface temperature of the copper mold The inverse calculation using 1D-IHCP can be referenced from existing technologies.

[0075] The third step is thermal resistance calculation, which involves: first, establishing a one-dimensional heat transfer model; then, for each time point, performing 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, calculating the interfacial thermal resistance of the molten steel during the heat transfer process on the copper mold surface using the following formula. :

[0076] ;

[0077] in: for Temperature of the spatial node at the contact boundary between molten steel and copper mold at any given moment; for The surface temperature of the copper mold at any given time; for Heat flow at the interface between the steel sample and the copper substrate.

[0078] Details are as follows:

[0079] In a one-dimensional heat transfer model, heat conduction in steel follows Fourier's law of thermal conductivity:

[0080] ;

[0081] in: The specific heat capacity of the steel sample is expressed in J / K kg. The density of the steel sample is expressed in kg / m³. 3 ; For temperature; It refers to time, and its unit is seconds; This refers to the location, and its unit is meters (m). 0 ~ A one-dimensional computational domain within the range;

[0082] The initial temperature conditions are as follows:

[0083] ;

[0084] Because the interface between the steel droplet and the copper mold is very thin, the heat flow from the bottom of the steel droplet can be considered equal to the heat flow into the copper mold calculated from the experimental data, as shown in the following equation:

[0085] ;

[0086] This represents the value of heat flux over time obtained from the experiment.

[0087] To simulate the effect of heat dissipation from the top of the sample to the atmosphere, considering both thermal radiation and natural convection heat transfer from the atmosphere, the heat flux density at the top of the sample is expressed as follows:

[0088] ;

[0089] in: It is the total emissivity of the steel sample; It is the Boltzmann constant; It is the natural convection heat transfer coefficient; The temperature at the top of the steel droplet; It is the heat flow at the top of the steel droplet;

[0090] For details on calculating the internal heat transfer process of molten steel using the finite difference method, see [link to relevant documentation]. Figure 3 , Indicates the first 1 node For the first The temperature of the node. Flowing into the first node. Total heat flow at each spatial node Calculate using the following formula:

[0091] ;

[0092] in: For the first The spatial node flows into the first Heat flux density of each spatial node; For the first The spatial node flows into the first Heat flux density of each spatial node; For the first The temperature of each spatial node, such as Figure 3 As shown.

[0093] To account for the solidification phase transition stage, the enthalpy change during solidification is introduced. According to the law of conservation of energy, the first... The spatial node and the first enthalpy at each time point Calculate using the following formula:

[0094] ;

[0095] in: It is the cross-sectional area perpendicular to the heat transfer direction;

[0096] Enthalpy per unit volume Applying one-dimensional control volume Then the heat conduction equation becomes the following:

[0097] ;

[0098] in: For the first The spatial node and the first Enthalpy per unit volume at a given time point;

[0099] Expression for the relationship between enthalpy and temperature It can be expressed as follows:

[0100] ;

[0101] in: Indicates reference temperature; express Location at Temperature at any moment;

[0102] While the enthalpy method can well represent the solidification process, the equivalent specific heat capacity method can better reflect the temperature changes during solidification. Using the equivalent specific heat capacity value corresponding to each temperature during solidification to represent the specific heat capacity, and considering the density change, we have the following expression:

[0103] ;

[0104] ;

[0105] Both heat capacity and density are functions of temperature, and are respectively represented by... and express, Indicates the node at time step The amount of temperature change inside, if Small enough to make The value of is small enough that and Then we have the following expression:

[0106] ;

[0107] Then we get:

[0108] ;

[0109] Based on the above formula, for the first... The nth spatial node is obtained. The temperature at the time point is used as the _ ... Temperature at each time point Described as follows:

[0110] ;

[0111] When considering boundary conditions, the thickness of the control volume will have a slightly different expression, such as Figure 3 As shown, for the boundary conditions of the heat transfer interface, its thickness is... Then we have:

[0112] ① For the contact boundary between molten steel and copper mold node temperature as follows:

[0113] ;

[0114] ② The spatial node advances to the boundary of the molten steel-atmosphere interface. Regarding the boundary of the molten steel-atmosphere interface... node temperature as follows:

[0115] ;

[0116] in: For time difference; For the first The first time point and the first Total heat flow at each spatial node; for Specific heat capacity of steel samples under temperature conditions; for Density of steel samples under temperature conditions; , This indicates that the first spatial node is in the [location missing]. The temperature at the time point is determined by the _ ... Temperature at each time point Calculated; Subscript Represents the corresponding spatial node and ; and These represent the node spatial scale and the total number of nodes, respectively. For the first Total heat flow at the steel-copper mold contact boundary at each time point; for Specific heat capacity of steel samples under temperature conditions; for Density of steel samples under temperature conditions; is the thermal conductivity of the steel sample, and its unit is W / mK.

[0117] 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 interfacial thermal resistance changes over time as follows: Figure 5 As shown.

[0118] While droplet solidification devices can effectively measure interfacial heat flux during molten steel solidification, the obtained heat flux results are still difficult to quantitatively apply directly to actual production processes or directly use as parameters of the heat transfer interface in numerical simulations. This embodiment, based on experiments using a droplet solidification device, establishes a one-dimensional heat transfer model, incorporating relevant parameters (including the molten steel drop temperature). Temperature data from two thermocouples and Heat flow at the interface between the steel sample and the copper substrate Surface temperature of copper mold Density of steel samples Specific heat capacity thermal conductivity Total emissivity σ and natural convection heat transfer coefficient The overall temperature distribution of the molten steel was calculated. The interfacial thermal resistance of the molten steel on the copper mold surface is calculated using the following formula based on the overall temperature distribution of the molten steel. This allows it to be used as a thermal resistance parameter of the heat transfer interface in the numerical simulation calculation process, thereby guiding production.

