Industrial digital twin heating furnace mechanism model verification method and system

Abstract

The invention provides a heating furnace mechanism model verification method and system in industrial digital twin, and the method comprises the steps: S1, constructing a heating furnace two-dimensional unstable billet heat conduction model, and determining the initial conditions and boundary conditions of the heating furnace two-dimensional unstable billet heat conduction model; s2, based on the constructed heating furnace two-dimensional unstable billet heat conduction model and initial conditions and boundary conditions thereof, establishing an energy balance equation set by using a ternary method; wherein the energy balance equation set comprises a steel billet section energy balance equation, a furnace gas section energy balance equation and a furnace wall section energy balance equation; s3, determining a billet computational domain, and dividing billet computational domain grids; constructing a discrete billet internal heat conduction equation based on the divided billet computational domain grids; and S4, coupling and solving the internal heat conduction equation and the energy balance equation set of the discrete steel billet to obtain the steel billet temperature and the furnace gas temperature.

Description

Technical Field

[0001] The present invention relates to the technical field of heating furnaces, and specifically, to a method and system for verifying the mechanism model of a heating furnace in industrial digital twins. Background Art

[0002] In the iron and steel industry, the heating furnace is a key equipment in the rolling production line, and its function is to heat the billet to the target temperature to meet the requirements of subsequent rolling processes. The heating efficiency, temperature uniformity, and energy consumption level of the heating furnace directly affect the product quality and production cost. Therefore, establishing an accurate mechanism model of the heating furnace and verifying it is of great significance for optimizing the heating process, improving energy efficiency, and realizing intelligent control.

[0003] In recent years, digital twin technology has been increasingly widely used in the industrial field. Its core lies in constructing a high-fidelity mechanism model and fusing it with real-time data to achieve dynamic optimization and prediction. However, there are still deficiencies in the verification of the mechanism model of existing heating furnace digital twins, especially problems such as accurate modeling of the unsteady heat transfer process, coupled solution of multi-region energy balance, and reasonable setting of boundary conditions have not been effectively solved.

[0004] Therefore, there is an urgent need for a high-precision and high-efficiency method for verifying the mechanism model of a heating furnace, which can comprehensively consider the heat transfer coupling relationship between the billet, furnace gas, and furnace wall, and establish an energy balance equation based on reasonable boundary conditions (such as the third-kind boundary condition) to improve the accuracy of the digital twin model and provide a reliable theoretical support for the intelligent optimization control of the heating furnace.

[0005] Patent document CN118052087A (application number: 202410455626.5) discloses a method for synchronously constructing online and offline digital twin models based on three-dimensional heat transfer, belonging to the field of heat transfer model construction, including the following steps: S1, dividing the heating furnace into multiple furnace sections, and setting that each furnace section includes multiple billets; S2, establishing a three-dimensional radiation heat transfer model for each furnace section and a three-dimensional transient heat conduction model for each billet; S3, collecting heating furnace parameters; S4, using the three-dimensional transient heat conduction model to calculate the three-dimensional temperature field of each billet in the furnace section in parallel; S5, updating the simulation time, judging whether to interrupt. If so, output the three-dimensional temperature field results of each billet, and if not, return to step S3 for iteration until interrupted, and output the three-dimensional temperature field results. Summary of the Invention

[0006] Aiming at the deficiencies in the prior art, the purpose of the present invention is to provide a method and system for verifying the mechanism model of a heating furnace in industrial digital twins.

[0007] According to a method for verifying the mechanism model of a heating furnace in industrial digital twins provided by the present invention, it includes: Step S1: Construct a two-dimensional unsteady billet heat conduction model for the reheating furnace, and determine the initial conditions and boundary conditions of the two-dimensional unsteady billet heat conduction model for the reheating furnace; Step S2: Based on the constructed two-dimensional unsteady billet heat conduction model for the reheating furnace and its initial conditions and boundary conditions, establish an energy balance equation set by using the three-element method; among them, the energy balance equation set includes: the energy balance equation for the billet section, the energy balance equation for the flue gas section, and the energy balance equation for the furnace wall section; Step S3: Determine the billet calculation domain and divide the grid of the billet calculation domain; construct a discrete internal heat conduction equation for the billet based on the divided grid of the billet calculation domain; Step S4: Coupled solve the discrete internal heat conduction equation for the billet and the energy balance equation set to obtain the billet temperature and the flue gas temperature.

[0008] Preferably, the two-dimensional unsteady billet heat conduction model for the reheating furnace includes: +

[0009] Among them, is the density of the billet; is the specific heat capacity of the billet; is the thermal conductivity of the billet; The initial conditions of the two-dimensional unsteady billet heat conduction model for the reheating furnace include: billet size, physical properties, sizes of each section of the reheating furnace, and the initial furnace temperature; The boundary condition of the two-dimensional unsteady billet heat conduction model for the reheating furnace is the third-kind boundary condition.

