Ladle heat transfer characteristic parameter inversion calculation method and molten steel temperature drop calculation method

Abstract

The invention provides a ladle heat transfer characteristic parameter inversion calculation method and a molten steel temperature drop calculation method, and belongs to the field of steel smelting. The method comprises the following steps: acquiring and simplifying geometric structure parameters of a steel ladle and thermophysical parameters of a refractory material, and constructing a three-dimensional model of the steel ladle; the steel ladle turnover process is simplified into baking, heavy ladle and empty ladle; grid division is conducted on the steel ladle three-dimensional model, the steel ladle three-dimensional model is divided into a spatial discrete structure composed of a plurality of nodes, and then a steel ladle finite difference heat transfer positive problem calculation model is constructed; performing grid and time step size independence verification, and solving a steel ladle temperature field based on the optimal discrete parameters; and an LM algorithm is adopted to construct a heat transfer characteristic parameter inversion calculation model, heat transfer inverse problem correction calculation is carried out, and corrected heat transfer characteristic parameters are obtained until the last procedure of all procedures of N turnover furnaces before baking and on-line operation. According to the method, the correction precision of the heat transfer characteristic parameters is improved, and the temperature drop value, closer to the true value, of the molten steel in the steel ladle is obtained.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of steel smelting, and particularly relates to a ladle heat transfer characteristic parameter inversion calculation method and a molten steel temperature drop calculation method. BACKGROUND

[0002] In the steel smelting process, the ladle is a key equipment for containing and transporting molten steel, and is also an important reaction container for off-furnace refining. The ladle turnover process is compact and has a large spatial span, which makes it difficult to perceive the state of the ladle, resulting in frequent ladle burn-through accidents and causing huge property losses and casualties. The research on the heat transfer of the temperature field of the ladle is beneficial to analyzing the change law of the temperature field in the ladle turnover process, providing theoretical support for molten steel temperature control, and guiding the optimization of molten steel temperature control process parameters to realize precise regulation and control of the molten steel temperature, improve the quality and qualification rate of cast products, and reduce production costs. In addition, it can also provide an important reference for the rationalization of ladle design and prolong the service life of the equipment.

[0003] The research methods for the thermal behavior of the ladle mainly include the measurement method and the numerical simulation method. The measurement is mostly based on devices such as thermocouples and infrared thermometers; the numerical simulation method is mainly based on finite difference method or finite volume method, etc., and simulates and analyzes the temperature field change under the conditions of ladle structure, lining baking, heavy ladle and empty ladle. The comprehensive research method considering the measurement method and the mathematical simulation method is the most widely used research method. In the research on the thermal behavior of the ladle, the accurate calculation of the heat transfer characteristic parameters of the ladle and the temperature field is the key to the safety evaluation of the ladle and the molten steel temperature control in the steelmaking process. Due to the heterogeneous heat transfer characteristics of the multi-layer composite structure of the ladle and the complex turnover conditions, the heat transfer characteristic parameters show significant nonlinear dynamic change characteristics, which makes it difficult for the traditional calculation method to accurately characterize and accurately calculate the molten steel temperature drop in the ladle. SUMMARY

[0004] In order to solve the above problems, the present application provides a ladle heat transfer characteristic parameter inversion calculation method and a molten steel temperature drop calculation method, which improves the correction accuracy of the heat transfer characteristic parameters and obtains a more accurate molten steel temperature drop value in the ladle.

[0005] In order to achieve the above purpose, the technical scheme adopted by the embodiments of the present application is as follows:

[0006] In a first aspect, the embodiments of the present application provide a ladle heat transfer characteristic parameter inversion calculation method, which comprises the following steps:

[0007] Step S11, obtain and simplify the geometric structure parameters of the ladle and the thermal physical property parameters of the refractory material, and construct a three-dimensional model of the ladle according to the geometric structure parameters;

[0008] Step S12, simplify the ladle circulation process into three working conditions of baking, heavy ladle and empty ladle, determine the boundary conditions of each working condition; meanwhile, determine all process stages including the baking stage and the heavy ladle and empty ladle stages of the first N circulation ladles in the on-line operation which need to be calculated by the heat transfer characteristic parameter inversion calculation;

[0009] Step S13, divide the ladle three-dimensional model into a spatial discrete structure composed of a plurality of nodes;

[0010] Step S14, construct a finite difference heat transfer positive problem calculation model of the ladle according to the heat conduction control equation and the divided nodes;

[0011] Step S15, verify the grid and time step independence of the finite difference heat transfer positive 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 by using the LM algorithm; specifically including:

[0013] Step S161, construct a temperature objective function based on the ladle temperature field;

[0014] Step S162, let the partial derivative of the temperature objective function with respect to the ladle heat transfer characteristic parameter P be 0, construct a partial differential equation, and introduce a Jacobian matrix in the equation, and the elements in the Jacobian matrix are sensitivity coefficients;

[0015] Step S163, expand the Jacobian matrix to construct a sensitivity matrix, and block the sensitivity matrix according to the process stage, and establish the sensitivity relationship of the residual to the heat transfer parameter;

[0016] Step S164, based on the temperature objective function and the sensitivity matrix, set the heat transfer characteristic parameter iteration update rule, introduce a damping coefficient adaptive adjustment mechanism in the iteration update rule, and set a convergence criterion;

[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 the baking and the first N circulation ladles in the on-line 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.

[0019] As a preferred embodiment of the present application, in step S12, when determining the boundary limit condition of each working condition, the heat exchange between the refractory materials in the ladle is through heat conduction, the initial temperature field of the ladle is room temperature, and the third type of boundary condition is used for the inner and outer walls of the ladle in the baking stage and the empty ladle stage; the inner wall of the ladle is in the first type of boundary condition in the ladle filling 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.

[0020] As a preferred embodiment of the present application, in step S13, the nodes 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 intersection lines of the surfaces of the three-dimensional model of the ladle, and the second type of boundary nodes are located on the surfaces of the three-dimensional model of the ladle.

