A Modeling Method for the Two-Dimensional Temperature Field of a Unidirectionally Heated Round Steel

Abstract

The present invention belongs to the technical field of intelligent control in the production process of billet heating, and discloses a modeling method for a two-dimensional temperature field model of unidirectionally heated round steel. By calculating the temperature field of the cylindrical billet in the heating furnace in real time, the core temperature of the billet is determined, and the air-fuel ratio of each heating section in the heating furnace is adjusted according to the calculation results, so as to save the consumption of gas while meeting the requirements of the production process for billet heating.

Description

Technical Field

[0001] The present invention belongs to the technical field of related application methods in the production process of billet heating. The present invention relates to a method for modeling a two-dimensional temperature field of a round steel with unidirectional heating. It is specifically applied to the production process of billet heating in a heating furnace. Background Art

[0002] As can be seen from the process design of the heating furnace, the process of the billet heating from entering the furnace to normal discharging is a slow temperature rising process of the billet. If the heating rate is too slow, it will affect the discharging temperature of the billet and the uniformity of the billet temperature, and cannot meet the requirements of rolling; if the heating rate is too fast, that is, entering the high temperature state too early, it will reduce the heat transfer efficiency of the billet in the heating furnace, cause the furnace temperature and the flue gas temperature to be too high, resulting in unnecessary excessive consumption of fuel gas, and at the same time increase the probability of oxidation loss and nitrogen oxide formation.

[0003] In the heating furnace, it takes a long time for the billet to be heated from the initial temperature (the temperature when entering the furnace) to the target process temperature value. There are many uncertain factors in the heating process, such as abnormal fluctuations in the production rhythm, fluctuations in the calorific value of fuel gas, etc., which make the temperature rising process of the billet inevitably deviate from the target trajectory, and phenomena such as underburning or overheating of the billet often occur, and even make it difficult to achieve the quality and cost targets of rolling production. Therefore, the autonomous control task of the heating furnace is attributed to the effective control of the billet temperature rising process, and the key to the control lies in the core temperature of the billet calculated by using the temperature field model of the cylindrical billet. Summary of the Invention

[0004] In order to overcome the deficiencies of the prior art, the present invention provides a method for modeling a two-dimensional temperature field of a round steel with unidirectional heating. By calculating the temperature field of the cylindrical billet in the heating furnace in real time, the core temperature of the billet is determined, and the air-fuel ratio of each heating section in the heating furnace is adjusted according to the calculation results, so as to save the consumption of fuel gas on the premise of meeting the requirements of the production process for billet heating.

[0005] The above object of the present invention is achieved by the following technical solutions:

[0006] A method for modeling a two-dimensional temperature field of a round steel with unidirectional heating, which is specifically applied to the production process of billet heating in a heating furnace; the method includes establishing a temperature field prediction model of a square billet and establishing a temperature field prediction model of a cylindrical billet. The expression for establishing the temperature field prediction model of the cylindrical billet is:

[0007]

[0008] Wherein, λ is the thermal conductivity of the steel plate, λ w and λ e are the thermal conductivities of the front surface and the rear surface of the micro-element billet respectively; x is the length of the micro-element of the billet, ρ is the density of the billet, c is the specific heat capacity of the billet, t is the time, Ti is the temperature field of the steel plate at time i. The circular cross-section of the billet is divided into a 31*31 square billet network. After the boundary conditions of the billet are determined, the complete temperature field data of the cylindrical billet are obtained by first performing iterative calculations of the heat flux density column by column and then row by row.