[0010] Preferably, the energy balance equation for the billet section includes: radiative heat transfer between the billet and the flue gas and the furnace wall, convective heat transfer between the billet and the flue gas, and internal heat conduction of the billet; the energy balance equation is as follows:

[0011] In the formula, , are respectively the total exchange areas from the gas zone to the billet surface zone and from the furnace wall surface zone to the billet surface zone in the model section, is the convective heat transfer coefficient between the billet and the flue gas in the model section, is the convective heat transfer area between the billet and the flue gas in the model section, is the internal heat conduction heat flux of the billet in the model section; represents the Stefan-Boltzmann constant; The energy balance equation for the flue gas section includes: radiative heat transfer term, combustion and heat source term, flue gas flow term, and convective loss term; the energy balance equation formula is as follows:

[0012] In the formula, , , are respectively the temperatures of the billet in the model section, the furnace gas and the furnace wall, are respectively the total exchange areas from the surface area of the billet in the model section to the gas area and from the surface area of the furnace wall to the gas area;

[0013] In the formula, is the heat of fuel reaction, is the fuel quantity in the model section, and the lower calorific value of the supplied fuel;

[0014] In the formula, is the fuel quantity in the model section, is the actual air consumption, is the specific heat of air, is the air preheating temperature;

[0015] In the formula, is the fuel quantity in the model section, is the specific heat of the gas, is the gas preheating temperature;

[0016] In the formula, is the fuel quantity in the model section, is the flue gas volume generated per unit fuel, is the specific heat capacity of the flue gas in the model section, is the temperature of the flue gas leaving the regenerator and entering the heating furnace;

[0017] In the formula, , are respectively the convective heat transfer coefficients between the billet and the furnace gas, and between the furnace wall and the furnace gas in the model section, , are respectively the convective heat transfer areas between the billet and the furnace gas, and between the furnace wall and the furnace gas in the model section, , , The temperatures of the model-section billet, furnace gas, and furnace wall are respectively; the model-section billet, furnace gas, and furnace wall; The energy balance equation of the furnace wall section includes: radiative heat transfer between the furnace wall and the furnace gas and the billet, convective heat transfer between the inner surface of the furnace wall and the furnace gas, heat conduction from the inner surface to the outer surface of the furnace wall, and convective heat transfer between the outer surface of the furnace wall and the environment; the energy balance equation of the furnace wall section is as follows: + +

[0018] In the formula, , The overall exchange areas from the gas zone of the model section to the furnace wall surface zone and from the billet surface zone to the furnace wall surface zone are respectively; the overall exchange areas from the gas zone of the model section to the furnace wall surface zone and from the billet surface zone to the furnace wall surface zone; is the convective heat transfer coefficient between the furnace wall and the furnace gas in the model section; is the heat transfer area between the inner furnace wall and the furnace gas in the model section;

[0019] In the formula, is the heat flux of heat conduction from the inner surface to the outer surface of the furnace wall and the heat flux of convective heat transfer between the outer surface and the environment, is the ambient temperature, is the convective heat transfer coefficient between the outer surface of the furnace wall and the environment, is the outer surface area of the furnace wall, is the thickness of the furnace wall, is the thermal conductivity of the furnace wall.

[0020] Preferably, the step S3 includes: Step S3.1: Select half of the interface in the length and thickness directions of the billet as the calculation domain; Step S3.2: Divide the billet calculation domain grid by the finite volume method, and the billet calculation domain grid is divided into the non-corner points at the center of the control volume block and the corner points at the center of the control volume block; Step S3.3: Construct the discrete equations at the non-corner points at the center of the control volume block and the discrete equations at the corner points at the center of the control volume block; construct the internal heat conduction equation of the discrete slab based on the constructed discrete equations at the non-corner points at the center of the control volume block and the discrete equations at the corner points at the center of the control volume block.

[0021] Preferably, the step S4 includes: assuming an initial temperature field of the heating furnace, including: the initial furnace gas temperature, the initial furnace wall temperature, and the initial billet temperature; substituting the initial temperature field of the heating furnace into the energy balance equation of the furnace gas section and the energy balance equation of the furnace wall section successively to obtain the furnace gas temperature and the furnace wall temperature of the next cycle; substituting the calculated furnace gas temperature and furnace wall temperature into the billet energy equation to obtain the billet heat flux density, and then substituting it into the discrete billet internal heat conduction equation to obtain the billet temperature of the next cycle; determining whether the current billet temperature meets the preset requirements. When the preset requirements are not met, the initial temperature field of the heating furnace is reset, and the execution is triggered repeatedly until the billet temperature meets the preset requirements, and the current billet temperature and furnace gas temperature are obtained.

[0022] Preferably, the method further includes: comparing the obtained current billet temperature and furnace gas temperature with the actual heating data of the steel mill heating furnace, and modifying and optimizing the billet heating model according to the comparison result to obtain a modified billet heating model; The billet heating model includes: a discrete billet internal heat conduction equation and an energy balance equation set; The modification and optimization of the billet heating model include: iteratively updating the billet heating model by introducing a parameter optimization and boundary condition correction mechanism.

[0023] According to a heating furnace mechanism model verification system in industrial digital twin provided by the present invention, it includes: Module M1: constructing a two-dimensional unsteady billet heat conduction model of the heating furnace, and determining the initial conditions and boundary conditions of the two-dimensional unsteady billet heat conduction model of the heating furnace; Module M2: based on the constructed two-dimensional unsteady billet heat conduction model of the heating furnace and its initial conditions and boundary conditions, establishing an energy balance equation set by using the three-element method; wherein, the energy balance equation set includes: a billet section energy balance equation, a furnace gas section energy balance equation, and a furnace wall section energy balance equation; Module M3: determining the billet calculation domain, dividing the billet calculation domain grid; constructing a discrete billet internal heat conduction equation based on the divided billet calculation domain grid; Module M4: coupling and solving the discrete billet internal heat conduction equation and the energy balance equation set to obtain the billet temperature and the furnace gas temperature.