[0021] As a preferred embodiment of the present application, in step S14, the finite difference heat transfer positive problem calculation model of the ladle is constructed, and specifically includes:

[0022] In step S141, the conditional assumptions are made for the physical model and the heat transfer model of the ladle, and the heat transfer parameters and the boundary conditions are defined;

[0023] In step S142, based on the assumed conditions, the three-dimensional non-steady-state heat conduction partial differential control equation in the rectangular coordinate system is used to describe the heat transfer process of the ladle;

[0024] In step S143, based on the spatial discrete structure, the Taylor expansion method is used to replace the derivatives in the heat conduction partial differential control equation with the difference approximation expressions, the first-order derivatives are processed by the first-order forward difference, and the second-order derivatives are processed by the second-order central difference, so as to obtain the heat transfer difference expression of the internal node, the heat transfer difference expression of the first type of boundary node and the heat transfer difference expression of the second type of boundary node; the heat transfer difference equations of the internal node A, the first type of boundary node B and the second type of boundary node C jointly constitute the finite difference heat transfer positive problem calculation model.

[0025] As a preferred embodiment of the present application, in step S5, when the irrelevance verification is performed, four grid division modes are set, and the temperature values of the nodes are calculated under each grid division mode according to the finite difference heat transfer positive problem calculation model; and then according to the accuracy and the calculation speed of the calculation results, the optimal discrete parameters are obtained.

[0026] As a preferred embodiment of the present application, the temperature target function constructed in step S161 is as follows:

[0027] (12)

[0028] In formula (12), is the target function; I is the time step number; is the measured temperature value of the measuring point at the moment t; is the measured temperature value of the measuring point at the moment t; 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, It is 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: (16) Construct the sensitivity matrix based on the transposed Jacobian matrix, and then divide the sensitivity matrix into blocks, including:

[0038]

[0039] (17)

[0040] 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: (18)

[0041] In equation (18), the parameter disturbance value is solved. ;

[0042] 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.

[0043] In a preferred embodiment of the present invention, the iterative update rule in step S164 is expressed as follows: (twenty two)

[0044] 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 .

[0045] 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.

[0046] In a preferred embodiment of the present invention, the convergence criterion in step S164 is set as follows:

[0047] 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...

[0048] (twenty four)

[0049] In equation (24), and The first Second and third The heat transfer characteristic parameter vector obtained from the next iteration; ; This represents the change in the parameter to be solved during the two iterations.

[0050] When this condition is met, the algorithm is considered to have converged, and the iteration stops.

[0051] In a second aspect, the embodiments of the present application also provide a molten steel temperature drop calculation method for a ladle circulation process, comprising:

[0052] In step S21, the heat flux density of the ladle lining is calculated according to the heat transfer characteristic parameters calculated by the inverse calculation method of the ladle heat transfer characteristic parameters and the ladle temperature field.

[0053] In step S22, the temperature drop of the molten steel in the ladle is calculated according to the heat flux density calculation value of the ladle inner wall and the adjacent space node and the ladle heavy ladle state duration parameter.

[0054] The scheme of the embodiments of the present application has the following beneficial effects:

[0055] The ladle heat transfer characteristic parameter inverse calculation method and the molten steel temperature drop calculation method provided by the embodiments of the present application first establish a three-dimensional finite difference heat transfer positive model of the ladle, simulate the process of the temperature field of the ladle baking for a predetermined time and the Nth time temperature field changing with time before the online circulation, and obtain 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 inner wall heat transfer coefficient and the outer wall heat transfer coefficient in the baking stage. Finally, based on the corrected ladle temperature field data of the heat transfer inverse problem, the heat flux density of the space node near the inner surface in the ladle baking and online circulation stages is calculated, and the molten steel temperature drop in the heavy ladle stage of the ladle online circulation is calculated. The results show that after the parameter inversion correction, for example, for 10 furnace times, the average accuracy of the temperature correction value of the measuring point in the baking stage and the online running stage is increased by 3.24% and 10.15%, respectively. The heat accumulation characteristics of the ladle lining in the circulation process directly affect the temperature drop of the molten steel, and the temperature drop of the first furnace time reaches 170.02K, and the temperature drop of the 10th furnace time is stabilized at 90.55K. The present application provides reliable technical support for online monitoring of the ladle temperature field and optimization of the circulation process.

[0056] Of course, implementing any product or method of the present application does not necessarily require all the advantages described above. BRIEF DESCRIPTION OF DRAWINGS

[0057] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0058] Figure 1 It is a flow chart of the ladle heat transfer characteristic parameter inverse calculation method described in the embodiments of the present application.

[0059] Figure 2 is a schematic diagram of a simplified ladle structure in an embodiment of the present application;

[0060] Figure 3 is a simplified ladle circulation flow chart in an embodiment of the present application;

[0061] Figure 4 is a schematic diagram of a unit control volume of an internal node A and its adjacent nodes in an embodiment of the present application;

[0062] Figure 5 is a schematic diagram of a unit control volume of a first type boundary node B and a second type boundary node C in an embodiment of the present application;

[0063] Figure 6 is an iteration principle diagram of a heat transfer inverse problem calculation model in an embodiment of the present application;

[0064] Figure 7 is a calculated value of a space node temperature of a ladle side wall in a baking stage in a specific application of an embodiment of the present application;

[0065] Figure 8 is a calculated value of a space node temperature of a ladle side wall at the end of each process in an online running stage in a specific application of an embodiment of the present application;

[0066] Figure 9 is a measured value and a calculated value of a temperature of a ladle outer wall temperature measuring point in a specific application of an embodiment of the present application;

[0067] Figure 10 is a corrected value of a temperature of a ladle outer wall temperature measuring point in a baking stage in a specific application of an embodiment of the present application;

[0068] Figure 11 is an error of a corrected value of a temperature of a ladle outer wall temperature measuring point in a baking stage in a specific application of an embodiment of the present application;

[0069] Figure 12 is a corrected value of a temperature of a ladle outer wall temperature measuring point in an online running stage in a specific application of an embodiment of the present application;

[0070] Figure 13 is an error of a corrected value of a temperature of a ladle outer wall temperature measuring point in an online running stage in a specific application of an embodiment of the present application;

[0071] Figure 14 is a heat flux density and temperature change of an inner wall and adjacent nodes in a baking stage in a specific application of an embodiment of the present application;

[0072] Figure 15 is a heat flux density and temperature change of an inner wall and adjacent nodes at the end of each ladle in a specific application of an embodiment of the present application;

[0073] Figure 16The heat flux density of the inner wall of the ladle in the heavy ladling stage of each ladle and the adjacent nodes to which the embodiment of the application is applied;

[0074] Figure 17 The molten steel temperature drop in the heavy ladling stage of the ladle in the ladle turnaround process to which the embodiment of the application is applied;

[0075] Figure 18 The molten steel temperature drop in the heavy ladling stage of each ladle to which the embodiment of the application is applied.

