Method for calculating ladle heat transfer characteristic parameter and molten steel temperature drop calculation method

Abstract

This invention provides a method for inverting and calculating heat transfer characteristic parameters of a ladle and a method for calculating the temperature drop of molten steel, belonging to the field of iron and steel smelting. The method obtains and simplifies the geometric structural parameters and refractory material thermophysical parameters of the ladle, constructing a three-dimensional ladle model; simplifies the ladle turnover process to baking, reloading, and empty ladle; meshes the three-dimensional ladle model into a spatial discrete structure composed of several nodes, and then constructs a finite difference heat transfer forward problem calculation model for the ladle; verifies the independence of the mesh from the time step, and solves the ladle temperature field based on the optimal discrete parameters; uses the LM algorithm to construct an inverted calculation model for heat transfer characteristic parameters, performs heat transfer inverse problem correction calculations, and obtains the corrected heat transfer characteristic parameters up to the last process of all processes in the N turnover furnaces before baking and online operation. This invention improves the accuracy of the correction of heat transfer characteristic parameters and obtains a temperature drop value of molten steel inside the ladle that is closer to the true value.

Description

Technical Field

[0001] This invention belongs to the field of iron and steel smelting, and specifically relates to a method for calculating the inversion of heat transfer characteristic parameters of a ladle and a method for calculating the temperature drop of molten steel. Background Technology

[0002] In the steel smelting process, the ladle is a crucial piece of equipment for holding and transporting molten steel, and also an important reaction vessel for ladle refining. The compact turnover process and large spatial span of the ladle make it difficult to perceive its condition, leading to frequent ladle burn-through accidents that cause significant property damage and casualties. Research on heat transfer in the ladle temperature field is beneficial for analyzing the temperature field changes during ladle turnover, providing theoretical support for molten steel temperature control, and guiding the optimization of molten steel temperature control process parameters to achieve precise temperature regulation. Simultaneously, it improves the quality and yield of castings, reduces production costs, and provides important references for the rationalization of ladle design, extending equipment service life.

[0003] Methods for studying the thermal behavior of steel ladles are mainly divided into experimental methods and numerical simulation methods. Experimental methods primarily rely on equipment such as thermocouples and infrared thermometers; numerical simulation methods, mainly based on the finite difference method or finite volume method, simulate and analyze temperature field changes under conditions such as ladle structure, lining baking, refilling, and empty ladle. The comprehensive research method, which integrates experimental and mathematical simulation methods, is the most widely used approach. In the study of ladle thermal behavior, the accurate calculation of ladle heat transfer characteristic parameters and temperature field is crucial for ladle safety assessment and molten steel temperature control during steelmaking. Due to the heterogeneous heat transfer characteristics of the ladle's multi-layered composite structure and complex turnover conditions, its heat transfer characteristic parameters exhibit significant nonlinear dynamic changes, making it difficult for traditional calculation methods to accurately characterize and calculate the temperature drop of the molten steel inside the ladle. Summary of the Invention

[0004] To address the aforementioned issues, this invention provides a method for inverting and calculating the heat transfer characteristic parameters of a ladle and a method for calculating the temperature drop of molten steel, thereby improving the accuracy of the correction of the heat transfer characteristic parameters and obtaining a temperature drop value of molten steel in the ladle that is closer to the true value.

[0005] To achieve the above objectives, the technical solutions adopted in the embodiments of the present invention are as follows:

[0006] In a first aspect, embodiments of the present invention provide a method for inverting and calculating heat transfer characteristic parameters of a steel ladle, the method comprising the following steps:

[0007] Step S11: Obtain and simplify the geometric structure parameters and refractory material thermophysical parameters of the ladle, and construct a three-dimensional model of the ladle based on the geometric structure parameters;

[0008] Step S12: Simplify the ladle turnover process into three working conditions: baking, refilling, and empty ladle, and determine the boundary conditions for each working condition; at the same time, determine all process stages that need to be calculated by inversion of heat transfer characteristic parameters, including the baking stage and the refilling and empty ladle stages of the first N turnover furnaces in operation.

[0009] Step S13: Mesh the three-dimensional model of the steel ladle into a spatial discrete structure consisting of several nodes.

[0010] Step S14: Based on the heat conduction control equation and the divided nodes, construct a calculation model for the finite difference heat transfer forward problem of the ladle.

[0011] Step S15: Verify the independence of the grid and time step for the finite difference heat transfer forward problem calculation model, and solve the ladle temperature field based on the optimal discrete parameters.

[0012] Step S16: Based on the solved ladle temperature field, construct a heat transfer characteristic parameter inversion calculation model using the LM algorithm; specifically including:

[0013] Step S161: Construct a temperature objective function based on the ladle temperature field;

[0014] Step S162: Set the partial derivative of the temperature objective function with respect to the heat transfer characteristic parameter P of the ladle to 0, construct a partial differential equation, and introduce the Jacobian matrix into the equation, with the elements in the Jacobian matrix being sensitivity coefficients.

[0015] Step S163: Expand the Jacobian matrix to construct the sensitivity matrix, and divide the sensitivity matrix into blocks according to the process stage to establish the sensitivity relationship between the residual and the heat transfer parameters.

[0016] Step S164: Based on the temperature objective function and the sensitivity matrix, set the iterative update rules for the heat transfer characteristic parameters, introduce an adaptive adjustment mechanism for the damping coefficient in the iterative update rules, and set the convergence criteria.

[0017] Step S17: Based on the constructed heat transfer characteristic parameter inversion calculation model, perform heat transfer inverse problem correction calculation on the heat transfer characteristic parameters of the ladle temperature field to obtain the corrected heat transfer characteristic parameters.

[0018] Step S18: Determine whether the current process stage is the last process of all processes in the N turnover furnaces before baking and online operation; if not, proceed to step S17; if yes, all stages are completed, and output the heat transfer characteristic parameters and temperature field calculation results after the whole process correction.

[0019] In a preferred embodiment of the present invention, in step S12, when determining the boundary conditions for each working condition, heat is exchanged between the refractory materials lining the ladle through thermal conduction, the initial temperature field of the ladle is room temperature, and the inner and outer walls of the ladle in the baking stage and the empty ladle stage adopt the third type of boundary conditions; in the refilling stage, the inner wall of the ladle is under the first type of boundary conditions, the temperature of the molten steel is the inner wall temperature, and the outer wall is under the third type of boundary conditions.

[0020] In a preferred embodiment of the present invention, the nodes in step S13 include internal nodes, first-type boundary nodes and second-type boundary nodes, wherein the first-type boundary nodes are located on the surface intersection line of the three-dimensional model of the ladle and the second-type boundary nodes are located on the surface of the three-dimensional model of the ladle.

[0021] In a preferred embodiment of the present invention, step S14, which constructs a calculation model for the finite-difference heat transfer forward problem of the ladle, specifically includes:

[0022] Step S141: Make conditional assumptions for the physical model and heat transfer model of the ladle, and define the heat transfer parameters and boundary conditions.

[0023] Step S142: Based on the assumptions, the heat transfer process of the ladle is described by the three-dimensional unsteady heat conduction partial differential control equation in the rectangular coordinate system.

[0024] Step S143: Based on the spatial discrete structure, the Taylor expansion method is applied to replace the derivatives in the heat conduction partial differential control equations with difference approximation expressions. The first derivative is processed by first-order forward difference, and the second derivative is processed by second-order central difference, to obtain the heat transfer difference expressions for internal nodes, first-type boundary nodes, and second-type boundary nodes, respectively. The heat transfer difference equations of internal node A, first-type boundary node B, and second-type boundary node C together constitute the finite difference heat transfer forward problem calculation model.

[0025] In a preferred embodiment of the present invention, when performing irrelevance verification in step S5, four mesh partitioning methods are set, and the temperature values ​​of the nodes are calculated according to the finite difference heat transfer forward problem calculation model under each mesh partitioning method; then, the optimal discrete parameters are obtained based on the accuracy of the calculation results and the calculation speed.