[0024] Preferably, the billet section energy balance equation includes: including the radiative heat transfer between the billet and the furnace gas and the furnace wall, the convective heat transfer between the billet and the furnace gas, and the internal heat conduction of the billet; the energy balance equation is as follows:

[0025] In the formula, , are respectively the total exchange areas from the gas zone to the billet surface zone and from the furnace wall surface zone to the billet surface zone of the model section, is the convective heat transfer coefficient between the billet in the model section and the furnace gas, is the convective heat transfer area between the billet in the model section and the furnace gas, is the internal heat conduction heat flux of the billet in the model section; represents the Stefan - Boltzmann constant; The energy balance equation of the furnace gas section includes: radiative heat transfer term, combustion and heat source term, flue gas flow term, convective loss term; The energy balance equation formula is as follows:

[0026] In the formula, , , are respectively the temperatures of the billet in the model section, furnace gas and furnace wall, are respectively the total exchange area from the surface area of the billet in the model section to the gas area, total exchange area from the surface area of the furnace wall to the gas area;

[0027] In the formula, is the heat of fuel reaction, is the fuel quantity in the model section, lower calorific value of the supplied fuel;

[0028] In the formula, is the fuel quantity in the model section, is the actual air consumption, is the specific heat of air, is the air preheating temperature;

[0029] In the formula, is the fuel quantity in the model section, is the specific heat of gas, is the gas preheating temperature;

[0030] In the formula, is the fuel quantity in the model section, is the flue gas volume generated per unit fuel, is the specific heat capacity of the flue gas in the model section, is the temperature of the flue gas leaving the regenerator and entering the heating furnace;

[0031] In the formula, , are respectively the convective heat transfer coefficients between the billet and the flue gas, and between the furnace wall and the flue gas in the model section; , are respectively the convective heat transfer areas between the billet and the flue gas, and between the furnace wall and the flue gas in the model section; , , are respectively the temperatures of the billet, the flue gas and the furnace wall in the model section; The energy balance equation of the furnace wall section includes: radiative heat transfer between the furnace wall and the flue gas, and between the billet; convective heat transfer between the inner surface of the furnace wall and the flue gas; heat conduction from the inner surface to the outer surface of the furnace wall; and convective heat transfer between the outer surface of the furnace wall and the environment. The energy balance equation of the furnace wall section is as follows: + +

[0032] In the formula, , are respectively the total exchange areas from the gas zone to the furnace wall surface zone, and from the billet surface zone to the furnace wall surface zone in the model section; is the convective heat transfer coefficient between the furnace wall and the flue gas in the model section; is the heat transfer area between the inner furnace wall and the flue gas in the model section;

[0033] In the formula, is the heat flux of heat conduction from the inner surface to the outer surface of the furnace wall and the heat flux of convective heat transfer between the outer surface and the environment; is the environmental temperature; is the convective heat transfer coefficient between the outer surface of the furnace wall and the environment; is the outer surface area of the furnace wall; is the thickness of the furnace wall; is the thermal conductivity of the furnace wall.

[0034] Preferably, the module M3 includes: Module M3.1: Select half of the interfaces in the length and thickness directions of the billet as the calculation domain; Module M3.2: Divide the grid of the billet calculation domain by the finite volume method. The grid of the billet calculation domain is divided into the non-corner points at the center of the control volume block and the corner points at the center of the control volume block; Module M3.3: Construct the discrete equations at the non-corner points of the center of the control volume block and the discrete equations at the corner points of the center of the control volume block; construct the internal heat conduction equation of the discrete slab based on the constructed discrete equations at the non-corner points of the center of the control volume block and the discrete equations at the corner points of the center of the control volume block.

[0035] Preferably, the module M4 includes: assuming the initial temperature field of the reheating furnace, including: the initial flue gas temperature, the initial furnace wall temperature, and the initial billet temperature; substituting the initial temperature field of the reheating furnace into the energy balance equation of the flue gas section and the energy balance equation of the furnace wall section successively to obtain the flue gas temperature and the furnace wall temperature of the next cycle; substituting the calculated flue gas temperature and furnace wall temperature into the billet section energy equation to obtain the billet heat flux density, and then substituting it into the discrete internal heat conduction equation of the billet to obtain the billet temperature of the next cycle; determining whether the current billet temperature meets the preset requirements. When the preset requirements are not met, reset the initial temperature field of the reheating furnace, trigger and execute repeatedly until the billet temperature meets the preset requirements, and obtain the current billet temperature and flue gas temperature.