[0076] Legend of reference signs:

[0077] 1 - working layer; 2 - permanent layer; 3 - steel shell. DETAILED DESCRIPTION

[0078] The inventors of the present application found the above problems after careful research on the existing ladle heat transfer research and characterization methods. Research has found that by studying heat transfer in a reverse problem, measured data can be used to correct possible deviations in mathematical calculation models, which can significantly improve the accuracy and reliability of temperature field calculation results. Common algorithms for heat transfer inverse problems include the steepest descent method, Newton's method, Gauss-Newton method, LM method, quasi-Newton method, etc. Currently, some scholars have completed the calculation of the heat flux density value of the pipe wall under forced convection heat transfer based on the conjugate gradient method, and the temperature correction value error is less than 2.58%; some scholars have also corrected and calculated the material thermal conductivity, specific heat capacity, density and heat transfer coefficient value based on the LM algorithm, and the temperature correction value error is less than 1.25 K based on the actual measured temperature value.

[0079] However, in the numerical simulation of the thermal behavior of the ladle, it is generally based on one-dimensional or two-dimensional coordinate system; in numerical calculation, the heat transfer calculation boundary conditions are mostly obtained based on experience or formula calculation, and are fixed values, without considering the real-time influence of factors such as changes in the surrounding environment and ladle structure in actual production from the perspective of three-dimensional coordinate system, the error of heat transfer calculation parameters leads to the inaccuracy of the temperature field calculation results. Through heat transfer inverse problem calculation, accurate heat transfer calculation characteristic parameters can be obtained. Therefore, on the basis of comprehensive consideration of the measured method and the numerical simulation method, accurate heat transfer characteristic parameters are obtained based on the heat transfer inverse problem calculation, which is an effective way to obtain accurate values of the ladle temperature field.

[0080] It should be noted that the defects of the above prior art solutions are the result of the inventors' careful research and practice, therefore, the discovery process of the above problems and the solutions proposed by the embodiments of the present application to solve the above problems should be the contribution of the inventors to the present application.

[0081] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. The components of the embodiments of the present application described and shown in the drawings can be arranged and designed in various different configurations. It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict.

[0082] It should be noted that similar reference numerals and letters represent similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings. In the description of the present application, the terms "first", "second", "third", "fourth" and the like are only used to distinguish the description, and cannot be understood as indicating or implying relative importance.

[0083] Based on the above in-depth analysis, the present application provides a ladle heat transfer characteristic parameter inversion calculation method and a molten steel temperature drop calculation method. First, a three-dimensional finite difference heat transfer positive model of the ladle is established to simulate the process of the temperature field changing with time during the ladle baking for a predetermined length of time and N heats (for example, 10 heats) before the online turnover, and an initial error calculation distribution is obtained. Then, based on the Levenberg-Marquardt (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 inner wall heat transfer coefficient and the outer wall heat transfer coefficient during the baking stage. Finally, based on the corrected ladle temperature field data of the heat transfer inverse problem, the calculation of the heat flux density of the space nodes near the inner surface during the ladle baking and online turnover stages is completed, and the calculation of the molten steel temperature drop during the different heats of the ladle during the ladle online turnover is completed. The results show that after the parameter inversion correction, the average accuracy of the temperature correction value of the temperature measuring point during the baking stage and the online running stage is increased by 3.24% and 10.15%, respectively. Further analysis shows that the heat storage characteristics of the ladle lining during the turnover process directly affect the molten steel temperature drop, and the first heat temperature drop reaches 170.02K, and the tenth heat is stabilized at 90.55K, which provides reliable technical support for online monitoring of the ladle temperature field and optimization of the turnover process.

[0084] As shown in Figure 1 The ladle heat transfer characteristic parameter inversion calculation method includes the following steps:

[0085] Step S11, obtain and simplify the geometric structure parameters of the ladle and the thermal physical parameters of the refractory material, and construct a three-dimensional model of the ladle according to the geometric structure parameters.

[0086] In this step, the geometric structure parameters of the ladle include the structure, material and size of the ladle, and in this embodiment, the structure of the ladle is simplified, as shown in Figure 2As shown, including the working layer (spinel brick) 1, permanent layer (spinel castable) 2 and steel shell 3 three-layer structure. The thermal parameters of the refractory material are described in the three-layer structure after simplification, including material type, thermal conductivity, specific heat and density, etc.

[0087] Step S12, the ladle turnover process is simplified into three working conditions of baking, heavy package and empty package, the boundary limit conditions of each working condition are determined; at the same time, all process stages including the baking stage and the heavy package and empty package stages of the first N turnover furnace times of the on-line operation which need to carry out the heat transfer characteristic parameter inversion calculation are determined.

[0088] In this step, as shown in the figure, Figure 3 As shown, the heat transfer boundary conditions are different in different process stages of the ladle turnover, in order to facilitate calculation, the ladle turnover process is simplified into three stages of baking, heavy package and empty package. The ladle baking, heavy package and empty package stages are all covered with ladle covers for heat preservation. In the actual production process, the first N turnover furnace times (usually N=10) of the on-line operation of the ladle, the ladle lining continuously accumulates heat, and its temperature field presents non-steady-state characteristics, which affects the accurate control of the molten steel temperature on site. With the increase of the turnover number, the molten steel temperature drop tends to be stable by the Nth furnace time, therefore, it is generally necessary to calculate the heat transfer characteristic parameters of the first N furnace times, so as to accurately predict the molten steel temperature drop in the formal production. According to the ladle turnover process, all process stages including the baking stage and the heavy package and empty package stages of the first N turnover furnace times of the on-line operation which need to carry out the heat transfer characteristic parameter inversion calculation. Taking the baking of 14 hours and 10 furnace times as an example, the time nodes corresponding to the parameters are the end of each hour of baking, the end of heavy package of each furnace time and the space end time point, a total of 34 prediction time points, corresponding to 34 groups of heat transfer characteristic parameters.