[0009] The basis for establishing the temperature field prediction model of the cylindrical billet is as follows:

[0010] 1) Divide the circular cross-section of the billet into a 31*31 square billet network;

[0011] 2) First perform iterative calculations of the heat flux density column by column and then row by row;

[0012] 3) Each time an iteration of the square billet network is completed, a tridiagonal matrix of the heat flux density is formed, and the TDMA algorithm is used to solve this matrix;

[0013] 4) According to the symmetry of the circle, only the temperature field of a semi-circle needs to be calculated for each direction of scanning, and the temperature field data of the other semi-circle are exactly the same as those of the calculated semi-circle temperature field;

[0014] By calculating the heat transfer between adjacent modules, all the modules included in the circular cross-section are calculated to form a tridiagonal matrix, and this matrix is solved to calculate the internal temperature of the entire cylindrical billet; the matrix is as follows

[0015]

[0016] Furthermore, in the basis 1), the circular cross-section of the billet is divided into a square billet network, and the temperature field model of the square billet is used to approximately simulate the temperature field model of the cylindrical billet; in the basis 2), iterative calculations of the heat flux density are performed longitudinally and transversely respectively; in the basis 3), a tridiagonal matrix of the heat flux density of the square billet network is formed after one iteration calculation of the circular cross-section, and the TDMA (Thomas algorithm) is used for solution; in the basis 4), the symmetry of the circle is utilized to simplify the calculation amount.

[0017] The beneficial effects of the present invention compared with the prior art are as follows:

[0018] A method for modeling the two-dimensional temperature field of a single-direction heated round steel provided by the present invention determines the core temperature of the billet by performing real-time calculations on the temperature field of the cylindrical billet in the heating furnace, and adjusts the air-fuel ratio of each heating section in the heating furnace according to the calculation results, so as to save the consumption of gas on the premise of meeting the production process requirements. Description of the Drawings

[0019] Figure 1 It is a schematic diagram of the square billet network of the present invention.

[0020] Figure 2 The picture of the temperature at the core of the steel billet calculated by the program designed after applying the method of the present invention.

[0021] Figure 3 Schematic diagram defining the control volume integration element.

[0022] Figure 4 Schematic diagram of the integration path (profile).

[0023] Figure 5 Schematic diagram A of the operation page for applying this algorithm in Application Example 1.

[0024] Figure 6 Schematic diagram B of the operation page for applying this algorithm in Application Example 1.

[0025] Figure 7 Conceptual diagram of the micro-element cuboid inside the steel billet.

[0026] Figure 8 Stratification structure diagram of the steel plate.

[0027] Figure 9 Schematic diagram of the heat transfer in the square steel billet.

[0028] Figure 10 Schematic diagram of the transverse iterative calculation.

[0029] Figure 11 Schematic diagram of the longitudinal iterative calculation. Detailed implementation manners

[0030] The present invention will be described in detail below through specific embodiments, but the protection scope of the present invention is not limited. Unless otherwise specified, the experimental methods adopted in the present invention are all conventional methods, and the experimental equipment, materials, reagents, etc. used can all be obtained from commercial channels.

[0031] Embodiment 1

[0032] A modeling method for the two-dimensional temperature field of a unidirectionally heated round steel, specifically applied to the heating production process of steel billets in a heating furnace; the method includes establishing a temperature field prediction model for a square steel billet and establishing a temperature field prediction model for a cylindrical steel billet. The expression for establishing the temperature field prediction model for the cylindrical steel billet is:

[0033]

[0034] where, λ is the thermal conductivity of the steel plate, λ w and λ e are the thermal conductivities of the front and rear surfaces of the micro-element steel billet respectively; x is the length of the steel billet micro-element, ρ is the density of the steel billet, c is the specific heat capacity of the steel billet, t is the time, T iis the temperature field of the steel plate at time i. The circular cross-section of the billet is divided into a 31*31 square billet network. After the boundary conditions of the billet are determined, the complete temperature field data of the cylindrical billet are obtained by first performing iterative calculations of the heat flux density column by column and then row by row for the heat flux density;

[0035] The specific steps for deriving the expression are as follows:

[0036] The present invention uses the control volume integration method to discretize the partial differential equation of the temperature field model, that is, to perform integral processing on the microelement in space and time. Figure 3 Describes the microelement defined by the control volume integration method and the definition of related variables.