[0036] Compared with the prior art, the present invention has the following beneficial effects: 1. The present invention realizes the rapid calculation of the slab radiation conditions in the furnace, so as to quickly obtain the slab temperature field and the classical position temperature data, and completes the establishment of the coupled heat transfer model of the heating furnace combustion field and the billet; thus deeply exploring the temperature field distribution in the heating furnace and its influence on the coupled heat transfer of the billet, improving the billet heating quality and economic benefits; 2. There are many influencing factors in the actual production process of the heating furnace. Working conditions such as complex and changeable heating processes, aging of model parameters, cold-hot mixed charging, and roll change and waiting for rolling will all interfere with the accurate tracking and control of the steel temperature; the present invention realizes the intelligent and accurate control of the billet heating process, which is an important link for energy saving and consumption reduction in the production of heating furnaces. Description of the Drawings

[0037] By reading the detailed description of the non-restrictive embodiments with reference to the following drawings, other features, objects, and advantages of the present invention will become more obvious: Figure 1 It is a schematic diagram of the billet calculation domain.

[0038] Figures 2a to 2b It is a schematic diagram of the discrete control volume grid.

[0039] Figure 3 It is a schematic diagram of the comprehensive heat transfer relationship in the furnace.

[0040] Figure 4 It is a flow chart of the coupled solution of the internal heat transfer equation of the slab and the ternary method energy balance equation set.

[0041] Figure 5 It is a schematic diagram of the interaction interface.

[0042] Figure 6 This is the input-output process of the mechanism model. Specific implementation mode

[0043] The present invention will be described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but do not limit the present invention in any form. It should be noted that those of ordinary skill in the art can make several changes and improvements without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0044] Embodiment 1 A method for verifying the heating furnace mechanism model in industrial digital twins provided by the present invention, as Figure 6 shown, includes: Step 1: Establish a two-dimensional unsteady billet heat conduction model of the heating furnace, and determine the initial conditions and boundary conditions of the heat conduction model; Among them, the two-dimensional unsteady billet heat conduction model of the heating furnace includes: +

[0045] In the formula: is the density of the billet; is the specific heat capacity of the billet; is the thermal conductivity of the billet.

[0046] The total absorption rate method is adopted for radiative heat transfer. The total heat absorption rate method is one of the simplest calculation methods for the furnace heat transfer process. For an online heat transfer model that requires calculation speed, the total heat absorption rate is an effective processing method. Conducting in-depth research on the refined distribution and application of the total heat absorption rate of the furnace chamber is of great value for improving the accuracy of steel temperature tracking and control.

[0047] In practical applications, combined with some temperature parameters that are easily measured through experiments, such as the temperature distribution of the furnace thermocouples, the position change and heating process of the billet in the furnace, etc., the distribution law of the total heat absorption rate deduced theoretically can be corrected, and the convection term can be ignored at the same time, so as to obtain a total heat absorption rate based on the furnace temperature that is more suitable for the actual situation of the furnace .

[0048]

[0049] In the formula: represents the radiative heat flux density on the billet surface; is the Stefan-Boltzmann constant; represents the corrected total heat absorption rate; represents the furnace gas temperature; represents the billet surface temperature.

[0050] The initial conditions are obtained from the database, including the billet size, physical properties, dimensions of each section of the reheating furnace, initial furnace temperature, etc.

[0051] The initial boundary conditions include: the common third-kind boundary conditions.

[0052] Step 2: Determine the billet calculation domain and divide the grid of the billet calculation domain; discretize the internal heat conduction equation of the slab using the finite volume method; Specifically, the said Step 2 includes: Step 2.1: For the billet calculation domain, in order to minimize the calculation cost while ensuring the key temperature characteristics of the billet, choose half of the cross-section in the length and thickness directions of the billet as the calculation domain, as Figure 1 shown; Step 2.2: Divide the grid of the calculation domain. Use the finite volume method to divide the grid. The grid is divided into the non-corner points at the center of the control volume block and the corner points at the center of the control volume block, as Figures 2a to 2b shown; The finite volume method is a numerical method based on the integral form of the conservation equation. Its core idea is to discretize the conservation law. By dividing the calculation region into control volumes (grid cells) and integrating the conservation equation for each cell, the heat conduction equation of the billet is discretized using the finite volume method in the model, and the continuous billet model is discretized. The finite volume method is chosen because of its good convergence and high accuracy, and it can solve to obtain the slab temperature data. The discretization of the heat conduction equation is also divided into the non-corner points at the center of the control volume block and the corner points at the center of the control volume block. The following is the specific form of the finite volume method: Discrete equation at the non-corner points at the center of the control volume block:

[0053]

[0054] Discrete equation at the corner points at the center of the control volume block:

[0055]

[0056] In the formula: 、 are the step lengths in the direction respectively; 、 、 and are the temperatures at the discrete points point, point, point and point respectively; 、 and are the discrete points point, Point and the thermal conductivity of the point; 、 is the heat flux density transferred from the outside to the billet. Step 3: Use the three - element method to establish an energy balance equation system, which is divided into the energy balance equation of the billet section, the energy balance equation of the flue gas section, and the energy balance equation of the furnace wall section.

[0057] Specifically, the said Step 3 includes: The three - element model is a simplification based on the section method model. It is a mechanism model established based on laws such as energy balance equations, heat and mass transfer, and energy flow. When calculating, it ignores the influence of other model sections on this section. Therefore, the temperature of each part within the model section is only affected by the temperature of other parts within the section. This simplification realizes the decoupling of the energy balance equation within the section. When solving, only the three temperatures within each model section need to be iteratively solved respectively. Therefore, the three - element model has a great advantage in calculation speed compared with the section method model. So, on the premise of meeting the accuracy, the three - element model can be applied to the on - line control of the heating furnace. The schematic diagram of the three - element model is as Figure 3 shown.