[0089] When determining the boundary limit conditions of each working condition, the heat exchange between the ladle lining refractory materials is carried out through heat conduction, the initial temperature field of the ladle is room temperature, the inner and outer walls of the ladle in the baking stage and the empty package stage adopt the third type of boundary condition; the inner wall of the ladle in the heavy package stage is in the first type of boundary condition, and the molten steel temperature is the inner wall temperature, and the outer wall is in the third type of boundary condition.

[0090] Step S13, the ladle three-dimensional model is meshed, which is divided into a spatial discrete structure composed of a plurality of nodes, the nodes include internal nodes, first type of boundary nodes and second type of boundary nodes, each internal node has its own unit control volume and adjacent node distribution, the first type of boundary node is located on the surface intersection line of the ladle three-dimensional model, and the second type of boundary node is located on the surface of the ladle three-dimensional model.

[0091] In this step, as shown in the figure, Figure 4As shown, the unit control volume of each internal node A and the adjacent node distribution are as follows: for each internal node A, there is a unit control volume Δx×Δy×Δz belonging to itself; there are adjacent nodes O, L, N, D, W, and E in six directions (front / back, up / down, left / right); the heat exchange of these internal nodes is expressed in the form of finite difference; and the adopted node arrangement mode is a structured regular grid. 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 convective heat transfer, and the heat transfer coefficient is Each boundary space node has no internal heat source, and the heat transfer calculation difference equation is derived from the energy conservation law of the control volume. Among them, the first type of boundary node B(i,j,k) is located on the intersection line of the model surface, and the length is , the width is , and the height is ; the second type of boundary node C(i,j,k) is located on the model surface, and the length is , the width is , and the height is .

[0092] Step S14, according to the heat conduction control equation and the divided nodes, a finite difference heat transfer positive problem calculation model of the ladle is constructed.

[0093] In this step, it specifically includes:

[0094] Step S141, make conditional assumptions for the ladle physical model and the heat transfer model, and define the heat transfer parameters and boundary conditions.

[0095] Before constructing the heat transfer model of the nodes based on the heat conduction control equation, due to the complex and variable heat transfer boundary conditions in the actual turnover process of the ladle, and the complex physical and chemical changes between the lining refractory material and the molten steel, the thermal physical property parameters of the refractory material change. In order to ensure the smooth and efficient heat transfer calculation, the following assumptions are made for the ladle physical model and its heat transfer model:

[0096] The molten steel is stable during the process of the ladle containing molten steel, and the stratification phenomenon of the molten steel is not considered;

[0097] The lining of the ladle is regarded as a cylinder, and the unsteady heat transfer is carried out;

[0098] The heat radiation and heat convection boundary conditions are converted into a comprehensive heat transfer coefficient;

[0099] The thermal deformation of the interface between different refractory material layers in the ladle turnover process and the change of thermal physical property parameters caused by the thermal deformation are ignored;

[0100] The air temperature around the ladle is constant during the ladle turnover process.

[0101] Secondly, the heat transfer state of the ladle turnover process is complex and changeable, the inner wall heat transfer boundary condition changes constantly, and the outer wall heat transfer boundary condition is relatively stable, including convective heat transfer and radiation heat transfer. The actual object radiation energy is mainly related to the object temperature, and the calculation process of the radiation coefficient is complex. According to the measured temperature data, the outer wall temperature of the ladle during the turnover process will not be higher than 350℃, and the radiation heat transfer coefficient between the ladle and the surrounding environment is small. Therefore, the convective heat transfer is the main heat dissipation mode between the outer wall of the ladle and the surrounding environment, and the radiation heat transfer coefficient is usually converted into a comprehensive heat transfer coefficient in the actual heat transfer calculation. The relevant formula for calculating the heat transfer coefficient is defined as follows:

[0102] (1)

[0103] (2)

[0104] (3)

[0105] (4)

[0106] In formula (1)-(4), Nu is the Nusselt number, and the subscript m represents the Nusselt number at a qualitative temperature; Tm represents the qualitative temperature, which is the arithmetic average of the boundary layer fluid temperature and the side wall temperature, , Tw is the wall temperature, T∞ is the ambient temperature; β is the body expansion coefficient; P r Pr is the Prandtl number of the boundary layer fluid; μ is the kinematic viscosity of the boundary layer fluid, with a unit of m 2 / s; k is the thermal conductivity of the boundary layer fluid, with a unit of W / (m·K). The Prandtl number, kinematic viscosity, and thermal conductivity are obtained by looking up the table; K and n are constants related to the shape, position, and flow state of the heat transfer surface; g and h are the gravitational acceleration and characteristic length, respectively, and g is taken as 9.81 m / s 2 during calculation; h is the ladle wall heat transfer coefficient.

[0107] The boundary conditions for ladle heat transfer calculation are obtained from the convective heat transfer calculation formula and Fluent simulation. The heat transfer boundary condition values of the ladle lining during the 14h roasting and the first 10 heats before the online turnover are shown in Table 1.

[0108] Table 1 Heat transfer boundary conditions of ladle lining

[0109]

[0110] Step S142, based on the assumption condition, a three-dimensional unsteady heat conduction partial differential control equation in a rectangular coordinate system is used to describe the heat transfer process of the ladle.

[0111] The three-dimensional unsteady heat conduction partial differential control equation in the rectangular coordinate system is:

[0112] (5)

[0113] In formula (5), is the density, with the unit of kg / m 3 ; c is the specific heat, with the unit of J / (kg·K); is the thermal conductivity, with the unit of W / (m·K); is the source term, and it is considered that there is no internal heat source in the ladle lining, that is, =0.

[0114] Step S143, based on the spatial discrete structure, the Taylor expansion method is used to replace the derivative in the heat conduction partial differential control equation with a difference approximation expression, the first-order derivative is processed by a first-order forward difference, and the second-order derivative is processed by a second-order central difference, to obtain a heat transfer difference expression of an internal node, a heat transfer difference expression of a first-type boundary node and a heat transfer difference expression of a second-type boundary node, respectively.

[0115] In this step, the heat transfer difference model is constructed for each node in the above manner, but the internal node, the first-type boundary node and the second-type boundary node have different parameters.

[0116] For the internal node A, the heat transfer difference expression is: (6)

[0117] In formula (6), T A , T O , T L , T W , T E , T N , T D respectively represent the temperature values of the corresponding subscript nodes at time t, represents the temperature value of the A node at time t+Δt, . .

[0118] Preferably, when the model in the three-dimensional rectangular coordinate system has a uniform grid spacing, that is, , formula (6) can be simplified as: (7)

[0119] In formula (7), is the Fourier number, .