[0037] In the solution calculation of problems related to heat transfer, it is necessary to know the temperature distribution of the object. The temperature distribution reflects the transfer of heat flux density in the billet. To model the temperature field of the square billet, it is first necessary to establish a heat transfer differential equation for describing the heat transfer process. According to Fourier's law, assuming that there is no energy loss during the transfer of energy inside the billet, a microelement cuboid inside the billet ( Figure 7 )

[0038] Use q x , q y , q z to represent the projection components of the heat flux density in the x, y, and z coordinate axes directions. Let x = x, y = y, z = z. The amount of heat flux density entering from the surface of the microelement can be written as:

[0039]

[0040]

[0041]

[0042] From Equation (2.21), the amount of heat entering the microelement cuboid in the x direction at any time is:

[0043]

[0044] In the x direction, the temperature change of the right surface of the microelement cuboid is The current value of the temperature of the right surface is The heat of the right surface of the microelement cuboid is:

[0045]

[0046] Simplified to:

[0047]

[0048] Then the amount of heat obtained by the microelement cuboid in the x direction is:

[0049]

[0050] That is:

[0051]

[0052] Similar to the x-direction, the heat entering the differential cuboid from the y-direction and z-direction at any moment can be respectively written as:

[0053]

[0054]

[0055] Meanwhile, the heat obtained by the differential cuboid from the y-direction and z-direction is respectively:

[0056]

[0057]

[0058] In summary, the total heat obtained by the differential cuboid is the superposition of the heat in the x-direction, y-direction, and z-direction, as shown in Equation (2.33):

[0059]

[0060] Assume that there is no energy loss during the process of the differential cuboid absorbing and releasing heat, and all the energy is effectively transferred. According to the laws of thermodynamics, the change process of heat can be described by the following thermal energy relationship:

[0061] Change in internal energy = Total heat absorbed – Total heat released + Heat generated by internal phase change (2.34)

[0062] Where:

[0063]

[0064]

[0065] In Equations (2.35) and (2.36):

[0066] ρ—Density of the steel billet, unit: kg / m 3 ;

[0067] c—Specific heat capacity of the steel billet, unit: kJ / (kg·K);

[0068] t—Time, unit: s;

[0069] Heat generated by internal phase change per unit volume and time of a steel billet, unit: W / m3 ;

[0070] Substitute equations (2.33), (2.35) and (2.36) into (2.34) and after rearrangement, we get:

[0071]

[0072] Equation (2.37) represents the three-dimensional form of the differential equation for heat conduction in an infinitesimal cuboid.

[0073] If it is assumed that there is no heat generated by phase change inside the infinitesimal cuboid, equation (2.37) can be simplified to:

[0074]

[0075] Where: ρ is the density of the steel plate in kg / m 3 ; c is the specific heat capacity of the steel plate (W / kg℃); λ is the thermal conductivity of the steel plate (W / m℃); T is the temperature field of the steel plate at time t.

[0076] To calculate the temperature field inside the billet, it is necessary to first establish the differential equation for heat conduction inside the billet.

[0077] After the section steel billet is heated, there is a heat transfer process in the following form during the natural cooling process:

[0078] (1) Heat conduction from the steel plate to the roller table;

[0079] (2) Heat released due to phase change inside the steel plate;

[0080] (3) Heat conduction inside;

[0081] (4) Convective heat transfer between the surface and the external environment;

[0082] (5) Radiative heat transfer between the steel plate and the external environment;

[0083] Among them, (2), (3) and (4) are the main forms of heat flow, and (1) and (5) can be ignored.

[0084] To reduce the computational amount and complexity of the discretization process, the following assumptions are made:

[0085] (1) The density of the steel plate is a fixed value, and other physical properties are related to temperature;

[0086] (2) Heat is transferred uniformly in the same direction of the steel plate;

[0087] According to the above assumptions, the heating process of the billet can be expressed by the following formula:

[0088]

[0089] The temperature field model of the steel billet needs to be discretized. In the process of discretizing the temperature field model, the control volume integral method is selected in this paper. As Figure 3 Select a micro-element of the steel billet and perform integrations on it in time and space respectively.