[0058] The following is the specific solution method for the three energy balance equations.

[0059] Energy balance equation of the flue gas section The energy balance equation of the flue gas section of the heating furnace consists of a radiation heat transfer term, a combustion and heat source term, a flue gas flow term, and a convective loss term. The formula of the energy balance equation is as follows:

[0060] In the formula, , , are the temperatures of the billet, flue gas, and furnace wall of the model section respectively, are the total exchange areas from the billet surface area to the gas area and from the furnace wall surface area to the gas area of the model section respectively.

[0061]

[0062] In the formula, is the heat of fuel reaction, is the fuel quantity of the model section, is the lower calorific value of the fuel supplied.

[0063]

[0064] In the formula, is the fuel quantity of the model section, is the actual air consumption, is the specific heat of air, is the preheating temperature of air.

[0065]

[0066] In the formula, is the fuel quantity of the model section, is the specific heat of gas, is the preheating temperature of gas.

[0067]

[0068] In the formula, is the fuel quantity of the model section, is the flue gas quantity generated by unit fuel, is the specific heat capacity of the flue gas in the model section, is the temperature of the flue gas leaving the regenerator and entering the heating furnace.

[0069]

[0070] In the formula, , are respectively the convective heat transfer coefficients between the billet and the flue gas, and between the furnace wall and the flue gas in the model section, , are respectively the convective heat transfer areas between the billet and the flue gas, and between the furnace wall and the flue gas in the model section, , , are respectively the temperatures of the billet, flue gas and furnace wall in the model section.

[0071] Energy equation of the billet section including the radiative heat transfer between the billet and the flue gas, furnace wall, the convective heat transfer between the billet and the flue gas, and the internal heat conduction of the billet. The energy balance equation is as follows:

[0072] In the formula, , are respectively the total exchange areas from the gas zone to the billet surface zone and from the furnace wall surface zone to the billet surface zone in the model section, is the convective heat transfer coefficient between the billet and the flue gas in the model section, is the convective heat transfer area between the billet and the flue gas in the model section, is the For the internal heat conduction heat flux of the model section billet, the finite volume method is used to solve it in this paper.

[0073] Energy equation of the furnace wall section It includes the radiative heat transfer between the furnace wall, the furnace gas and the billet, the convective heat transfer between the inner surface of the furnace wall and the furnace gas, the heat conduction from the inner surface to the outer surface of the furnace wall, and the convective heat transfer between the outer surface of the furnace wall and the environment. The energy balance equation of the furnace wall section is as follows: + +

[0074] In the formula, , are the total exchange areas from the gas zone to the furnace wall surface zone and from the billet surface zone to the furnace wall surface zone in the model section respectively, is the convective heat transfer coefficient between the furnace wall and the furnace gas in the model section, is the heat transfer area between the inner furnace wall and the furnace gas in the

[0075]

[0076] In the formula, is the heat conduction heat flux from the inner surface to the outer surface of the furnace wall and the convective heat transfer heat flux between the outer surface and the environment, is the ambient temperature, is the convective heat transfer coefficient between the outer surface of the furnace wall and the environment, is the outer surface area of the furnace wall, is the thickness of the furnace wall, is the thermal conductivity of the furnace wall.

[0077] Step 4: Coupled solution of the internal heat transfer equation of the slab and the energy balance equation set of the three - element method.

[0078] As Figure 4 shown, the discrete equation in Step 2 is coupled with the energy balance equation set of the three - element method in Step 3. The furnace gas temperature of each heating section of the heating furnace is obtained by the three - element method, and the furnace gas temperature distribution of the heating furnace is obtained by linear interpolation. The furnace gas temperature and the internal temperature field of the billet are coupled by the overall absorption method in Step 1.

[0079] As a means of solving the energy balance of the heating furnace, the three - element method separately considers three main energy terms, namely fuel input, slab heat absorption, and heat carried away by flue gas in the heating section. By establishing an energy conservation equation, the average flue gas temperature in each heating section is iteratively solved. This method has the advantages of high calculation efficiency and clear physical meaning, and is applicable to large - scale modeling of industrial heating furnaces. Since the three - element method can essentially only obtain the sectional average temperature distribution in the heating section, it is necessary to further adopt a linear interpolation method to establish a continuous flue gas temperature field between sections, so as to obtain the accurate boundary thermal environment at the position of the slab.

[0080] To achieve heat coupling between the slab and the flue gas, the overall absorptivity method is used to model the surface radiation heat transfer. Based on the theory of radiative heat conduction, this method comprehensively considers thermal radiation parameters such as the view factor, absorption coefficient, and emissivity between the slab surface and the furnace wall and flue gas, simplifies the complex radiative heat transfer process in space into the form of an overall heat transfer coefficient, enabling the flue gas temperature to be directly related to the heat flux on the slab surface. Finally, the boundary condition of the slab heat conduction equation is included in the slab energy balance equation. By solving the slab energy balance equation to obtain the boundary condition, and then substituting the obtained boundary condition into the slab heat conduction equation in step 2, the slab temperature is obtained. It can accurately predict the temperature evolution process of the slab during heating, providing theoretical support for temperature control strategies and heating regime optimization.