[0120] 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.

[0121] 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.

[0122] 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): (8)

[0123] 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: (9)

[0124] In equation (9), ; ; , The ambient temperature.

[0125] 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: (10) (11)

[0126] In equations (10)-(11), For Fourier numbers, ; For the Pythagorean theorem, ; where h is the surface heat transfer coefficient, and the unit is W / (m 2 ·K).

[0127] Therefore, the heat transfer difference equation of the internal node A, the first type of boundary node B and the second type of boundary node C jointly constitutes a finite difference heat transfer forward problem calculation model.

[0128] In step S15, the grid and time step independence verification is performed on the finite difference heat transfer forward problem calculation model, and the ladle temperature field is solved based on the optimal discrete parameters.

[0129] Based on the temperature change of the ladle in the first hour of roasting, the grid of the heat transfer difference calculation of the ladle lining is verified for independence; when verifying the independence, four grid division 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 grid division method; and then according to the accuracy and calculation speed of the calculation results, the optimal discrete parameters are obtained.

[0130] The four grid division methods are as follows: in method 1, =20 mm, =5 s; in method 2, =30 mm, =5 s; in method 3, =30 mm, =10 s; and in method 4, =40 mm, =10 s.

[0131] Among the four grid division methods, the spatial step and the time step of method 1 are the smallest, and the calculation result is the most accurate. The temperature calculation result of method 1 is taken as the standard value, the temperature calculation result of method 3 is the closest to method 1, followed by method 2, and the grid division of method 4 is the sparsest, and the temperature error between the temperature calculation values of the other three groups is the largest. Therefore, the grid division method 4 is discarded. The calculation time of method 1 is 3 times that of method 2 and 6 times that of method 3. Considering the accuracy and speed of the calculation result, =30 mm, =10 s is the optimal choice for grid division in the numerical calculation of the ladle temperature field.

[0132] Based on the above verification results, the grid division parameters of =30 mm, =10 s are used to solve the forward problem of the temperature field of the ladle in the entire roasting process (14 hours) and the first 10 turnover furnace times before the on-line operation, and the initial temperature field distribution is obtained. The initial temperature field will be used as the calculation basis for parameter inversion in the subsequent heat transfer inverse problem, and will be used to construct the objective function and sensitivity analysis.

[0133] Step S16: Based on the solved ladle temperature field, the LM algorithm is used to construct a heat transfer characteristic parameter inversion calculation model.

[0134] 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:

[0135] Step S161: Construct a temperature objective function based on the ladle temperature field.

[0136] (12)

[0137] 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 .

[0138] Temperature objective function Represented in matrix form:

[0139] (13)

[0140] In equation (13), Let be the measured temperature vector. To calculate the temperature vector, This is the residual vector.

[0141] 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.

[0142] In this step, the partial differential equation of the temperature objective function is as follows:

[0143] (14)

[0144] The Jacobian matrix is introduced:

[0145] (15)

[0146] In formula (15), is the Jacobian matrix, which is the key to the iterative solution of the optimization problem by the LM algorithm. is the matrix representation of the partial differential equation of the temperature objective function, that is, the gradient vector of the objective function with respect to the parameter vector P, and the components correspond to the partial derivatives in each parameter direction.

[0147] In step S163, the Jacobian matrix is unfolded to construct the sensitivity matrix, and the sensitivity matrix is blocked according to the process stages, to establish the sensitivity relationship between the residual and the heat transfer parameters, so as to depict the partial derivative law of temperature change with heat transfer parameters.

[0148] Wherein, the Jacobian matrix expansion formula is:

[0149] (16)

[0150] In order to facilitate expression, the sensitivity matrix is constructed by using the transposed Jacobian matrix and blocking, as follows: (17)

[0151] In formula (17), the elements in the transposed Jacobian matrix are Sensitivity coefficient; T1,…,T H represent the temperatures of the heat transfer characteristic parameter sampling time points 1~H in the baking stage, T H+1 ,…, T I represent the temperatures of the heat transfer characteristic parameter sampling points H+1~I in the on-line running stage; is the corresponding temperature calculation value at each time, and j is the partial derivative of the ladle heat transfer characteristic parameter P , which is represented as (18)

[0152] In formula (18), the parameter perturbation value is solved. Wherein, n=3, the three heat transfer characteristic parameters P j are T gas , α wl and α shell , and in T i , i=1,2,…,34.

[0153] In the process of constructing the sensitivity matrix, the ladle turnover process is divided into blocks, which are divided into baking blocks and online running blocks. The first H rows of the matrix in formula (17) correspond to the ladle baking stage, and the H+1 to I rows correspond to the end time of the first N heats of the ladle and the end time of the empty ladle in the ladle online running stage. In formula (17) of the embodiment, the first 10 heats of N=10 are taken as an example, and the first 14 rows of the matrix correspond to the temperature measuring points in the ladle baking stage; the 15th to 34th rows correspond to the ladle online running stage, including the end time of the first 10 heats of the ladle and the end time of the empty ladle.

[0154] The block division in this step refers to the stage division of the entire sensitivity matrix row vector according to different working conditions in the ladle turnover process, so that the sensitivity of different process stages is distributed in the matrix to form independent sub-blocks. Through this processing mode, the mutual interference of residuals in different stages in the full-time domain target function can be avoided, and the stability and convergence of the LM iteration in each stage can be ensured; at the same time, different sub-blocks correspond to different physical characteristics of different processes, which facilitates targeted correction of parameters such as heat transfer coefficients of inner and outer walls, thereby improving the temperature field calculation accuracy and the engineering interpretability of the results.

[0155] In step S164, an iterative updating rule of the heat transfer characteristic parameter is set based on the temperature target function and the sensitivity matrix, so as to gradually correct the heat transfer characteristic parameter; in order to ensure the stability and finite step convergence of the iterative calculation process, a damping coefficient adaptive adjustment mechanism is introduced, and a convergence criterion is set.