[0026] In a preferred embodiment of the present invention, the temperature objective function constructed in step S161 is as follows:

[0027] (12)

[0028] In equation (12), Let I be the objective function; I be the number of time steps; for The actual measured temperature value at each temperature measurement point at any given time; for The calculated temperature values ​​at each measurement point are given. P represents the set of heat transfer characteristic parameters of the ladle, corrected by the inverse heat transfer problem, containing n heat transfer characteristic parameters p1, p2, ..., p. n ;

[0029] Temperature objective function Represented in matrix form:

[0030] (13)

[0031] In equation (13), This is the measured temperature vector. To calculate the temperature vector, The residual vector;

[0032] The partial differential equation for the temperature objective function mentioned in step S162 is as follows:

[0033] (14)

[0034] Introducing the Jacobian matrix:

[0035] (15)

[0036] In equation (15), This is the matrix representation of the partial differential equation with temperature as the objective function. It is a Jacobian matrix;

[0037] The Jacobian matrix expansion in step S163 is as follows:

[0038] (16)

[0039] Construct the sensitivity matrix based on the transposed Jacobian matrix, and then divide the sensitivity matrix into blocks, including:

[0040]

[0041] (17)

[0042] In equation (17), the elements in the transposed Jacobian matrix are... For sensitivity coefficients; T1,…,T H T represents the temperature at sampling time points 1 to H during the baking stage, representing the heat transfer characteristic parameters. H+1 ,…, T I This represents the temperature of the heat transfer characteristic parameters sampling points H+1~I during the online operation phase; These are the calculated temperature values ​​for each time point. For the heat transfer characteristic parameter P of the ladle j The partial derivatives are expressed as The solution is obtained using the finite difference method, and the calculation formula is as follows:

[0043] (18)

[0044] In equation (18), the parameter disturbance value is solved. ;

[0045] The sensitivity matrix is ​​divided into blocks. In the matrix of equation (17), the first H rows correspond to the ladle baking stage, and the H+1 to I rows correspond to the end time of the first N heats of refilled ladle and the end time of empty ladle in the ladle online operation stage.

[0046] In a preferred embodiment of the present invention, the iterative update rule in step S164 is expressed as follows:

[0047] (twenty two)

[0048] In equation (22), These are the heat transfer characteristic parameters solved in the previous and current rounds, respectively; These are the calculated temperature values ​​and sensitivity matrix of the temperature measurement point at the k-th iteration, respectively. The damping coefficient; It is a unit diagonal matrix. ; This is the measured temperature vector. express The transpose of .

[0049] In a preferred embodiment of the present invention, step S164 introduces an adaptive damping coefficient adjustment mechanism, which controls... ,ensure The positive definiteness of the arithmetic ensures the convergence speed and convergence of the iterative calculation.

[0050] In a preferred embodiment of the present invention, the convergence criterion in step S164 is set as follows:

[0051] The iteration termination condition for the LM algorithm is set as follows: the change in the parameter vector to be solved between two consecutive iterations is less than the preset convergence accuracy, i.e., it satisfies...

[0052] (twenty four)

[0053] In equation (24), and The first Second and third The heat transfer characteristic parameter vector obtained from the next iteration;

[0054] ; This represents the change in the parameter to be solved during the two iterations.

[0055] When this condition is met, the algorithm is considered to have converged, and the iteration stops.

[0056] Secondly, embodiments of the present invention also provide a method for calculating the temperature drop of molten steel during the ladle turnover process, including:

[0057] Step S21: Calculate the heat flux density of the ladle lining based on the heat transfer characteristic parameters calculated by the inversion calculation method of the ladle heat transfer characteristic parameters as described above and the ladle temperature field.

[0058] Step S22: Based on the calculated heat flux density of the inner wall of the ladle and the adjacent spatial nodes, and the duration parameter of the ladle reloading state, calculate the temperature drop of the molten steel inside the ladle under the reloading state.

[0059] The solutions of the embodiments of the present invention have the following beneficial effects:

[0060] The ladle heat transfer characteristic parameter inversion calculation method and molten steel temperature drop calculation method provided in this invention first establish a three-dimensional finite difference heat transfer positive model of the ladle to simulate the temperature field change over time during the predetermined baking time and N heats before online turnover, obtaining the initial error calculation distribution; then, based on the LM algorithm and the heat transfer characteristic parameter correction method of the heat transfer inverse problem, the characteristic parameters are corrected by simultaneously correcting the heat transfer coefficients of the inner wall and the outer wall during the baking stage; finally, based on the ladle temperature field data corrected by the heat transfer inverse problem, the heat flux density of spatial nodes near the inner surface is calculated during the ladle baking and online turnover stages, and the molten steel temperature drop during the re-ladle stage of different heats is calculated. The results show that, after parameter inversion correction, the average accuracy of the temperature correction value at the temperature measurement point improved by 3.24% and 10.15% respectively during the baking stage and the online operation stage, taking 10 heats as an example. The heat storage characteristics of the ladle lining during the turnover process directly affect the temperature drop of the molten steel. The temperature drop reached 170.02K in the first heat and stabilized at 90.55K by the 10th heat, providing reliable technical support for online monitoring of the ladle temperature field and optimization of the turnover process.

[0061] Of course, implementing any product or method of the present invention does not necessarily require achieving all of the advantages described above at the same time. Attached Figure Description

[0062] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0063] Figure 1 This is a flowchart of the ladle heat transfer characteristic parameter inversion calculation method according to an embodiment of the present invention;

[0064] Figure 2 This is a simplified schematic diagram of the steel ladle structure in an embodiment of the present invention;

[0065] Figure 3 This is a simplified ladle turnover flowchart in an embodiment of the present invention;

[0066] Figure 4 This is a schematic diagram of the unit control volume of internal node A and its adjacent nodes in an embodiment of the present invention;

[0067] Figure 5 This is a schematic diagram of the unit control volume of the first type of boundary node B and the second type of boundary node C in an embodiment of the present invention;

[0068] Figure 6 This is an iterative principle diagram of the heat transfer inverse problem calculation model in this embodiment of the invention;

[0069] Figure 7 These are the calculated temperatures of the space nodes on the side wall of the ladle during the baking stage, as specifically applied in this embodiment of the invention.

[0070] Figure 8 These are the calculated temperatures of the sidewall space nodes at the end of each process during the online operation phase of this invention embodiment.

[0071] Figure 9 These are the measured and calculated temperatures of the temperature measuring points on the outer wall of the ladle, specifically applied in this embodiment of the invention.

[0072] Figure 10 This is the temperature correction value of the temperature measuring point on the outer wall of the ladle during the baking stage, specifically applied in the embodiments of the present invention.

[0073] Figure 11 This refers to the temperature correction value error of the temperature measuring point on the outer wall of the ladle during the baking stage, as specifically applied in this embodiment of the invention.

[0074] Figure 12 This is the temperature correction value of the ladle outer wall temperature measuring point during the online operation phase of a specific application of this invention embodiment;

[0075] Figure 13 This refers to the temperature correction value error of the ladle outer wall temperature measuring point during the online operation phase of a specific application of this invention embodiment;

[0076] Figure 14 This describes the changes in heat flux density and temperature between the inner wall and adjacent nodes during the baking stage in a specific application of this invention embodiment;

[0077] Figure 15This describes the changes in heat flux density and temperature of the inner wall and adjacent nodes at the end of each repacking cycle in specific applications of this invention.

[0078] Figure 16 This refers to the heat flux density of the inner wall and adjacent nodes in each repacking stage of the present invention in specific applications.

[0079] Figure 17 This is a specific application of the present invention regarding the temperature drop of molten steel during the re-laundering stage of the ladle turnover process;

[0080] Figure 18 This describes the temperature drop of molten steel during the re-laundering stage in each heat of this invention, as specifically applied in the embodiments of the present invention.

[0081] Explanation of reference numerals in the attached figures:

[0082] 1-Working layer; 2-Permanent layer; 3-Steel shell. Detailed Implementation

[0083] After discovering the aforementioned problems, the inventors of this application conducted a detailed study of existing methods for researching and characterizing heat transfer in steel ladles. The study found that by studying heat transfer through an inverse problem approach, measured data can be used to correct potential biases in mathematical calculation models, significantly improving the accuracy and reliability of temperature field calculation results. Commonly used algorithms for inverse heat transfer problems include the steepest descent method, Newton's method, Gauss-Newton method, LM method, and quasi-Newton method. Currently, some scholars have used the conjugate gradient method to calculate the heat flux density of the pipe wall under forced convection heat transfer, with a temperature correction error of less than 2.58%; others have used the LM algorithm to correct the thermal conductivity, specific heat capacity, density, and heat transfer coefficient of the material, using the actual measured temperature as the standard, with a temperature correction error of less than 1.25 K.