[0081] Step 5: Write it in the form of computer source code using software.

[0082] Write the slab internal heat transfer equation and the three - element method energy balance equations in step 4 in the form of computer source code using Python for trial calculation. Develop an interactive interface for the source code program. The interface can display temperature contour maps and typical position curve graphs, as Figure 5 shown. In the upper left corner of the figure is the temperature contour map of the slab about to be discharged from the furnace. In the upper right corner is the temperature change graph of the typical position of this slab in the furnace. The bar graph below shows the average temperature and the highest temperature distribution of all slabs in the furnace at the current moment.

[0083] Step 6: Compare the trial calculation data with the actual heating data of the steel mill heating furnace, modify and optimize the slab heating program to ensure the accuracy of the slab heating model.

[0084] If a large deviation is found between the simulation results and the on - site data during the comparison process, it is necessary to analyze the error sources, which may include inaccurate setting of model boundary conditions, unreasonable values of thermal parameters, or uncertainties in on - site operating conditions, etc. To further improve the prediction accuracy and adaptability of the model, the model is iteratively updated by introducing a parameter optimization and boundary condition correction mechanism. Compare the calculated slab discharge temperature, flue gas temperature in each heating section, and fuel quantity of the heating furnace with the on - site data, and then by modifying boundary conditions such as And certain thermal parameter optimization programs to ensure the accuracy of the billet heating model.

[0085] In this embodiment, by comparing the on-site data with the simulation data, the heat transfer boundary conditions are corrected. , and the specific operation process is as follows: 1) First, obtain the heat transfer parameters according to manual experience , and perform steel temperature calculation.

[0086] 2) Accumulate a certain number of calculated tapping temperatures of the steel billet and the corresponding measured tapping temperatures of the billet, minimize the square of the difference between the two, and obtain the overall heat absorption rate suitable for this heating furnace. ; 3) Write the steel billet temperature field equation in matrix form:

[0087] Among them, The temperature of the steel billet at the next time step, is the temperature of the steel billet at the current time step, , are all integrated coefficient matrices.

[0088] Then, the predicted steel temperature = is derived, and the heat transfer parameters are written in the form of a column matrix .

[0089] The actually measured temperature of the steel billet , and the residual function is derived:

[0090] Using the least squares method, after minimizing the residual function, X is obtained, that is, the overall heat absorption rate suitable for this heating furnace ; Then, the newly obtained heat transfer parameters are used as the initial values in step 1), and iterative calculations are continued to obtain a more accurate steel temperature calculation model.

[0091] The present invention also provides a verification system for the heating furnace mechanism model in industrial digital twin. The verification system for the heating furnace mechanism model in industrial digital twin can be implemented by executing the process steps of the verification method for the heating furnace mechanism model in industrial digital twin, that is, those skilled in the art can understand the verification method for the heating furnace mechanism model in industrial digital twin as the preferred implementation manner of the verification system for the heating furnace mechanism model in industrial digital twin.

[0092] Those skilled in the art know that, in addition to implementing the systems, devices, and their respective modules provided by the present invention in the form of pure computer-readable program code, the method steps can be logically programmed to enable the systems, devices, and their respective modules provided by the present invention to be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers, etc. to achieve the same program. Therefore, the systems, devices, and their respective modules provided by the present invention can be considered as a kind of hardware components, and the modules included therein for implementing various programs can also be regarded as the structures within the hardware components; the modules for implementing various functions can also be regarded as either software programs for implementing methods or structures within hardware components.

[0093] The specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. Without conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A method for verifying the mechanism model of a reheating furnace in industrial digital twins, characterized in that, Including: Step S1: Construct a two-dimensional unsteady billet heat conduction model for the reheating furnace, and determine the initial conditions and boundary conditions of the two-dimensional unsteady billet heat conduction model for the reheating furnace; Step S2: Based on the constructed two-dimensional unsteady billet heat conduction model for the reheating furnace and its initial conditions and boundary conditions, establish an energy balance equation set using the three-element method; among them, the energy balance equation set includes: the energy balance equation for the billet section, the energy balance equation for the flue gas section, and the energy balance equation for the furnace wall section; Step S3: Determine the billet calculation domain, and divide the grid of the billet calculation domain; based on the divided grid of the billet calculation domain, construct a discrete internal heat conduction equation for the billet; Step S4: Coupledly solve the discrete internal heat conduction equation for the billet and the energy balance equation set to obtain the billet temperature and the flue gas temperature.

2. The method for verifying the heating furnace mechanism model in industrial digital twins according to claim 1, characterized in that The two-dimensional unsteady billet heat conduction model for the reheating furnace includes: + Among them, is the density of the steel billet; is the specific heat capacity of the steel billet; is the thermal conductivity of the steel billet; The initial conditions of the two-dimensional unsteady billet heat conduction model for the reheating furnace include: billet dimensions, physical properties, dimensions of each section of the reheating furnace, and the initial furnace temperature; The boundary condition of the two-dimensional unsteady billet heat conduction model for the reheating furnace is the third-kind boundary condition.