[0156] In this step, the iterative updating rule includes:

[0157] The expression is expressed as:

[0158] (19)

[0159] Formula (19) is solved by iterative calculation to update the numerical value of the heat transfer characteristic parameter P. In the specific iterative process, only the corresponding block of the sensitivity matrix and the residual vector are called according to the current process stage to participate in the calculation, and the remaining blocks do not participate in this stage; the temperature vector T(P) composed of the temperature calculation values of the temperature measuring points is Taylor expanded around P at the kth iteration:

[0160] (20)

[0161] In formula (20), T(P) and S are the temperature calculation value of the temperature measuring point and the sensitivity matrix at the kth iteration, respectively. The above formula is substituted into the expression to obtain the iterative equation of the to-be-solved heat transfer characteristic parameter P:

[0162] ​​ (21)

[0163] In formula (21), represents the transpose matrix of .

[0164] The iterative calculation formula (21) requires that the matrix be non-singular, that is, it is required that The LM algorithm avoids becoming a non-singular matrix by the following processing: (22)

[0165] In formula (22), and are the heat transfer characteristic parameters solved in the last round and the current round, respectively; is a damping coefficient; is a unit diagonal matrix, .

[0166] The damping coefficient is introduced to adaptively adjust the mechanism, and by controlling , the positive definiteness of is ensured, and thus the convergence speed and convergence of the iterative calculation are ensured.

[0167] The convergence criterion is set as follows:

[0168] The change of the to-be-solved parameter in the two iterations is:

[0169] (23)

[0170] The iteration termination condition of the LM algorithm is that the change of the to-be-solved parameter between adjacent iterations is small enough; the iteration termination condition of the LM algorithm is set as: the change of the to-be-solved parameter vector between the two iterations is less than the preset convergence precision, that is, it satisfies

[0171] (24)

[0172] In formula (24), and are the heat transfer characteristic parameter vectors obtained in the th and the th iteration, respectively. When this condition is met, it is determined that the algorithm converges, and the iteration is stopped.

[0173] In step S17, the heat transfer characteristic parameters of the ladle temperature field are corrected by the heat transfer inverse problem correction calculation based on the constructed heat transfer characteristic parameter inversion calculation model, and the corrected heat transfer characteristic parameters are obtained.

[0174] The step specifically comprises: determining the current process stage (such as baking, re-packing or empty ladle) and its duration according to the ladle turnover process, and determining the to-be-inverted parameters according to Table 3 Assigning an initial value P0 as the starting point of iterative calculation; at the same time, setting a damping coefficient and a convergence precision threshold, preferably, the convergence precision is set to 10 -10 ; as shown in the formula, inputting the P0 into the heat transfer characteristic parameter inversion calculation model to output a corrected heat transfer characteristic parameter until the model converges, so as to obtain the optimal heat transfer characteristic parameter and the corrected temperature field of the stage. Figure 6

[0175] Step S18, judging whether the current process stage is the last process of the first N turnover heats of the ladle in the baking and on-line operation; if not, turning to step S17; if yes, all stages are completed, and then outputting the corrected heat transfer characteristic parameter and the temperature field calculation result of the whole process.

[0176] In this step, in the actual production process, the first N turnover heats of the ladle in the on-line operation, and N is preferably 10; the ladle lining continuously accumulates heat, and its temperature field presents a non-steady-state characteristic, which affects the accurate control of the molten steel temperature on site, and with the increase of the turnover number, the molten steel temperature drop tends to be stable at the 10th heat. The research on the first 10 turnover heats of the ladle in the baking and on-line operation captures the most critical dynamic heat transfer process and meets the special monitoring requirements of the ladle in the actual production of the steel plant.

[0177] Based on the above ladle heat transfer characteristic parameter inversion calculation method, the embodiment of the present application also provides a molten steel temperature drop calculation method for the ladle turnover process. The molten steel temperature drop calculation method comprises the following steps:

[0178] Step S21, calculating the heat flux density of the ladle lining according to the heat transfer characteristic parameters and the ladle temperature field calculated by the ladle heat transfer characteristic parameter inversion calculation method.

[0179] In this step, the ladle temperature field data calculated by the ladle lining heat transfer positive problem can obtain the heat flux density of the ladle lining, and then reflect the heat exchange between the ladle lining and the high-temperature molten steel. The accurate heat flux density value of the ladle lining is beneficial to improve the hit rate of molten steel temperature prediction and ensure the product quality. The heat flux density and heat exchange amount calculation formula between the ladle lining and the high-temperature molten steel are as follows:

[0180] (25)

[0181] (26)

[0182] In formula (25)-(26), is the thermal conductivity of the ladle lining, and the unit is W / (m·K); A​s A is the inner wall area of the ladle, and the unit is m 2 ; q is the heat flux, and the unit is W / m 2 ; A is the inner wall area of the ladle, and the unit is m

[0183] In step S22, according to the heat flux calculation value of the inner wall of the ladle and the adjacent space node, the ladle heavy ladle state duration and other parameters, the temperature drop of the molten steel in the ladle is calculated under the heavy ladle state, and the calculation formula is as follows:

[0184] (27)

[0185] (28)

[0186] In formula (27)-(28), Q is heat energy, the unit is J; m is the mass of molten steel, and the value is 120 t; c is the specific heat capacity, and the value is 879 J / (kg·K); is the temperature drop of the molten steel, that is, the solving parameter.

[0187] The ladle heat transfer characteristic parameter inversion method and the molten steel temperature drop calculation method described in the embodiment of the application are applied to the heat transfer characteristic parameter inversion calculation and the molten steel temperature drop calculation of a 130t ladle of a certain steel plant.

[0188] As shown in Figure 2 , a quarter structure of a 130t ladle of a certain steel plant is taken as an example for description, and after the ladle is simplified, the related structure size is shown in Table 2.

[0189] Table 2 Size parameters of the simplified ladle

[0190]

[0191] The required thermal physical property parameters of the refractory material in the ladle temperature field heat transfer calculation are shown in Table 3.

[0192] Table 3 Thermal physical property parameters of the ladle lining refractory material

[0193]

[0194] As shown in Figure 7The temperature changes of the space nodes at different positions of the ladle side wall during the ladle baking stage are shown as follows: node 1 is located at the inner surface of the ladle side wall, node 2 is 120 mm away from the inner surface of the ladle side wall in the radial direction, node 3 is 240 mm away from the inner surface of the ladle side wall in the radial direction, and node 4 is located at the outer surface of the ladle side wall. The closer the space node is to the inner surface of the ladle side wall, that is, the closer the distance between the space node and the heat source (baking flue gas) is, the higher the temperature is. After baking for 7-9 hours, the temperature gradient (i.e. the temperature difference between nodes 1 and 4) of the space nodes at the inner and outer walls of the ladle reaches a maximum of 579 K.