[0090] Integrate the one-dimensional mathematical model equation of the steel plate for Figure 3 the control volume P shown in the time interval of Δt, and obtain:

[0091]

[0092]

[0093] Where:

[0094] Integrating Equation 2.1 and Equation 2.2, the discretized temperature field model can be obtained as follows;

[0095]

[0096] To complete the integration in the above equation, a choice needs to be made on the linear type of how T changes with time in the right-hand side term of Equation 2.3. There are 3 commonly used linear types, as Figure 4 shown:

[0097] According to numerical heat transfer, they can all be expressed by the following general formula:

[0098]

[0099] Where: when f = 0, it is the explicit format; when f = 1, it is the implicit format; when, it is the C-N format.

[0100] Expand the right-hand side term of Equation 2.3 in the way of Equation 2.4 to obtain the discretized general formula of the one-dimensional mathematical model of the steel plate as follows:

[0101]

[0102] For the C-N format:

[0103]

[0104] Where q e and q w are the heat flux densities on the front and back surfaces of the micro-element steel billet respectively. λ w and λ eThey are the thermal conductivities of the front and back surfaces of the infinitesimal billet respectively. During the calculation, the physical property parameter values are taken at the points stored at the node positions, while the values in the formula are at the points on the interface. Here, the harmonic mean method is adopted to determine the thermal conductivities λ w and λ e .

[0105] According to the principle that the heat flux density from point P to point E (see Figure 3 ) is equal, the following equation can be obtained:

[0106]

[0107] After deformation processing, the new equation is as follows:

[0108]

[0109] The numerators on both sides of the equation in Equation 2.8 are equal, and thus the following formula (harmonic mean method) is obtained:

[0110]

[0111] Because the grid is equally divided in the x direction, that is:

[0112]

[0113]

[0114] Similarly, it can be obtained that:

[0115]

[0116] The present invention adopts the C-N format of the one-dimensional heat transfer model, and simplifies Equation 2.6 to obtain:

[0117]

[0118] To facilitate the definition of boundary conditions, the steel plate adopts the Figure 8 shown layering method in the thickness direction.

[0119] When the control volume is at the boundary, there is:

[0120]

[0121]

[0122] where HF U represents the heat flux density at the top of the steel plate in the thickness direction, and HF D represents the heat flux density at the bottom of the steel plate in the thickness direction.

[0123] The general formula for the discretization of the one-dimensional heat transfer model is obtained as:

[0124] a i T i-1 +b i T i +c o T i+1 =d i (3.19)

[0125]

[0126] Boundary conditions:

[0127] (1) Air-cooled zone

[0128] Adopting the third kind of boundary condition, then:

[0129]

[0130]

[0131] Where: ε—radiation coefficient;

[0132] σ—Boltzmann constant;

[0133] T a —Surrounding temperature, °C;

[0134] T b —Slab surface temperature, °C;

[0135] T aroll -Roll temperature

[0136] h roll -Heat transfer coefficient between the roll and the slab, generally taking the empirical value of 200 - 300

[0137] And θ1 + θ2 = 1

[0138] (2) Water-cooled zone

[0139] If the relationship between the density of the cooling water in each section of the secondary cooling zone and the overall heat transfer coefficient h is clear, then the third kind of boundary condition is expressed as follows:

[0140] Upper surface

[0141] Lower surface

[0142] Where: T b —Billet surface temperature, °C;

[0143] Tw—Cooling water temperature, °C;

[0144] h—Overall heat transfer coefficient between the cooling water and the billet, kcal / m 2·S·°C;

[0145]

[0146] The cylindrical billet temperature field modeling method proposed by this method is based on the temperature field model of square billets. Since it is difficult to directly model a circular cross-section, this method uses the method of circular segmentation to simulate the temperature field of the cylindrical billet.

[0147] For the temperature field of the cylindrical billet of this method, the heat transfer form in each divided small square billet module is deduced, and then the temperature value inside the whole billet is calculated.

[0148] On the surface of the cylindrical billet, heat is mainly transferred in the form of convective heat transfer and radiative heat transfer between the furnace gas and the furnace wall. Therefore, the internal temperature of the square billet module close to the surface of the cylindrical billet is calculated by using the comprehensive heat transfer coefficient; the main form of heat transfer during the heating process inside the billet is heat conduction. Therefore, the temperature of the square billet module inside the billet is calculated by using heat conduction.