3. The method for verifying the heating furnace mechanism model in industrial digital twins according to claim 1, characterized in that, The energy balance equation for the billet section includes: the radiative heat transfer between the billet and the flue gas and the furnace wall, the convective heat transfer between the billet and the flue gas, and the internal heat conduction of the billet; the energy balance equation is as follows: In the formula, , are respectively the total exchange areas from the gas zone to the billet surface zone and from the furnace wall surface zone to the billet surface zone in the model section, is the convective heat transfer coefficient between the billet and the furnace gas in the model section, is the convective heat transfer area between the billet and the furnace gas in the model section, is the internal heat conduction heat flux of the billet in the model section; represents the Stefan - Boltzmann constant; The energy balance equation for the flue gas section includes: radiative heat transfer terms, combustion and heat source terms, flue gas flow terms, and convective loss terms; the formula of the energy balance equation is as follows: In the formula, , , are respectively the temperatures of the billet in the model section, the furnace gas, and the furnace wall, are respectively the total exchange areas from the surface area of the billet in the model section to the gas area and from the surface area of the furnace wall to the gas area; In the formula, is the heat of combustion of fuel, is the fuel quantity of the model section, and the lower calorific value of the fuel fed in; In the formula, is the fuel quantity of the model section, is the actual air consumption, is the specific heat of air, is the air preheating temperature; In the formula, is the fuel quantity of the model section, is the specific heat of the gas, is the preheating temperature of the gas; In the formula, is the fuel quantity of the model section, is the flue gas quantity generated by unit fuel, is the specific heat capacity of the flue gas in the model section, is the temperature of the flue gas leaving the regenerator and entering the heating furnace; Wherein, , are respectively the convective heat transfer coefficients between the billet of the model section and the furnace gas, and between the furnace wall and the furnace gas, , are respectively the convective heat transfer areas between the billet of the model section and the furnace gas, and between the furnace wall and the furnace gas, , , are respectively the temperatures of the billet of the model section, the furnace gas and the furnace wall; The energy balance equation for the furnace wall section includes: the radiative heat transfer between the furnace wall and the flue gas and the billet, the convective heat transfer between the inner surface of the furnace wall and the flue gas, the heat conduction from the inner surface to the outer surface of the furnace wall, and the convective heat transfer between the outer surface of the furnace wall and the environment; the energy balance equation for the furnace wall section is as follows: + + Wherein, , are respectively the total exchange areas from the gas zone of the model section to the furnace wall surface zone, and from the billet surface zone to the furnace wall surface zone, is the convective heat transfer coefficient between the furnace wall and the furnace gas in the model section, is the heat transfer area between the furnace wall and the furnace gas in the model section; In the formula, is the heat conduction heat flux from the inner surface to the outer surface of the furnace wall and the convective heat transfer heat flux between the outer surface and the environment, is the environmental temperature, is the convective heat transfer coefficient between the outer surface of the furnace wall and the environment, is the outer surface area of the furnace wall, is the thickness of the furnace wall, is the thermal conductivity of the furnace wall.

4. The method for verifying the heating furnace mechanism model in industrial digital twins according to claim 1, characterized in that, The said Step S3 includes: Step S3.1: Select half of the interface in the length and thickness directions of the billet as the calculation domain; Step S3.2: Use the finite volume method to divide the grid of the billet calculation domain, and the grid of the billet calculation domain is divided into the non-corner points at the center of the control volume block and the corner points at the center of the control volume block; Step S3.3: Construct a discrete equation at the non-corner points at the center of the control volume block and a discrete equation at the corner points at the center of the control volume block; based on the constructed discrete equations at the non-corner points at the center of the control volume block and the discrete equations at the corner points at the center of the control volume block, construct a discrete internal heat conduction equation for the slab.

5. The method for verifying the heating furnace mechanism model in industrial digital twins according to claim 1, characterized in that The said Step S4 includes: Assume the initial temperature field of the reheating furnace, including: the initial flue gas temperature, the initial furnace wall temperature, and the initial billet temperature; the initial temperature field of the initial reheating furnace is successively substituted into the energy balance equation for the flue gas section and the energy balance equation for the furnace wall section to obtain the flue gas temperature and the furnace wall temperature in the next cycle; substitute the calculated flue gas temperature and furnace wall temperature into the energy equation for the billet section to obtain the billet heat flux density, and then substitute it into the discrete internal heat conduction equation for the billet to obtain the billet temperature in the next cycle; judge whether the current billet temperature meets the preset requirements, when it does not meet the preset requirements, reset the initial temperature field of the reheating furnace, repeat the trigger execution until the billet temperature meets the preset requirements, and obtain the current billet temperature and flue gas temperature.

6. The method for verifying the heating furnace mechanism model in industrial digital twins according to claim 1, wherein The method further includes: Compare the obtained current billet temperature and flue gas temperature with the actual heating data of the steel mill reheating furnace, and according to the comparison result, modify and optimize the billet heating model to obtain the modified billet heating model; The billet heating model includes: a discrete internal heat conduction equation and an energy balance equation set of the billet; The modified and optimized billet heating model includes: iteratively updating the billet heating model by introducing a parameter optimization and boundary condition correction mechanism.