[0195] As shown in Figure 8 After the ladle is baked for 14 hours and put into operation, the temperature changes of the four space nodes in the first 10 heats of the ladle operation are calculated as follows: the closer the space node is to the inner surface of the ladle, the greater the temperature fluctuation after the heavy ladle and the empty ladle are switched. The temperature values of the space nodes 1 and 2 that are close to the inner surface of the ladle during the heavy ladle stage are higher than those during the empty ladle stage, and the temperature presents an alternating rising and falling rule, but as the heats increase, the space nodes 1 and 2 are in a general trend of heat accumulation and temperature rise, indicating that the heat accumulation capacity during the heavy ladle stage is strong and the heat dissipation capacity during the empty ladle stage is weak. The temperature of the space nodes 3 and 4 that are far away from the inner wall of the ladle continuously rises during the first 10 heats of the ladle operation, that is, they are always in a heat accumulation state. In summary, the first 10 heats of the ladle turnover process are in a general heat accumulation state, but the heat accumulation or heat dissipation change rules of the nodes at different radial positions in the ladle are different.

[0196] As shown in Figure 9 The error conditions of the temperature calculation values and the measured values of the temperature measuring points during the ladle baking stage are shown as follows: taking the measured value of the temperature measuring point at the outer wall of the ladle as the standard, the average accuracy of the temperature calculation values during the baking stage is 95.32%, the root mean square error is 9.91 K, and the maximum temperature error occurs at 14 hours, which is 18.92 K; the average accuracy of the temperature calculation values during the ladle operation stage is 89.45%, the root mean square error is 22.08 K, and the maximum temperature error occurs at the end of the heavy ladle in the first heat, which is 53.75 K, and the temperature error at the end of the heavy ladle in each heat is large. Therefore, correcting the heat transfer characteristic parameters through the inverse heat transfer problem is the key to improving the accuracy of the temperature field calculation.

[0197] 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.

[0198] To determine which combination is better, this embodiment sets the inversion parameters to the five groups in Table 4.

[0199] Table 4 Calculation Scheme for Heat Transfer Characteristic Parameters of Steel Ladle

[0200]

[0201] 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.

[0202] 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 11 As 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.

[0203] The maximum error of the temperature correction value of the ladle roasting stage in schemes 2 and 3 is 41.87 K and 40.64 K, respectively. Taking the measured temperature value as the standard, the accuracy of the temperature correction value of the roasting stage in schemes 2 and 3 is 91.44% and 91.69%, respectively, which is higher than the average accuracy of the initial temperature calculation value by-3.88% and-3.63%, respectively. After the inversion correction of schemes 1, 4 and 5, the temperature correction value of the temperature measuring point in the roasting stage has better fitting degree with the measured temperature value. The maximum temperature error occurs within 7-12 h, which is 18.87 K, 6.42 K and 6.56 K, respectively. The average accuracy of the temperature correction value of schemes 1, 4 and 5 is 95.87%, 98.51% and 98.56%, respectively, which is higher than the average accuracy of the initial temperature calculation value by 0.55%, 3.19% and 3.24%, respectively.

[0204] The temperature correction value of the temperature measuring point after the inversion calculation in the ladle online operation stage is shown in Figure 12 The error between the temperature correction value and the measured value is shown in Figure 13 Combining the two figures, it can be concluded that the temperature correction value error of schemes 2 and 3 is much higher than that of the other three groups compared with the initial temperature calculation value. After the inversion correction of schemes 4 and 5, the temperature correction value of the temperature measuring point has the best fitting degree with the measured temperature value, and the fitting degree of the temperature correction value curve of scheme 1 with the measured temperature value curve is only second to that of schemes 4 and 5.

[0205] In the first 10 heats before the ladle online operation, the temperature correction value error of schemes 2 and 3 is large, with the maximum error value being 37.41 K and 38.89 K, respectively. The average accuracy of the temperature correction value is 92.66% and 92.37%, respectively, which is higher than the average accuracy of the initial temperature calculation value by 3.21% and 2.92%, respectively. The temperature correction value error of schemes 1, 4 and 5 is small, with the maximum error value being 4.56 K, 3.88 K and 2.33 K, respectively. The average accuracy of the temperature correction value of the temperature measuring point is 99.18%, 99.34% and 99.6%, respectively. Compared with the initial temperature calculation value of the temperature measuring point, the average accuracy of the temperature correction value of the temperature measuring point after the correction of schemes 1, 4 and 5 is increased by 9.73%, 9.89% and 10.15%, respectively, which has a good temperature correction effect.

[0206] Accuracy evaluation of the calculation results of the heat transfer characteristic parameters. In order to test the accuracy of the temperature correction value of different inversion schemes, the measured temperature value of the temperature measuring point on the outer wall of the ladle is taken as the standard value, and the accuracy of the above five groups of ladle heat transfer inverse problem calculation schemes is evaluated by using the root mean square error, and the results are shown in Tables 5 and 6.

[0207] Table 5 Temperature calculation value error of the temperature measuring point on the outer wall of the ladle in the roasting stage

[0208]

[0209] Table 6 Temperature calculation error of ladle outer wall temperature measurement point in on-line running stage

[0210]

[0211] Compared with the heat transfer positive problem calculation, the root mean square error of the temperature correction value after the correction of schemes 2 and 3 in the baking stage increases, and the accuracy of the temperature correction value within the range of ±3 K and ±5 K also decreases. Compared with the heat transfer positive problem, the root mean square error of schemes 1, 4 and 5 decreases to different degrees, and the accuracy increases. In the ladle on-line running stage, the root mean square error of the temperature correction value of the five groups of heat transfer inverse problem calculation schemes decreases, and the accuracy of the temperature calculation value of schemes 1, 4 and 5 significantly improves. Comprehensive analysis is shown in Tables 5 and 6. Compared with schemes 1, 2 and 3 of single heat transfer characteristic parameter inversion calculation, the accuracy of the calculation results of schemes 4 and 5 of multiple heat transfer characteristic parameter inversion correction significantly increases, and the temperature correction effect is better.