[0084] However, numerical simulation studies of ladle thermal behavior are generally based on one-dimensional or two-dimensional coordinate systems. In these numerical calculations, heat transfer boundary conditions are mostly derived empirically or through formulas and are constant values. They fail to consider the real-time impact of factors such as the surrounding environment and ladle structure changes during actual production from a three-dimensional coordinate system perspective. Errors in the heat transfer calculation parameters lead to inaccuracies in the temperature field calculation results. Accurate heat transfer characteristic parameters can be obtained through inverse heat transfer problem calculations. Therefore, considering both experimental and numerical simulation methods, obtaining accurate heat transfer characteristic parameters through inverse heat transfer problem calculations is an effective way to obtain accurate values ​​of the ladle temperature field.

[0085] It should be noted that the defects in the above-mentioned prior art solutions are all the result of the inventors' practice and careful research. Therefore, the discovery process of the above problems and the solutions proposed by the embodiments of the present invention in the following text should be the inventors' contributions to the present invention.

[0086] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. It should be noted that, without conflict, the embodiments and features in the embodiments of the present invention can also be combined with each other.

[0087] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. In the description of this invention, the terms "first," "second," "third," "fourth," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0088] Based on the above in-depth analysis, this invention provides a method for inverting and calculating the heat transfer characteristic parameters of a ladle and a method for calculating the temperature drop of molten steel. First, a three-dimensional finite-difference heat transfer positive model of the ladle is established to simulate the temperature field changes over time during the predetermined baking period and N heats (e.g., 10 heats) before online turnover, obtaining the initial error calculation distribution. Then, based on the Levenberg-Marquardt (LM) algorithm and the heat transfer characteristic parameter correction method of the inverse heat transfer problem, the characteristic parameters are corrected by simultaneously correcting the heat transfer coefficients of the inner and outer walls during the baking stage. Finally, based on the ladle temperature field data corrected by the inverse heat transfer problem, the heat flux density of spatial nodes near the inner surface is calculated during the ladle baking and online turnover stages, and the temperature drop of molten steel during the re-ladle stage of different heats is calculated. The results show that after parameter inversion correction, the average accuracy of the temperature correction values ​​at the temperature measurement points is improved by 3.24% and 10.15% during the baking and online operation stages, respectively. Further analysis shows that the heat storage characteristics of the ladle lining during turnover directly affect the temperature drop of the molten steel. The temperature drop in the first heat reached 170.02K, and stabilized at 90.55K by the 10th heat, providing reliable technical support for online monitoring of the ladle temperature field and optimization of the turnover process.

[0089] like Figure 1 As shown, the method for inverting and calculating the heat transfer characteristic parameters of the ladle includes the following steps:

[0090] Step S11: Obtain and simplify the geometric structural parameters and refractory material thermal property parameters of the ladle, and construct a three-dimensional model of the ladle based on the geometric structural parameters.

[0091] In this step, the geometric parameters of the ladle include the ladle structure, material, and dimensions. In this embodiment, the ladle structure is simplified, as follows: Figure 2 As shown, the refractory material comprises a three-layer structure: a working layer (spinel brick) 1, a permanent layer (spinel castable) 2, and a steel shell 3. The thermal parameters of the refractory material are described using a simplified three-layer structure, including material type, thermal conductivity, specific heat, and density.

[0092] Step S12 simplifies the ladle turnover process into three working conditions: baking, refilling, and empty ladle, and determines the boundary conditions for each working condition; at the same time, it determines all process stages that need to be calculated by inversion of heat transfer characteristic parameters, including the baking stage and the refilling and empty ladle stages of the first N turnover furnaces in operation.

[0093] In this step, such as Figure 3 As shown, the heat transfer boundary conditions differ in different processes during ladle turnover. For ease of calculation, the ladle turnover process is simplified into three stages: baking, refilling, and empty ladle. Ladle covers are used for insulation during the baking, refilling, and empty ladle stages. In actual production, during the first N heats of ladle operation (typically N=10), the ladle lining continuously accumulates heat, exhibiting a non-steady-state temperature field that affects precise control of the molten steel temperature. As the number of turnovers increases, the molten steel temperature drop tends to stabilize by the Nth heat. Therefore, it is generally necessary to calculate the heat transfer characteristic parameters for the first N heats to accurately predict the molten steel temperature drop during formal production. Based on the ladle turnover process, all process stages requiring inversion calculation of heat transfer characteristic parameters include the baking stage and the refilling and empty ladle stages during the first N heats of operation. Taking a baking time of 14 hours and 10 batches as an example, the time nodes corresponding to the parameters are the end of each hour of baking, the end of the repacking of each batch, and the end of the space, which correspond to a total of 34 predicted time points and 34 sets of heat transfer characteristic parameters.

[0094] When determining the boundary conditions for each working condition, heat exchange occurs between the refractory lining materials inside the ladle through thermal conduction. The initial temperature field of the ladle is room temperature. During the baking stage and the empty ladle stage, the inner and outer walls of the ladle are subject to the third type of boundary conditions. During the refilling stage, the inner wall of the ladle is subject to the first type of boundary conditions, the temperature of the molten steel is the inner wall temperature, and the outer wall is subject to the third type of boundary conditions.

[0095] Step S13: Mesh the three-dimensional model of the ladle into a spatial discrete structure composed of several nodes. The nodes include internal nodes, first-type boundary nodes, and second-type boundary nodes. Each internal node has its own unit control volume and distribution of adjacent nodes. The first-type boundary nodes are located on the intersection lines of the surface of the three-dimensional model of the ladle, and the second-type boundary nodes are located on the surface of the three-dimensional model of the ladle.

[0096] In this step, such as Figure 4 As shown, the element control volume and adjacent node distribution of each internal node A are as follows: Each internal node A has its own element control volume Δx×Δy×Δz; it has adjacent nodes O, L, N, D, W, and E in all six directions (front / back, up / down, left / right); the heat exchange of these internal nodes is expressed in finite difference form; the node arrangement adopted is a structured regular mesh. Figure 5 As shown, the first type of boundary node B and the second type of boundary space node C exchange heat with the surrounding environment through convection, and the heat transfer coefficient is... Each boundary node has no internal heat source, and its heat transfer calculation difference equation is derived from the energy conservation law of the control volume. The first type of boundary node B(i,j,k) is located on the intersection line on the model surface, with a length of... Width is Height is The primitive body; the second type of boundary node C(i,j,k) lies on the model surface and has a length of Width is Height is The metabody.

[0097] Step S14: Based on the heat conduction control equation and the divided nodes, construct a calculation model for the finite difference heat transfer problem of the ladle.

[0098] This step specifically includes:

[0099] Step S141: Make conditional assumptions for the physical model and heat transfer model of the ladle, and define the heat transfer parameters and boundary conditions.

[0100] Before constructing the heat transfer model of the nodes based on the heat conduction governing equation, the heat transfer boundary conditions during the actual turnover of the ladle are complex and variable, and the refractory lining undergoes complex physicochemical changes with the molten steel, leading to changes in the thermophysical parameters of the refractory material. To ensure the smooth and efficient heat transfer calculation, the following assumptions are made regarding the physical model of the ladle and its heat transfer model:

[0101] The molten steel remains stable during the process of receiving molten steel in a ladle, and the phenomenon of molten steel stratification is not considered.

[0102] The ladle lining is considered as a cylinder, and unsteady heat transfer is performed.

[0103] The heat transfer boundary conditions of thermal radiation and thermal convection are transformed into a comprehensive heat transfer coefficient.

[0104] The thermal deformation of the interface between different refractory material layers and the changes in thermal properties caused by thermal deformation during the turnover of the steel ladle are ignored.

[0105] The ambient air temperature remains constant during the turnover of the steel ladle.