[0119] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for determining the interfacial thermal resistance during the solidification process of molten steel, characterized in that, Includes the following steps: The first step is to obtain experimental data. Specifically, this involves selecting a steel sample of the grade whose thermal resistance is to be measured and a copper mold with the corresponding surface condition, and conducting the experiment using a molten drop solidification apparatus to control the temperature of the molten steel drop. A suitable atmosphere was established, ensuring the sample center fell above the thermocouple measuring end; temperature data from two thermocouples were acquired and expressed as follows: and ; Obtain the height of the steel droplet and room temperature ; The second step involves preliminary processing of the experimental data, specifically: based on... and Heat flow at the interface between the steel sample and the copper substrate was obtained. and the surface temperature of the copper mold ; The third step is thermal resistance calculation, which involves: first, establishing a one-dimensional heat transfer model; then, for each time point, performing 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, calculating the interfacial thermal resistance of the molten steel during the heat transfer process on the copper mold surface using the following formula. : ； in: for Temperature of the spatial node at the contact boundary between molten steel and copper mold at any given moment; for The surface temperature of the copper mold at any given time; for Heat flow at the interface between the steel sample and the copper substrate at any given time; Regarding the first The spatial node, the first The temperature at the time point is used as the _ ... Temperature at each time point It is the following formula: ； For the boundary conditions of the heat transfer interface, its thickness is Then we have: ① For the contact boundary between molten steel and copper mold node temperature as follows: ； ② The spatial node advances to the boundary of the molten steel-atmosphere interface. Regarding the boundary of the molten steel-atmosphere interface... node temperature as follows: ； in: For time difference; For the first The heat flow at the top of the steel droplet at each time point; For the first The first time point and the first Total heat flow at each spatial node; for Specific heat capacity of steel samples under temperature conditions; for Density of steel samples under temperature conditions; , This indicates that the first spatial node is in the [location missing]. The temperature at the time point is determined by the _ ... Temperature at each time point Calculated; Subscript Represents the corresponding spatial node and ; and These represent the node spatial scale and the total number of nodes, respectively. For the first Total heat flow at the steel-copper mold contact boundary at each time point; for Specific heat capacity of steel samples under temperature conditions; for Density of steel samples under temperature conditions; The value is the thermal conductivity of the steel sample.

2. The method for determining the interfacial thermal resistance during the solidification process of molten steel according to claim 1, characterized in that, The experiment using the molten droplet solidification apparatus specifically involves: The steel sample is placed in a quartz tube with a small hole at the bottom and heated to melt by an induction coil; the temperature of the molten steel is measured by a thermometer, and a proportional-integral-derivative controller receives the temperature signal and controls the temperature by adjusting the power of the induction coil. When the target temperature is reached, molten steel is sprayed out by introducing a pulse of nitrogen or argon gas, the same atmosphere controlled during the experiment, into the tube. The molten steel falls onto the copper mold and the droplets fall 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 data.

3. The method for determining the interfacial thermal resistance during the solidification process of molten steel according to claim 1, characterized in that, In the second step: Input and The heat flow at the interface between the steel sample and the copper substrate was calculated using 1D-IHCP. and the surface temperature of the copper mold .

4. The method for determining the interfacial thermal resistance during the solidification process of molten steel according to claim 3, characterized in that, In the third step: In a one-dimensional heat transfer model, heat conduction in steel follows Fourier's law of thermal conductivity: ； in: This represents the specific heat capacity of the steel sample. The density of the steel sample; For temperature; For time; For location; 0 ~ A one-dimensional computational domain within the range; The initial temperature conditions are as follows: ； The heat flow from the bottom of the steel droplet is equal to the heat flow into the copper mold calculated from the experimental data, as shown in the following equation: ； Considering thermal radiation and natural convection heat transfer from the atmosphere, the heat flux density at the top surface of the sample is expressed as follows: ； in: It is the total emissivity of the steel sample; It is the Boltzmann constant; It is the natural convection heat transfer coefficient; The temperature at the top of the steel droplet; It is the heat flow at the top of the steel droplet; The heat transfer process inside molten steel is calculated using the finite difference method, with the flow into the first... Total heat flow at each spatial node Calculate using the following formula: ； in: For the first The spatial node flows into the first Heat flux density of each spatial node; For the first The spatial node flows into the first Heat flux density of each spatial node; For the first Temperature of each spatial node; Introducing the enthalpy change during solidification, according to the law of conservation of energy, the first... The spatial node and the first enthalpy at each time point Calculate using the following formula: ； in: It is the cross-sectional area perpendicular to the heat transfer direction; Enthalpy per unit volume Applying one-dimensional control volume Then the heat conduction equation becomes the following: ； in: For the first The spatial node and the first Enthalpy per unit volume at a given time point; Expression for the relationship between enthalpy and temperature It can be expressed as follows: ； in: Indicates reference temperature; express Temperature at a given time; Expressing the specific heat capacity using the equivalent specific heat capacity at each temperature during the solidification process, and considering the density change, we have the following expression: ； ； like and Then we have the following expression: ； Then we get: ； Based on the above formula, we obtain the... The temperature at the time point is used as the _ ... The temperature at each time point is described by the following formula: 。

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