[0149] The cylindrical billet temperature field modeling method proposed by this method divides the circular cross-section of the billet into several square billet networks. For each square billet module, the control volume method is used to establish the heat conduction differential equation, and discretization is carried out to calculate the heat transfer process in the effective square billet module, and the boundary conditions for the comprehensive heat exchange between the square billet module at the circular cross-section and the high-temperature furnace gas are determined, which can ensure the reliability of calculating the heat transfer inside the billet.

[0150] With the continuous development of computer technology, the computing power of the computer has been greatly improved. The discretization of the square billet temperature field model and the calculation formula of the TDMA Thomas algorithm are complex and computationally intensive. Therefore, the temperature field calculation process can be solved by computer programming. Relying on the powerful computing power of the computer processing system, the accurate result of the temperature field model can be solved in a short time, providing a reliable guarantee for the subsequent furnace temperature control based on the billet temperature.

[0151] The calculation of the temperature field model of the cylindrical billet by this method is based on the temperature field of the square billet. The circular cross-section is divided into several square billet modules to form a square billet network, as Figure 1 shown. The black dots in the figure represent the effective square billet modules included in the circular cross-section. By calculating the heat transfer between adjacent modules and calculating all the modules included in the circular cross-section, the internal temperature of the entire cylindrical billet can be calculated.

[0152] As Figure 9 shown, take one of the square billet modules for analysis.

[0153] For the selected square billet module located in the center (marked with a black dot), heat is transferred in four directions, namely, heat transferred from the upper square billet module to the lower side, heat transferred from the lower square billet module to the upper side, heat transferred from the left square billet module to the right side, and heat transferred from the right square billet module to the left side.

[0154] Therefore, to calculate the temperature of the central square billet module, it is necessary to calculate the heat transferred from four directions four times. The calculation method can be divided into horizontal iteration and vertical iteration.

[0155] First, perform transverse heat calculations on all the divided square billet modules. For any row of square billet modules, calculate the temperature of the effective square billet modules contained in the circular cross-section of the billet. Each transverse iterative calculation is divided into two steps: the first step is to calculate the heat value obtained by each square billet module when the heat enters the billet from the first square billet module on the left and transfers to the last square billet module to the right; the second step is to calculate the heat value obtained by each square billet module when the heat enters the billet from the first square billet module on the right and transfers to the last square billet module to the left. After completing the calculation of the heat transfer process in the left and right directions for each row of square billet modules, all transverse heat transfer calculations for a row of square billet modules are completed.

[0156] According to the above calculation method, the square billet module network is calculated row by row for transverse heat transfer starting from the first row. Once all calculations are completed, the transverse iteration of the temperature field of the billet cross section is completed. Figure 10 As shown in the figure, the circular section of the billet is divided into a 31*31 square billet network. When calculating the transverse heat transfer, the effective square billet modules included in the circular section of rows 13-19 are all 31 (the effective square billet modules are represented by black dots), and the furnace gas temperature around the billet is uniform, and the boundary conditions at the circular section are the same. Therefore, only the square billet modules in row 13 need to be discretized and integrated, and the Thomas algorithm is used to calculate the transverse heat transfer. The calculation results of the remaining rows 14-19 are consistent with those of row 13. After that, the transverse heat transfer calculation is continued for row 12, and so on, and finally the transverse heat transfer calculation is completed for all 31 rows.

[0157] After completing the lateral heat transfer calculation for the square billet module network row by row, the heat distribution of the billet in the horizontal direction is obtained. Continue to calculate the heat transfer and distribution in the vertical direction column by column starting from the first column of the square billet module network, and obtain the total heat distribution of each effective module in the square billet module network, and then calculate the temperature field distribution inside the entire cylindrical billet.

[0158] The calculation method of longitudinal heat transfer is the same as above, that is, to calculate the temperature of the effective square billet module contained in the circular cross-section of the billet. Each longitudinal iteration calculation is divided into two steps: the first step is to calculate the heat value obtained by each square billet module during the process of heat transfer from the first square billet module at the top of a certain column into the billet and then down to the last square billet module; the second step is to calculate the heat value obtained by each square billet module during the process of heat transfer from the first square billet module at the bottom of a certain column into the billet and then up to the last square billet module. In this way, the longitudinal heat transfer calculation of the square billet modules in a certain column is completed.