[0106] Secondly, the heat transfer state during the ladle turnover process is complex and variable. The heat transfer boundary conditions on the inner wall are constantly changing, while the heat transfer boundary conditions on the outer wall are relatively stable. This includes convective and radiative heat transfer. The amount of radiated energy from an actual object is mainly related to its temperature, and the calculation of the radiation coefficient is complex. Based on measured temperature data, the temperature of the outer wall of the ladle during turnover will not exceed 350℃, and the radiative heat transfer coefficient between it and the surrounding environment is relatively small. Therefore, convective heat transfer is the main heat dissipation method between the outer wall of the ladle and the surrounding environment. In actual heat transfer calculations, the radiative heat transfer coefficient is usually converted into a comprehensive heat transfer coefficient. The relevant formulas for calculating the heat transfer coefficient are defined as follows:

[0107] (1)

[0108] (2)

[0109] (3)

[0110] (4)

[0111] In equations (1)-(4), The number is the Nusselt number, and the subscript m indicates the Nusselt number at the qualitative temperature; The qualitative temperature is the arithmetic mean of the boundary layer fluid temperature and the sidewall temperature. , The wall temperature, The ambient temperature; P is the coefficient of volume expansion; r For the boundary layer fluid; The kinematic viscosity of the boundary layer fluid, in m³. 2 / s; The thermal conductivity of the boundary layer fluid is expressed in W / (m·K). Prandtl number, kinematic viscosity, and thermal conductivity are obtained from tables. K and n are constants, related to factors such as the shape and location of the heat transfer surface and the flow regime. g and h are the gravitational acceleration and characteristic length, respectively; in the calculation, g is taken as 9.81 m / s². 2 ; The heat transfer coefficient of the ladle wall is denoted as .

[0112] The heat transfer boundary conditions for the ladle were obtained from the convective heat transfer calculation formula and Fluent simulation. The heat transfer boundary conditions during the 14-hour ladle baking and the first 10 heats before online turnover are shown in Table 1.

[0113] Table 1 Heat transfer boundary conditions for ladle lining

[0114]

[0115] Step S142: Based on the assumed conditions, the heat transfer process of the ladle is described by the three-dimensional unsteady heat conduction partial differential control equation in the rectangular coordinate system.

[0116] The three-dimensional unsteady heat conduction partial differential governing equation in the rectangular coordinate system is:

[0117] (5)

[0118] In equation (5), Density, unit: kg / m³ 3 c represents specific heat, measured in J / (kg·K). is the thermal conductivity, with units of W / (m·K); As the source term, it is assumed that the ladle lining has no internal heat source, i.e. =0.

[0119] Step S143: Based on the spatial discrete structure, the Taylor expansion method is applied to replace the derivatives in the heat conduction partial differential control equations with difference approximation expressions. The first derivative is subjected to first-order forward difference processing, and the second derivative is subjected to second-order central difference processing, to obtain the heat transfer difference expressions for internal nodes, the heat transfer difference expressions for the first type of boundary nodes, and the heat transfer difference expressions for the second type of boundary nodes, respectively.

[0120] In this step, a heat transfer differential model is constructed for each node using the above method, but the internal nodes, the first type of boundary nodes, and the second type of boundary nodes have different parameters.

[0121] For internal node A, the differential heat transfer expression is:

[0122] (6)

[0123] In equation (6), T A T O T L T W T E T N T D These represent the temperature values ​​of the corresponding index nodes at time t. This represents the temperature value at node A at time t+Δt. ; .

[0124] Preferably, when the model in the three-dimensional Cartesian coordinate system has a uniform grid spacing, i.e. Then, equation (6) can be simplified to:

[0125] (7)

[0126] In equation (7), For Fourier numbers, .

[0127] The inner and outer walls of the ladle are under the first or third type of heat transfer boundary conditions. If only the heat transfer difference equations for the internal node A that conducts heat are established, the heat transfer difference equations are not closed and cannot be solved. Therefore, the heat transfer difference equations for the first type of boundary node B located on the intersection line of the surfaces and the second type of boundary node C located on the surface are constructed under the third type of heat transfer boundary conditions to close the equations and thus complete the solution of the temperature field of the ladle.

[0128] like Figure 5 As shown, when both the first type of boundary node B and the second type of boundary node C located on the surface exchange heat with the surrounding environment through convection, the heat transfer coefficient is: Since there are no internal heat sources at any of the spatial nodes at the boundaries, the heat transfer calculation difference equation is derived from the energy conservation law of the control volume.

[0129] Among them, the first type of boundary node B(i,j,k) is located on the intersection line on the model surface and is of length. Width is Height is The unsteady-state heat transfer difference equation of the element is shown in equation (8):

[0130] (8)

[0131] The second type of boundary node C(i,j,k) lies on the model surface and is of length [missing information]. Width is Height is The element, its unsteady heat transfer difference equation (9) is shown:

[0132] (9)

[0133] In equation (9), ; ; , The ambient temperature.

[0134] Preferably, similar to the difference expression for internal node A, when the spatial node mesh is uniformly divided, i.e. Figure 5 middle Then, equations (8) and (9) can be rearranged into equations (10) and (11) respectively:

[0135] (10)

[0136] (11)

[0137] In equations (10)-(11), For Fourier numbers, ; For the Pythagorean theorem, ; The surface heat transfer coefficient is expressed in W / (m²). 2 ·K).

[0138] Therefore, the heat transfer difference equations of internal node A, first-type boundary node B, and second-type boundary node C together constitute the finite difference heat transfer forward problem calculation model.

[0139] Step S15: Verify the independence of the grid and time step for the finite difference heat transfer forward problem calculation model, and solve the ladle temperature field based on the optimal discrete parameters.

[0140] Based on the temperature changes during the first hour of ladle baking, the independence of the mesh for differential heat transfer calculation of the ladle lining is verified. During the independence verification, four meshing methods are set, and the temperature values ​​of the nodes are calculated according to the finite difference heat transfer forward problem calculation model under each meshing method. Then, the optimal discrete parameters are obtained based on the accuracy and calculation speed of the calculation results.

[0141] The four grid division methods are set as follows: Method 1 =20 mm =5 s; in method 2 =30 mm =5 s; in method 3 =30 mm =10 s; in method 4 =40 mm =10 s.

[0142] Of the four mesh generation methods, Method 1 has the smallest spatial and temporal step size and the best accuracy. Using the temperature calculation result from Method 1 as the standard value, the temperature calculation result from Method 3 is closest to Method 1, followed by Method 2. Method 4 has the sparsest mesh and the largest temperature error compared to the other three sets of temperature calculations. Therefore, Mesh Generation Method 4 is discarded. The computation time for Method 1 is three times that of Method 2 and six times that of Method 3. Considering both accuracy and computation speed, =30 mm =10 s is the optimal choice for mesh generation in numerical calculations of the temperature field of a ladle.

[0143] Based on the above verification results, the following approach is adopted. =30 mm With a mesh generation parameter of 10 s, a forward problem was used to solve the temperature field of the ladle during the entire baking process (14 hours) and the first 10 cycles of operation, obtaining the initial temperature field distribution. This initial temperature field will serve as the basis for parameter inversion in the subsequent heat transfer inverse problem, used to construct the objective function and sensitivity analysis.

[0144] Step S16: Based on the solved ladle temperature field, the LM algorithm is used to construct a heat transfer characteristic parameter inversion calculation model.

[0145] In this step, the optimization problem calculation based on the Levenberg-Marquardt (LM) algorithm can be viewed as a combination of the Gauss-Newton method and the gradient descent method. It possesses the advantages of the Gauss-Newton method—fast convergence and resistance to local optima—and the characteristic of the gradient descent method—stable approximation of the optimal solution. This step uses the LM algorithm to invert the heat transfer characteristic parameters of the ladle temperature field. The process of constructing the heat transfer characteristic parameter inversion calculation model is as follows:

[0146] Step S161: Construct a temperature objective function based on the ladle temperature field.

[0147] (12)

[0148] In equation (12), Let I be the objective function; I be the number of time steps; for The actual measured temperature value at each temperature measurement point at any given time; for The calculated temperature values ​​at each measurement point are given. P represents the set of heat transfer characteristic parameters of the ladle, corrected by the inverse heat transfer problem, containing n heat transfer characteristic parameters p1, p2, ..., p. n In this embodiment, depending on the calculation scheme, parameter P includes parameters representing different times during ladle turnover. The temperature of the flue gas during the baking stage The heat transfer coefficient of the inner wall during the baking stage External wall heat transfer coefficient .