7. An industrial digital twin reheating furnace mechanism model verification system, characterized in that, It includes: Module M1: Construct a two-dimensional unsteady billet heat conduction model of the heating furnace, and determine the initial conditions and boundary conditions of the two-dimensional unsteady billet heat conduction model of the heating furnace; Module M2: Based on the constructed two-dimensional unsteady billet heat conduction model of the heating furnace and its initial conditions and boundary conditions, establish an energy balance equation set by using the three-element method; among them, the energy balance equation set includes: the energy balance equation of the billet section, the energy balance equation of the flue gas section, and the energy balance equation of the furnace wall section; Module M3: Determine the billet calculation domain and divide the grid of the billet calculation domain; construct a discrete internal heat conduction equation of the billet based on the divided grid of the billet calculation domain; Module M4: Coupledly solve the discrete internal heat conduction equation of the billet and the energy balance equation set to obtain the billet temperature and the flue gas temperature.

8. The verification system for the heating furnace mechanism model in industrial digital twins according to claim 7, characterized in that, The energy balance equation of the billet section includes: the radiative heat transfer between the billet and the flue gas and the furnace wall, the convective heat transfer between the billet and the flue gas, and the internal heat conduction of the billet; the energy balance equation is as follows: In the formula, , are respectively the total exchange areas from the gas zone to the billet surface zone and from the furnace wall surface zone to the billet surface zone in the model section, is the convective heat transfer coefficient between the billet and the furnace gas in the model section, is the convective heat transfer area between the billet and the furnace gas in the model section, is the internal heat conduction heat flux of the billet in the model section; represents the Stefan - Boltzmann constant; The energy balance equation of the flue gas section includes: a radiative heat transfer term, a combustion and heat source term, a flue gas flow term, and a convective loss term; the formula of the energy balance equation is as follows: In the formula, , , are respectively the temperatures of the billet in the model section, the furnace gas and the furnace wall, are respectively the total exchange areas from the surface area of the billet in the model section to the gas area and from the surface area of the furnace wall to the gas area; In the formula, is the fuel reaction heat, is the fuel quantity of the model section, and is the net calorific value of the supplied fuel; In the formula, is the fuel quantity of the model section, is the actual air consumption, is the specific heat of air, is the air preheating temperature; In the formula, is the fuel quantity of the model section, is the specific heat of the gas, is the preheating temperature of the gas; Wherein, is the fuel quantity of the model section, is the flue gas quantity generated by unit fuel, is the specific heat capacity of the flue gas in the model section, is the temperature of the flue gas leaving the regenerator and entering the heating furnace; In the formula, , are respectively the convective heat transfer coefficients between the billet of the model section and the furnace gas, and between the furnace wall and the furnace gas, , are respectively the convective heat transfer areas between the billet of the model section and the furnace gas, and between the furnace wall and the furnace gas, , , are respectively the temperatures of the billet of the model section, the furnace gas and the furnace wall; The energy balance equation of the furnace wall section includes: the radiative heat transfer between the furnace wall and the flue gas and the billet, the convective heat transfer between the inner surface of the furnace wall and the flue gas, the heat conduction from the inner surface to the outer surface of the furnace wall, and the convective heat transfer between the outer surface of the furnace wall and the environment; the energy balance equation of the furnace wall section is as follows: + + In the formula, , are respectively the total exchange areas from the gas zone of the model section to the furnace wall surface zone and from the billet surface zone to the furnace wall surface zone, is the convective heat transfer coefficient between the furnace wall and the furnace gas in the model section, is the heat transfer area between the furnace wall and the furnace gas in the model section; In the formula, is the heat conduction heat flux from the inner surface to the outer surface of the furnace wall and the convective heat transfer heat flux between the outer surface and the environment, is the ambient temperature, is the convective heat transfer coefficient between the outer surface of the furnace wall and the environment, is the outer surface area of the furnace wall, is the thickness of the furnace wall, is the thermal conductivity of the furnace wall.

9. The verification system for the heating furnace mechanism model in industrial digital twins according to claim 7, wherein, The module M3 includes: Module M3.1: Select half of the interfaces in the length and thickness directions of the billet as the calculation domain; Module M3.2: Divide the grid of the billet calculation domain by using the finite volume method, and the grid of the billet calculation domain is divided into the non-corner points at the center of the control volume block and the corner points at the center of the control volume block; Module M3.3: Construct a discrete equation at the non-corner points at the center of the control volume block and a discrete equation at the corner points at the center of the control volume block; construct a discrete internal heat conduction equation of the slab based on the constructed discrete equation at the non-corner points at the center of the control volume block and the discrete equation at the corner points at the center of the control volume block.

10. The verification system for the heating furnace mechanism model in industrial digital twins according to claim 7, wherein The module M4 includes: assuming the initial temperature field of the heating furnace, including: the initial flue gas temperature, the initial furnace wall temperature, and the initial billet temperature; substituting the initial temperature field of the initial heating furnace into the energy balance equation of the flue gas section and the energy balance equation of the furnace wall section in sequence to obtain the flue gas temperature and the furnace wall temperature of the next cycle; substituting the calculated flue gas temperature and furnace wall temperature into the energy equation of the billet section to obtain the billet heat flux density, and then substituting it into the discrete internal heat conduction equation of the billet to obtain the billet temperature of the next cycle; judge whether the current billet temperature meets the preset requirements, when it does not meet the preset requirements, reset the initial temperature field of the heating furnace, repeat the trigger execution until the billet temperature meets the preset requirements, and obtain the current billet temperature and the flue gas temperature.

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