[0159] According to the above calculation method, the longitudinal heat transfer calculation is carried out column by column for the square billet module network starting from the first column. After all are completed, a longitudinal iteration of the billet cross-section temperature field is completed, as Figure 11 shown.

[0160] Among the algorithms for solving the process involving heat transfer, the Thomas algorithm is one of the most frequently used and most effective algorithms, and has been widely used. The main function of the Thomas algorithm is to solve the tridiagonal matrix equation, also known as the TDMA algorithm. The TDMA method starts from the first row of the coefficient matrix, eliminates a parameter with the second row for the first row, eliminates a parameter with the third row for the second row, and so on. Each row eliminates a non-zero parameter, transforming the three-variable linear equation system into a two-variable linear equation system. When reaching the last row, the two-variable equation system is transformed into a one-variable equation system, and the solution of the unknown can be directly obtained. Substituting the obtained solution back into the previous row in turn, all solutions of the two-variable equation system can be solved successively. Calculating all the solutions completes the solution of a one-dimensional temperature field.

[0161] The basis for establishing the prediction model of the cylindrical billet temperature field is as follows:

[0162] 1) Divide the circular cross-section of the billet into a 31*31 square billet network;

[0163] 2) First perform iterative calculations of the heat flux density column by column and then row by row;

[0164] 3) Each time the iteration of the square billet network is completed, a tridiagonal matrix of the heat flux density is formed, and the TDMA algorithm is used to solve and calculate this matrix;

[0165] 4) According to the symmetry of the circle, only the temperature field of a semicircle needs to be calculated for each direction of scanning, and the temperature field data of the other semicircle is exactly the same as that of the calculated semicircle temperature field;

[0166] By calculating the heat transfer between adjacent modules, all the modules included in the circular cross-section are calculated to form a tridiagonal matrix, and the internal temperature of the entire cylindrical billet is calculated by solving this matrix; (the matrix is as follows)

[0167]

[0168] Further, in step 1), the circular cross-section of the steel billet is divided into a square steel billet network, and the temperature field model of the square steel billet is used to approximately simulate the temperature field model of the cylindrical steel billet; in step 2), iterative calculations of the heat flux density are performed longitudinally and transversely respectively; in step 3), after completing one iteration calculation of the circular cross-section, a tridiagonal matrix of the heat flux density of the square steel billet network is formed, and the TDMA (Thomas algorithm) is used for solution; in step 4), the symmetry of the circle is utilized to simplify the calculation amount.

[0169] Application Example 2

[0170] The present invention is applied to the annular reheating furnace control system of Jiangsu Jingjiang Special Steel Co., Ltd. The method provided in this application is specifically applied to a computer program.

[0171] The effectiveness of the temperature field model of the cylindrical steel billet is detected by detecting the temperature of the steel billet at the production site.

[0172] The main method is to install an infrared thermometer beside the roller table on the discharging side of the annular reheating furnace. Whenever a steel billet is discharged and enters the roller table, the infrared thermometer automatically performs infrared temperature measurement on the width direction of the steel billet to obtain the temperature value on the width direction of the outer surface of the steel billet.

[0173] 10 temperature measurement values are taken for each of the steel billets with diameters of 220 mm and 250 mm, and the specific measured data are shown in the following table.

[0174] Table 1 Outer surface temperature of 220mm billet

[0175] Tab.1 Surface temperature of 220mm billet

[0176]

[0177] Using the steel billet temperature field simulation calculation program, the parameters such as the furnace temperature of each section in the furnace where the above-mentioned temperature-measured steel billets are located and the residence time are substituted into the simulation calculation program. The calculated outer surface temperature is 1178.6 °C. Comparing the actual measured data and the simulation calculation data of the outer surface temperature of the steel billet, the details are shown in Table 2.