[0149] Temperature objective function Represented in matrix form:

[0150] (13)

[0151] In equation (13), Let be the measured temperature vector. To calculate the temperature vector, This is the residual vector.

[0152] Step S162: Set the partial derivative of the temperature objective function with respect to the heat transfer characteristic parameter P of the ladle to 0, construct a partial differential equation, and introduce the Jacobian matrix into the equation.

[0153] In this step, the partial differential equation of the temperature objective function is as follows:

[0154] (14)

[0155] Introducing the Jacobian matrix:

[0156] (15)

[0157] In equation (15), The Jacobian matrix is ​​key to the LM algorithm's iterative solution of optimization problems. This is the matrix representation of the partial differential equation of the temperature objective function, i.e., the gradient vector of the objective function with respect to the parameter vector P, whose components correspond to the partial derivatives in the directions of each parameter.

[0158] Step S163: Expand the Jacobian matrix to construct a sensitivity matrix, and divide the sensitivity matrix into blocks according to the process stage to establish the sensitivity relationship between the residual and the heat transfer parameters, so as to characterize the partial derivative law of temperature changing with the heat transfer parameters.

[0159] The Jacobian matrix expansion is as follows:

[0160] (16)

[0161] For ease of representation, the sensitivity matrix is ​​constructed using the transposed Jacobian matrix and divided into blocks, as shown below:

[0162] (17)

[0163] In equation (17), the elements in the transposed Jacobian matrix are... For sensitivity coefficients; T1,…,T H T represents the temperature at sampling time points 1 to H during the baking stage, representing the heat transfer characteristic parameters. H+1 ,…, T I This represents the temperature of the heat transfer characteristic parameters sampling points H+1~I during the online operation phase; These are the calculated temperature values ​​for each time point. For the heat transfer characteristic parameter P of the ladle j The partial derivatives are expressed as The solution is obtained using the finite difference method, and the calculation formula is as follows:

[0164] (18)

[0165] In equation (18), the parameter disturbance value is solved. Where n=3, and the three heat transfer characteristic parameters P j T respectively gas α wl and α shell T i In, i=1,2,…,34.

[0166] In the process of constructing the sensitivity matrix, the ladle turnover process is divided into blocks, namely the baking block and the online operation block. In the matrix of Equation (17), the first H rows correspond to the ladle baking stage, and the H+1 to I rows correspond to the end time of the refilled ladle and the end time of the empty ladle in the first N heats of the ladle online operation stage. In Equation (17) of this embodiment, taking the first 10 heats with N=10 as an example, the first 14 rows of the matrix correspond to the temperature measurement points in the ladle baking stage; the 15th to 34th rows correspond to the ladle online operation stage, including the end time of the refilled ladle and the end time of the empty ladle in the first 10 heats.

[0167] The block partitioning in this step refers to dividing the entire sensitivity matrix into stages based on different operating conditions during the ladle turnover process, so that the sensitivity of different process stages is distributed in the matrix as independent sub-blocks. This approach avoids mutual interference between residuals from different stages in the full-time objective function, ensuring better stability and convergence of the LM iteration in each stage. Simultaneously, different sub-blocks correspond to the physical characteristics of different processes, facilitating targeted adjustments to parameters such as the heat transfer coefficients of the inner and outer walls, thereby improving the accuracy of temperature field calculations and the engineering interpretability of the results.

[0168] Step S164: Based on the temperature objective function and the sensitivity matrix, set the iterative update rules for the heat transfer characteristic parameters to gradually correct the heat transfer characteristic parameters; to ensure the stability and finite-step convergence of the iterative calculation process, introduce an adaptive adjustment mechanism for the damping coefficient and set a convergence criterion.

[0169] In this step, the iterative update rules include:

[0170] Will The expression is represented as:

[0171] (19)

[0172] Equation (19) is solved through iterative calculation to update the value of the heat transfer characteristic parameter P. In the specific iteration process, only the corresponding block of the sensitivity matrix and the residual vector are called to participate in the calculation according to the current process stage, and the other blocks do not participate in the calculation at this stage. The temperature vector T(P) formed by the temperature calculation values ​​of the temperature measurement points is Taylor expanded near P in the k-th iteration:

[0173] (20)

[0174] In equation (20) Let be the calculated temperature value of the measuring point and the sensitivity matrix at the k-th iteration, respectively. Substituting the above formula into... From the expression, we can obtain the iterative equation for the heat transfer characteristic parameter P to be determined:

[0175] (twenty one)

[0176] In equation (21), express The transpose of .

[0177] The iterative calculation formula (21) requires the matrix It is a non-singular matrix, that is, it is required that The LM algorithm avoids To make it a non-singular matrix, perform the following processing:

[0178] (twenty two)

[0179] In equation (22), These are the heat transfer characteristic parameters solved in the previous and current rounds, respectively; The damping coefficient; It is a unit diagonal matrix. .

[0180] Introducing an adaptive damping coefficient adjustment mechanism, by controlling ,ensure The positive definiteness of the result ensures the convergence speed and convergence of the iterative calculation.

[0181] The convergence criterion is set as follows:

[0182] Changes in the parameters to be solved in two iterations for:

[0183] (twenty three)

[0184] The LM algorithm's iteration termination condition is: the change in the parameters to be solved between adjacent iterations is sufficiently small; the iteration termination condition of the LM algorithm is set as: the change in the parameter vector to be solved between two adjacent iterations is less than the preset convergence accuracy, i.e., it satisfies...

[0185] (twenty four)

[0186] In equation (24), and The first Second and third The heat transfer characteristic parameter vector obtained from the next iteration. When this condition is met, the algorithm is considered to have converged, and the iteration stops.

[0187] Step S17: Based on the constructed heat transfer characteristic parameter inversion calculation model, perform heat transfer inverse problem correction calculation on the heat transfer characteristic parameters of the ladle temperature field to obtain the corrected heat transfer characteristic parameters.

[0188] This step specifically includes: determining the current process stage (such as baking, repacking, or empty ladle) and its duration based on the ladle turnover process, and using Table 3 as the parameters to be inverted. An initial value P0 is assigned as the starting point for iterative calculations; simultaneously, a damping coefficient and a convergence accuracy threshold are set, preferably, the convergence accuracy... Set to 10 -10 ;like Figure 6 As shown, the P0 is input into the heat transfer characteristic parameter inversion calculation model, and the corrected heat transfer characteristic parameters are output until the model converges, thus obtaining the optimal heat transfer characteristic parameters and the corrected temperature field for this stage.

[0189] Step S18: Determine whether the current process stage is the last process of all processes in the first N turnover furnace cycles of baking and online operation; if not, proceed to step S17; if yes, all stages are completed, and output the heat transfer characteristic parameters and temperature field calculation results after full process correction.

[0190] In this step, during the actual production process, during the first N heat cycles of the ladle's operation (where N is preferably 10), the ladle lining continuously accumulates heat, resulting in a non-steady-state temperature field that affects the precise control of the molten steel temperature on-site. However, as the number of cycles increases, the temperature drop of the molten steel tends to stabilize by the 10th heat cycle. The study of ladle baking and the first 10 heat cycles before operation captures the most critical dynamic heat transfer process and meets the specific monitoring needs of steel mills for ladles in actual production.

[0191] Based on the inversion calculation method of the heat transfer characteristic parameters of the ladle described above, this embodiment of the invention also provides a method for calculating the temperature drop of molten steel during the ladle turnover process. The method for calculating the temperature drop of molten steel includes the following steps:

[0192] Step S21: Calculate the heat flux density of the ladle lining based on the heat transfer characteristic parameters calculated by the inversion calculation method of the ladle heat transfer characteristic parameters and the ladle temperature field.

[0193] In this step, based on the ladle temperature field data calculated using the forward problem of heat transfer within the ladle lining, the heat flux density of the ladle lining can be determined. This reflects the heat exchange between the ladle lining and the high-temperature molten steel. Accurate heat flux density values ​​on the ladle inner wall are beneficial for improving the accuracy of molten steel temperature prediction and ensuring product quality. The formulas for calculating the heat flux density and heat exchange between the ladle inner wall and the high-temperature molten steel are as follows:

[0194] (25)

[0195] (26)

[0196] In equations (25)-(26), A is the thermal conductivity of the ladle lining, expressed in W / (m·K); s This refers to the inner wall area of ​​the ladle, in meters (m²). 2 q represents heat flux density, with units of W / m³. 2 ; This represents the heat exchange between the ladle lining and the molten steel, expressed in W.