[0212] The temperature and heat flux density value changes of the adjacent space nodes in the ladle baking stage are shown in Figure 14 In the initial stage of baking, the initial temperature value of the ladle is low, the temperature difference between the inner wall and the baking flue gas is large, and the heat flux density value between the inner wall and the adjacent space nodes reaches the maximum. With the increase of the baking time, the temperature of the ladle lining rises, and the heat flux density value gradually decreases. The ladle is in a continuous heat accumulation state in the baking stage, and has strong heat accumulation capacity.

[0213] The temperature and heat flux density value changes of the adjacent space nodes in the ladle baking stage are shown in Figure 15 In the initial stage of baking, the initial temperature value of the ladle is low, the temperature difference between the inner wall and the baking flue gas is large, and the heat flux density value between the inner wall and the adjacent space nodes reaches the maximum. With the increase of the baking time, the temperature of the ladle lining rises, and the heat flux density value gradually decreases. The ladle is in a continuous heat accumulation state in the baking stage, and has strong heat accumulation capacity. Figure 16

[0214] Combined with Figure 15 and Figure 16 ​It can be seen that in the heavy ladle stage of 1-3 heats of ladle on-line operation, the heat flux value of the adjacent space nodes of the inner wall of the ladle gradually decreases, but is obviously higher than the heat flux value of 4-10 heats, and the ladle is still in a large heat storage state. In the 3rd-5th heats, the temperature of the adjacent space nodes of the inner wall of the ladle slowly rises, and the heat flux value slightly decreases, and the inner lining of the ladle is in a slow heat storage state. In the 5th-10th heats of ladle on-line operation, with the increase of the ladle turnover heats, the temperature of the inner lining of the ladle reaches the maximum value, and the temperature gradient between the high-temperature molten steel and the ladle decreases, and the temperature rise of the ladle is small, and the inner wall of the ladle and the adjacent space nodes are in a continuous heat storage and heat dissipation balance state.

[0215] According to Figure 16 the heat flux value of the inner surface of the ladle and the adjacent space nodes calculated, the change of the molten steel temperature drop in the heavy ladle stage of the first 10 heats of ladle on-line turnover can be calculated, as shown in Figure 17 In the heavy ladle stage of ladle on-line operation, the high-temperature molten steel directly contacts with the inner wall of the ladle, the inner lining temperature of the ladle is low in the first heat of ladle turnover, and the heat storage capacity is the strongest, and the molten steel temperature drop value is the largest, which is 170.02 K / heat. After 3 heats of ladle turnover, the temperature of the inner lining of the ladle continuously rises, and the heat exchange between the molten steel and the ladle gradually decreases, and the molten steel temperature drop per heat is reduced to below 100.00 K. In the 4th-10th heats of ladle turnover, the molten steel temperature drop value is in the range of 90.55-103.46 K / heat. The change of the molten steel temperature drop with the heavy ladle time in each heat of heavy ladle stage is shown in Figure 18 .

[0216] As shown in Figure 18 It can be concluded that the change of the molten steel temperature drop in the heavy ladle stage of ladle on-line turnover is similar to the heat flux change curve of the inner wall, and the molten steel temperature drop is the largest at the beginning of each heat of heavy ladle stage, and then gradually decreases to a stable state. Because the temperature of the inner lining of the ladle is low in the first 3 heats, the large heat storage of the inner lining of the ladle makes the molten steel temperature drop value larger in this stage. In the first 10 min of the first heat, the molten steel temperature drop is the largest, which is 2.51 K / min, and at the end of the first heat, the molten steel temperature drop decreases to 1.01 K; After 3 heats, the molten steel temperature drop gradually stabilizes, and in the beginning of each heat of heavy ladle, the molten steel temperature drop is in the range of 1.18-1.35 K / min, and with the increase of the heavy ladle time, the molten steel temperature drop value gradually decreases, and at the end of the heavy ladle stage, the temperature drop stabilizes in the range of 0.62-0.71 K / min.

[0217] It can be seen from the above technical solutions that the steel ladle heat transfer characteristic parameter inversion method and the molten steel temperature drop calculation method provided by the embodiment of the application, by establishing a three-dimensional finite difference heat transfer model, combining the LM algorithm, systematically studying the heat transfer characteristics and temperature field evolution law in the steel ladle turnover process, including: for different heat transfer boundary conditions of the inner lining in the steel ladle turnover process, based on the finite difference method, an explicit difference equation for three-dimensional unsteady heat transfer calculation is established, and the change of the temperature field with time is simulated within 14 h of the steel ladle roasting and 10 heats before the on-line turnover. In the on-line operation stage of the steel ladle, the closer the space node is to the inner surface of the steel ladle, the greater the temperature fluctuation in the heavy ladle and empty ladle stages; based on the LM algorithm, a calculation model for correcting the heat transfer characteristic parameters of the steel ladle lining is established, and the heat transfer characteristic parameters in the roasting stage and the 10 heats before the on-line operation are corrected. Taking the measured temperature value of the temperature measuring point as the standard, the calculation accuracy and stability of the five inversion correction schemes are compared, and the optimal comprehensive performance is calculated by simultaneously correcting the unknown heat transfer coefficients of the inner wall and the outer wall in the roasting stage. The root mean square error of the temperature correction value in the roasting stage is the lowest (2.85 K), the accuracy in the on-line operation stage is the largest (10.15%), and the temperature hit rate in the range of ±3 K reaches 100%; based on the heat transfer characteristic parameters corrected by scheme 5, the heat transfer process of the steel ladle roasting and the 10 heats before the turnover is calculated, and the following conclusion is drawn. The heat flux density of the inner wall of the steel ladle and the adjacent nodes and the molten steel temperature drop value are large within 3 heats before the on-line turnover of the steel ladle, and the molten steel temperature drop is in the range of 110.08-170.02 K / heat. The heat flux density of the inner wall and the adjacent space nodes and the molten steel temperature drop value gradually decrease to a stable state with the increase of the heavy ladle time, and at the end of the 10th heat, the molten steel temperature drop rate decreases to 0.62 K / min.

[0218] The above description is merely preferred embodiments of the application and a description of the principles of the technology used, and is not intended to limit the scope of the claimed application, but merely represents the preferred embodiments of the application. Those skilled in the art should understand that the scope of the application involved in the application is not limited to the technical solutions formed by the specific combinations of the above technical features, and should also cover other technical solutions formed by any combination of the above technical features or their equivalent features without departing from the inventive concept. Based on the embodiments of the application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of the application.

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 in 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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