[0178] Table 2 Comparison of simulated and measured values of billet surface temperature

[0179] Tab.2 Comparison of simulated and measured values of billet surface temperature

[0180]

[0181]

[0182] The data in Table 2 show that the relative error between the measured surface temperature value of the billet and the temperature value calculated by computer simulation is <5%, meeting the heating process requirements of the production site. It is proved that the temperature field model of the cylindrical billet can better reflect the temperature rise of the billet in the furnace, and the simulated calculation result of the surface temperature of the billet is basically consistent with the temperature value actually measured when the billet is taken out of the furnace.

[0183] Table 3 Surface temperature of 250mm billet when taken out of the furnace

[0184] Tab.3 Surface temperature of 250mm billet

[0185]

[0186] Using the billet temperature field simulation calculation program, modify the diameter value of the billet to 250mm, and keep the other physical parameters unchanged. Substitute the parameters such as the furnace temperature and residence time of each section in the furnace where the temperature-measuring billet in the above table is located into the simulation calculation program. The calculated surface temperature is 1182.2 °C. Comparing the actual measurement data and the simulation calculation data of the billet surface temperature, the details are shown in Table 4.

[0187] Table 4 Comparison of simulated and measured values of billet surface temperature

[0188] Tab.4 Comparison of simulated and measured values of billet surface temperature

[0189]

[0190]

[0191] The data in Table 4 show that the relative error between the measured surface temperature value of the billet and the temperature value calculated by computer simulation is <5%, meeting the heating process requirements of the production site. The calculation results can be provided to experts for judgment, and then decisions can be made. According to the decision results, the furnace temperature can be modified, and finally the gas consumption can be saved.

[0192] The above-described embodiments are only the preferred embodiments of the present invention, and not all the feasible embodiments of the present invention. For those of ordinary skill in the art, any obvious changes made without departing from the principles and spirit of the present invention should be considered to be included within the protection scope of the claims of the present invention.

Claims

1. A modeling method for a two-dimensional temperature field model of unidirectionally heated round steel, specifically applied to the billet heating production process in a heating furnace; the method includes establishing a temperature field prediction model for a square billet and establishing a temperature field prediction model for a cylindrical billet. The expression for establishing the temperature field prediction model for the cylindrical billet is: Among them, λ is the thermal conductivity of the steel plate, λ w and λ e are the thermal conductivities of the front and back surfaces of the infinitesimal billet respectively; x is the length of the billet infinitesimal, ρ is the density of the billet, c is the specific heat capacity of the billet, t is the time, and T i is the temperature field of the steel plate at the i-th moment; the circular cross-section of the billet is divided into a 31*31 square billet network. After the boundary conditions of the billet are determined, the complete temperature field data of the cylindrical billet are obtained by first performing iterative calculations of the heat flux density column by column and then row by row for the heat flux density. The basis for establishing the temperature field prediction model for the cylindrical billet is: 1) Divide the circular cross-section of the billet into a 31*31 square billet network; 2) Perform iterative calculations of the heat flux density column by column first, and then row by row; 3) After each iteration of the square billet network is completed, a tridiagonal matrix of the heat flux density is formed, and the TDMA algorithm is used to solve this matrix; 4) According to the symmetry of the circle, only the temperature field of a semi-circle needs to be calculated for each direction of scanning, and the temperature field data of the other semi-circle is exactly the same as that of the calculated semi-circle temperature field; By calculating the heat transfer between adjacent modules, all the modules included in the circular cross-section are calculated to form a tridiagonal matrix, and this matrix is solved to calculate the internal temperature of the entire cylindrical billet.

2. The modeling method of a one-way heated round steel two-dimensional temperature field model according to claim 1, characterized in that, In step 1), the circular cross-section of the billet is divided into a square billet network, and the temperature field model of the square billet is used to approximately simulate the temperature field model of the cylindrical billet.

3. A modeling method for a two-dimensional temperature field model of a unidirectionally heated round steel, as described in claim 1, wherein In step 2), iterative calculations of the heat flux density are performed longitudinally and transversely respectively.

4. A method for modeling a two-dimensional temperature field of a unidirectionally heated round steel, as described in claim 1, characterized in that, In step 3), a tridiagonal matrix of the heat flux density of the square billet network is formed after one iteration calculation of the circular cross-section, and TDMA is used for solving.

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