[0197] Step S22: Based on the calculated heat flux density of the inner wall of the ladle and adjacent spatial nodes, the duration of the ladle under reloading conditions, and other parameters, calculate the temperature drop of the molten steel inside the ladle under reloading conditions. The calculation formula is as follows:

[0198] (27)

[0199] (28)

[0200] In equations (27)-(28), Q is thermal energy in J; m is the mass of molten steel, which is 120 t; and c is the specific heat capacity, which is 879 J / (kg·K). The solution is to calculate the temperature drop of the molten steel, i.e., to solve for the parameters.

[0201] The method for inverting the heat transfer characteristic parameters of a ladle and the method for calculating the temperature drop of molten steel described in this embodiment of the invention are applied to the calculation of the heat transfer characteristic parameters and the calculation of the temperature drop of molten steel in a 130t ladle at a steel plant.

[0202] like Figure 2As shown in Table 2, the simplified structural dimensions of a 130t steel ladle from a steel plant are illustrated using a quarter-section structure as an example.

[0203] Table 2 Simplified ladle dimensions

[0204]

[0205] The thermophysical properties of refractory materials required for heat transfer calculations in the temperature field of steel ladles are shown in Table 3.

[0206] Table 3. Thermophysical properties of refractory lining materials for steel ladles

[0207]

[0208] like Figure 7 As shown, the temperature changes of spatial nodes at different locations on the sidewall during the ladle baking stage are as follows: Node 1 is located on the inner surface of the ladle sidewall; the radial distance from Node 2 to the inner surface of the ladle sidewall is 120 mm; the radial distance from Node 3 to the inner surface of the ladle sidewall is 240 mm; and Node 4 is located on the outer surface of the ladle sidewall. The closer the spatial node is to the inner surface of the ladle sidewall, i.e., the closer it is to the heat source (baking flue gas), the higher its temperature. After baking for 7–9 hours, the temperature gradient between the spatial nodes on the inner and outer walls of the ladle (i.e., the temperature difference between nodes 1 and 4) reaches its maximum of 579 K.

[0209] like Figure 8 As shown, the ladle was put into operation after 14 hours of baking. The temperature changes of the four spatial nodes in the first 10 heats of ladle operation are as follows: the closer the spatial node is to the inner surface of the ladle, the greater the temperature fluctuation after switching between a loaded and an empty ladle. Spatial nodes 1 and 2, which are closer to the inner surface of the ladle, have higher temperatures during the loaded stage than in the empty stage, showing an alternating pattern of rising and falling temperatures. However, as the number of heats increases, spatial nodes 1 and 2 generally show a trend of heat storage and temperature increase, indicating that the heat storage capacity is stronger during the loaded stage and weaker during the empty stage in the first 10 heats. Spatial nodes 3 and 4, which are farther from the inner wall of the ladle, show a continuous temperature increase during the first 10 heats of ladle operation, indicating that they are always in a heat storage state. In summary, the ladle is generally in a heat storage state during the first 10 heats of operation, but the patterns of heat storage or heat dissipation at different radial locations inside the ladle are different.

[0210] like Figure 9As shown, the errors between the calculated and measured temperatures at the temperature measurement points during the ladle baking stage are as follows: Using the measured values ​​at the temperature measurement points on the outer wall of the ladle as the standard, the average accuracy of the calculated temperature during the baking stage is 95.32%, with a root mean square error of 9.91 K. The maximum temperature error occurs at 14 hours, at 18.92 K. During the ladle's online operation stage, the average accuracy of the calculated temperature is 89.45%, with a root mean square error of 22.08 K. The maximum temperature error occurs at the end of the first re-ladle reloading, at 53.75 K. Temperature errors at the end of each re-ladle reloading are relatively large. Therefore, correcting the heat transfer characteristic parameters through the inverse heat transfer problem is key to improving the accuracy of temperature field calculations.

[0211] Because unsteady-state heat transfer is diffusion-type, it exhibits damping and delay characteristics. The inversion correction of heat transfer calculation characteristic parameters should be performed sequentially over time, rather than a single inversion calculation covering the entire time range. In the process of correcting heat transfer characteristic parameters using the inverse heat transfer problem, the known quantities are the measured temperature values ​​at the measurement points and the calculated temperatures obtained from the forward heat transfer problem. Unknown quantities include: the heat transfer coefficient of the inner wall during the baking stage, the heat transfer coefficient of the outer wall, and the temperature of the baking flue gas. Since the thermal conductivity, specific heat capacity, density, and other heat transfer characteristic parameters of the ladle material have been accurately obtained through experimental testing, while the heat transfer coefficient of the inner wall, the heat transfer coefficient of the outer wall, and the temperature of the baking flue gas during the baking stage are difficult to obtain accurately, they are treated as unknown quantities. In specific calculations, any one or any combination of the above unknown quantities can be used for the inversion calculation.

[0212] To determine which combination is better, this embodiment sets the inversion parameters to the five groups in Table 4.

[0213] Table 4 Calculation Scheme for Heat Transfer Characteristic Parameters of Steel Ladle

[0214]

[0215] Because the temperature at the external wall measuring point exhibits a delayed and damped effect on the change in the heat transfer boundary conditions of the internal wall, and because the calculated temperature at the measuring point is significantly lower than the measured value after 11 hours of ladle baking, the objective function S(P) for correcting the baking flue gas temperature and the internal wall heat transfer coefficient during the baking stage in schemes 2, 3, 4, and 5 is composed of the calculated and measured temperature values ​​at the measuring point at the end of 11 hours of baking. In contrast, the correction of the external wall heat transfer coefficient in schemes 1, 4, and 5 is performed according to the ladle turnover time sequence, and the objective function S(P) is composed of the calculated and measured temperature values ​​at different times.

[0216] Temperature correction values ​​at measurement points after inversion correction during the baking stage are as follows: Figure 10 As shown, using the measured temperature value at the temperature measuring point as the standard, the error of the temperature correction value is as follows: Figure 11As shown, compared to the initial calculated temperature values, the temperature correction curves of schemes 2 and 3 deviate significantly from the measured temperature curves, indicating large errors in the temperature correction values. After inversion corrections using schemes 1, 4, and 5, the temperature correction values ​​at the measurement points during the baking stage show good fit with the measured temperature values. During the 10-11 h baking stage, among the five temperature correction schemes, schemes 2 and 3 exhibit the smallest errors in temperature correction values. However, during the 1-10 h and 11-14 h baking stages, the temperature correction errors of schemes 2 and 3 are significantly higher than the other three groups and also higher than the initial calculated temperature values.

[0217] During the ladle baking stage, the maximum errors in temperature correction values ​​for schemes 2 and 3 were 41.87 K and 40.64 K, respectively. Using the measured temperature as the standard, the accuracy of the temperature correction values ​​at the measurement points for schemes 2 and 3 during the baking stage was 91.44% and 91.69%, respectively, representing an improvement of -3.88% and -3.63% compared to the average accuracy of the initial temperature calculation values. After inversion correction for schemes 1, 4, and 5, the temperature correction values ​​at the measurement points during the baking stage showed a better fit with the measured temperature values. The maximum temperature errors occurred within 7–12 hours, at 18.87 K, 6.42 K, and 6.56 K, respectively. The average accuracy of the temperature correction values ​​for schemes 1, 4, and 5 was 95.87%, 98.51%, and 98.56%, respectively, representing improvements of 0.55%, 3.19%, and 3.24% compared to the average accuracy of the initial temperature calculation values.

[0218] During the ladle's online operation phase, the temperature correction values ​​for the measuring points after inversion calculation are as follows: Figure 12 As shown, using the measured temperature at the temperature measuring point as the standard, the error between the temperature correction value and the measured value is as follows: Figure 13 As shown in the figures, combining the two figures, we can conclude that compared to the initial temperature calculation values, the temperature correction values ​​of schemes 2 and 3 have significantly higher errors than the other three groups. After inversion correction, schemes 4 and 5 show the best fit between the temperature correction values ​​at the measurement points and the measured temperature values. The temperature correction curve of scheme 1 has the second best fit with the measured temperature curve, after schemes 4 and 5.

[0219] Within the first 10 heats after the ladle went online, the temperature correction values ​​at the measuring points of Schemes 2 and 3 had larger errors, with maximum errors of 37.41 K and 38.89 K, respectively. The average accuracy of the temperature correction values ​​was 92.66% and 92.37%, respectively, which was an improvement of 3.21% and 2.92% compared to the average accuracy of the initial temperature calculation values. The temperature correction values ​​of Schemes 1, 4, and 5 had smaller errors, with maximum errors of 4.56 K, 3.88 K, and 2.33 K, respectively. The average accuracy of the temperature correction values ​​at the measuring points was 99.18%, 99.34%, and 99.6%. Compared to the initial calculated temperature values ​​at the measuring points, after corrections using Schemes 1, 4, and 5 during the ladle online operation phase, the average accuracy of the temperature correction values ​​at the measuring points improved by 9.73%, 9.89%, and 10.15%, respectively, demonstrating a good temperature correction effect.

[0220] Evaluation of the accuracy of the calculated heat transfer characteristic parameters. To verify the accuracy of the temperature correction values ​​of different inversion schemes, the measured temperature values ​​at the temperature measurement points on the outer wall of the ladle were used as the standard values. The root mean square error was used to evaluate the accuracy of the above five groups of ladle heat transfer inverse problem calculation schemes. The results are shown in Tables 5 and 6.

[0221] Table 5. Errors in the calculated temperatures of the ladle's outer wall measuring points during the baking stage.

[0222]

[0223] Table 6. Errors in the Calculated Temperature Values ​​of the Ladle Outer Wall Temperature Measurement Points During the Online Operation Phase

[0224]

[0225] Compared to the direct heat transfer problem calculation, the root mean square error (RMSE) actually increased after corrections using schemes 2 and 3 during the baking stage, and the accuracy of the temperature correction values ​​within the ±3 K and ±5 K ranges also decreased. Compared to the direct heat transfer problem, the RMSE of schemes 1, 4, and 5 decreased to varying degrees, and their accuracy improved. During the ladle operation phase, the RMSE of the temperature correction values ​​of all five heat transfer inverse problem calculation schemes decreased, especially the accuracy of the temperature calculation values ​​of schemes 1, 4, and 5, which significantly improved. A comprehensive analysis is shown in Tables 5 and 6. Compared to schemes 1, 2, and 3, which used inversion calculations based on a single heat transfer characteristic parameter, schemes 4 and 5, which used inversion corrections based on multiple heat transfer characteristic parameters, showed significantly higher accuracy and better temperature correction effects.

[0226] The changes in temperature and heat flux density at adjacent spatial nodes on the inner wall of the ladle during the baking stage are as follows: Figure 14As shown, in the initial stage of baking, the initial temperature of the ladle is relatively low, the temperature difference between the inner wall and the baking flue gas is large, and the heat flux density between the inner wall and adjacent spatial nodes reaches its maximum. As the baking time increases, the temperature of the ladle lining rises, and the heat flux density gradually decreases. During the baking stage, the ladle is in a continuous heat storage state with a strong heat storage capacity.

[0227] The changes in temperature and heat flux density of the inner surface of the ladle sidewall and adjacent spatial nodes during the first 10 heats of ladle operation are as follows: Figure 15 As shown in the diagram. During the re-boiling stage of the ladle's operation, the inner wall of the ladle is in direct contact with the high-temperature molten steel, causing the temperature of the inner wall and adjacent spatial nodes to rise rapidly to their maximum value, while the heat flux density between the inner wall and the nodes decreases significantly. The temperature and heat flux density changes of the inner wall and adjacent spatial nodes during the re-boiling stage of each heat are shown in the diagram. Figure 16 As shown.

[0228] Combination Figure 15 and Figure 16 It can be seen that during the first 1-3 heats of ladle operation, although the heat flux density of adjacent spatial nodes on the inner wall of the ladle gradually decreases, it is still significantly higher than that of heats 4-10, indicating that the ladle is still in a state of significant heat storage. During heats 3-5, the temperature of adjacent spatial nodes on the inner wall of the ladle rises slowly, and the heat flux density decreases slightly; during this stage, the ladle lining is in a state of slow heat storage. During heats 5-10, as the number of ladle cycles increases, the temperature of the ladle lining reaches its maximum, and the temperature gradient between the lining and the high-temperature molten steel decreases. During this stage, the temperature rise of the ladle is relatively small, and the inner wall of the ladle and adjacent spatial nodes are in a state of continuous heat storage and dissipation equilibrium.

[0229] according to Figure 16 The heat flux density values ​​between the inner surface of the ladle and adjacent spatial nodes, calculated in the calculation, can be used to determine the temperature drop of molten steel during the re-ladle stage in the first 10 heats before the ladle is put into service. Figure 17 As shown in the diagram. During the re-running phase of the ladle, the high-temperature molten steel is in direct contact with the inner wall of the ladle. In the first heat cycle, the inner lining temperature is relatively low, resulting in the strongest heat storage capacity and the largest temperature drop in the molten steel, at 170.02 K / heat. After three heat cycles, the ladle lining temperature continuously rises, and the heat exchange between it and the molten steel gradually decreases, with the temperature drop in each heat decreasing to below 100.00 K. From the 4th to the 10th heat cycles, the temperature drop in the molten steel ranges from 90.55 to 103.46 K / heat. The variation in molten steel temperature drop during each re-running phase with the re-running time is shown in the diagram. Figure 18 As shown.

[0230] As Figure 18It can be concluded that the temperature drop of molten steel during the ladle turnover and re-bundling stage is similar to the change curve of the heat flux density on the inner wall. The temperature drop is largest at the beginning of each re-bundling stage, and then gradually decreases to a stable state. Due to the low temperature of the ladle lining in the first three heats, the large amount of heat stored in the ladle lining results in a larger temperature drop of molten steel during this stage. In the first 10 minutes of the first heat, the temperature drop of molten steel is the largest, at 2.51 K / min. At the end of the first heat, the temperature drop of molten steel drops to 1.01 K. After the third heat, the temperature drop of molten steel gradually stabilizes. At the beginning of each re-bundling stage, the temperature drop of molten steel is in the range of 1.18-1.35 K / min. As the re-bundling time increases, the temperature drop of molten steel gradually decreases, and at the end of the re-bundling stage, the temperature drop of molten steel stabilizes in the range of 0.62-0.71 K / min.

[0231] As can be seen from the above technical solutions, the ladle heat transfer characteristic parameter inversion method and molten steel temperature drop calculation method provided in this embodiment of the invention, by establishing a three-dimensional finite difference heat transfer model and combining it with the LM algorithm, systematically studied the heat transfer characteristics and temperature field evolution law during the ladle turnover process. This includes: for different heat transfer boundary conditions of the ladle lining during the turnover process, establishing an explicit difference equation for three-dimensional unsteady-state heat transfer calculation based on the finite difference method, simulating the temperature field changes over time during the 14-hour ladle baking and the first 10 heats before online turnover. During the ladle online operation stage, the closer the spatial node is to the inner surface of the ladle, the greater the temperature fluctuation during the refill and empty ladle stages; establishing a calculation model for correcting the heat transfer characteristic parameters of the ladle lining based on the LM algorithm, correcting the heat transfer characteristic parameters during the baking stage and the first 10 heats before online operation. Using the measured temperature value at the temperature measurement point as the standard, the calculation accuracy and stability of five inversion correction schemes were compared systematically, and the optimal comprehensive performance was obtained by calculating the inner wall heat transfer coefficient and outer wall heat transfer coefficient during the synchronous correction baking stage as unknowns. The proposed scheme exhibits the lowest root mean square error (RMSE) in temperature correction during the baking stage (2.85 K) and the greatest improvement in accuracy during online operation (10.15%), achieving a 100% accuracy rate within a ±3 K range. Based on the heat transfer characteristic parameters corrected by Scheme 5, the heat transfer process during ladle baking and the first 10 heats of turnover was calculated, leading to the following conclusions: During the first 3 heats of ladle turnover, the heat flux density and molten steel temperature drop between the ladle inner wall and adjacent nodes were relatively large, ranging from 110.08 to 170.02 K per heat. The heat flux density and molten steel temperature drop between the inner wall and adjacent spatial nodes gradually decreased to a stable state with increasing ladle reloading time. By the end of the 10th heat, the molten steel temperature drop rate had decreased to 0.62 K / min.

[0232] The above description is merely a preferred embodiment of the present invention and an explanation of the technical principles employed, and is not intended to limit the scope of the claimed invention, but merely to illustrate preferred embodiments of the invention. Those skilled in the art should understand that the scope of the invention is not limited to the specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the inventive concept. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

Claims

1. A ladle heat transfer characteristic parameter inversion calculation method, characterized in that, The method comprises the following steps: Step S11, obtaining and simplifying the geometric structure parameters of the ladle and the thermal physical parameters of the refractory material, and constructing a three-dimensional model of the ladle according to the geometric structure parameters; Step S12, simplifying the ladle turnover process into three working conditions of baking, heavy ladling and empty ladling, determining the boundary conditions of each working condition; at the same time, determining all process stages including the baking stage and the heavy ladling and empty ladling stages of the first N turnover ladles in the online operation which need to be calculated by the heat transfer characteristic parameter inversion calculation; Step S13, meshing the three-dimensional model of the ladle into a spatial discrete structure composed of a plurality of nodes; Step S14, constructing a finite difference heat transfer positive problem calculation model of the ladle according to the heat conduction control equation and the divided nodes; Step S15, verifying the mesh and time step independence of the finite difference heat transfer positive problem calculation model, and solving the temperature field of the ladle based on the optimal discrete parameters; Step S16, constructing a heat transfer characteristic parameter inversion calculation model based on the solved temperature field of the ladle by using the LM algorithm; specifically comprising: Step S161, constructing a temperature objective function based on the temperature field of the ladle; Step S162, making the partial derivative of the temperature objective function with respect to the heat transfer characteristic parameter P of the ladle to be 0, constructing a partial differential equation, and introducing a Jacobian matrix into the equation, and the elements in the Jacobian matrix are sensitivity coefficients; Step S163, expanding the Jacobian matrix to construct a sensitivity matrix, and dividing the sensitivity matrix according to the process stages to establish the sensitivity relationship of the residual to the heat transfer parameters; Step S164, setting the heat transfer characteristic parameter iteration update rule based on the temperature objective function and the sensitivity matrix, introducing a damping coefficient adaptive adjustment mechanism into the iteration update rule, and setting a convergence criterion; Step S17, performing heat transfer inverse problem correction calculation on the heat transfer characteristic parameters of the ladle temperature field based on the constructed heat transfer characteristic parameter inversion calculation model, to obtain the corrected heat transfer characteristic parameters; Step S18, determining whether the current process stage is the last process of the baking and the first N turnover ladles before the online operation; if not, go to step S17; if yes, all stages are completed, and the corrected heat transfer characteristic parameters and the temperature field calculation results of the whole process are output.

2. The method of claim 1, wherein, In step S12, when determining the boundary limit conditions of each working condition, the heat exchange between the refractory materials of the ladle lining is carried out through heat conduction, the initial temperature field of the ladle is room temperature, and the third type of boundary condition is adopted for the inner and outer walls of the ladle in the baking stage and the empty ladling stage; the inner wall of the ladle is in the first type of boundary condition in the heavy ladling stage, the temperature of the molten steel is the temperature of the inner wall, and the outer wall is in the third type of boundary condition.

3. The method of claim 1, wherein, The nodes in step S13 include internal nodes, first type of boundary nodes and second type of boundary nodes, and the first type of boundary nodes are located on the surface intersection lines of the three-dimensional model of the ladle, and the second type of boundary nodes are located on the surface of the three-dimensional model of the ladle.

4. The method of claim 1, wherein, In step S14, the finite difference heat transfer positive problem calculation model of the ladle is constructed, specifically comprising: Step S141, making conditional assumptions for the physical model and the heat transfer model of the ladle, and defining the heat transfer parameters and the boundary conditions at the same time; Step S142, based on the assumption condition, a three-dimensional unsteady heat conduction partial differential control equation in the rectangular coordinate system is used to describe the heat transfer process of the ladle; Step S143, based on the spatial discrete structure, Taylor expansion method is applied to replace the derivative in the heat conduction partial differential control equation with a difference approximation expression, first-order derivative is processed by first-order forward difference, and second-order derivative is processed by second-order central difference, to obtain heat transfer difference expressions of internal nodes, first-type boundary nodes and second-type boundary nodes respectively; the heat transfer difference equations of the internal nodes A, the first-type boundary nodes B and the second-type boundary nodes C jointly constitute a finite difference heat transfer positive problem calculation model.

5. The method of claim 1, wherein, When the independence verification is performed in step S5, four grid division modes are set, and the temperature values of the nodes are calculated according to the finite difference heat transfer positive problem calculation model under each grid division mode; and according to the accuracy and calculation speed of the calculation results, the optimal discrete parameters are obtained.

6. The method of claim 1, wherein, The temperature objective function constructed in step S161 is as follows: (12) In formula (12), is the objective function; I is the number of time steps; is is the measured temperature value of the temperature measuring point at the moment; is is the calculated temperature value of the temperature measuring point at the moment, P is the set of steel ladle heat transfer characteristic parameters corrected by the inverse heat transfer problem, containing n heat transfer characteristic parameters p1, p2, …, p n ; The temperature objective function In matrix form, this is expressed as: (13) In formula (13), is a measured temperature vector, is a calculated temperature vector, is a residual vector; The partial differential equation of the temperature objective function in step S162 is as follows: (14) The Jacobian matrix is introduced: (15) In formula (15), is a matrix representation of the partial differential equation for the temperature objective function, is the Jacobian matrix; The Jacobian matrix expansion in step S163 is as follows: (16) The sensitivity matrix is constructed according to the transposed Jacobian matrix, and the sensitivity matrix is blocked, including: (17) In formula (17), the element in the transposed Jacobian matrix are sensitivity coefficients; T1,…,T H denote the temperature at sampling time point 1~H of the heat transfer characteristic parameter of the roasting stage, T H+1 ,…, T I denote the temperature at sampling point H+1~I of the heat transfer characteristic parameter of the on-line operation stage; is the calculated value of the temperature at each time point is the partial derivative of the ladle heat transfer characteristic parameter P j , which is expressed as is solved by using the difference method, and the calculation formula is: (18) In Equation (18), the parameter perturbation value is solved ; The sensitivity matrix is blocked and divided, the first H rows in the matrix (17) correspond to the ladle roasting stage, and the H+1th to Ith rows correspond to the end time of the ladle heavy ladle running stage and the empty ladle end time.

7. The method of claim 6, wherein, The iteration update rule in step S164 is represented as: (22) In formula (22), the heat transfer characteristic parameters solved in the last round and the current round, respectively; the calculated temperature of the temperature measurement point and the sensitivity matrix at the kth iteration, respectively, is a damping coefficient; is a unit diagonal matrix, ; is a measured temperature vector, denotes the transpose matrix of 8. The method of claim 1, wherein, In step S164, a damping coefficient adaptive adjustment mechanism is introduced to control , to ensure positive definite, to ensure the convergence speed and convergence of the iterative calculation.

9. The method of claim 1, wherein, The convergence criterion in step S164 is set as follows: The iteration termination condition of the LM algorithm is set as follows: the change amount of the to-be-solved parameter vector between adjacent two iterations is less than the preset convergence precision, that is, the following condition is met (24) In formula (24), and are the heat transfer characteristic parameter vectors obtained in the first and second iterations, respectively; ; is the variation of the to-be-solved parameter in the two iterations.​ When the condition is met, the algorithm converges, and the iteration is stopped.

10. A method of calculating a temperature drop of molten steel in a ladle changeover process, characterized by, Including: Step S21, according to the heat transfer characteristic parameters calculated by the inversion calculation method of the ladle heat transfer characteristic parameters in any one of claims 1-9 and the ladle temperature field, the heat flow density of the ladle lining is calculated; Step S22, according to the heat flow density calculation value of the ladle inner wall and the adjacent space node, and the ladle heavy ladle state duration parameter, the temperature drop of the molten steel in the ladle is calculated under the heavy ladle state.

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