CN116205076A - Analytical hierarchy process-based continuous casting secondary cooling heat exchange coefficient sensitivity quantification and determination method - Google Patents

Abstract

The invention discloses a method for quantifying and determining the sensitivity of heat transfer coefficient of continuous casting secondary cooling based on analytic hierarchy process, which belongs to the technical field of continuous casting in the metallurgical industry. The method includes: first, using the analytic hierarchy process to analyze and quantify the sensitivity of the empirical parameters in the heat transfer coefficient formula to the simulation results of the temperature field; The empirical parameters with high temperature field sensitivity can obtain the heat transfer boundary conditions of the secondary cooling zone that better match the actual production process, and achieve the purpose of improving the accuracy of temperature field simulation calculations. The analysis process of the present invention is more scientific and reasonable, and complex evaluation problems are decomposed hierarchically to form a hierarchical structure, making the problem evaluation clearer, clearer, and hierarchical; through parameter optimization, the evaluation factors with high sensitivity are adjusted and optimized in turn, Correcting the estimated value of the empirical parameters in the heat transfer model according to the measured temperature and optimizing the boundary conditions of the secondary cooling zone in the heat transfer calculation can improve the accuracy of the numerical simulation of the temperature field of the continuous casting slab and the solidification process.

Description

A method for quantifying and determining the sensitivity of the secondary cooling heat transfer coefficient of continuous casting based on the analytic hierarchy process

Technical Field

The invention belongs to the technical field of continuous casting in the metallurgical industry, and relates to a method for quantifying and determining the sensitivity of a continuous casting secondary cooling heat transfer coefficient based on a hierarchical analysis method.

Background Art

During the continuous casting process, the high-temperature molten steel undergoes crystallizer, spray secondary cooling and air-cooling radiation cooling in sequence, accompanied by the release of superheat, latent heat and sensible heat. Its essence is the transformation process of liquid steel into solid ingot. At the same time, the continuous casting solidification heat transfer controls the solute diffusion and phase change, microstructure transformation, ingot solidification shrinkage and the end position of solidification. The heat transfer condition of the continuous casting secondary cooling zone is the key factor in formulating reasonable secondary cooling zoning, the selection and arrangement of secondary cooling nozzles, and the distribution of water spray in the secondary cooling zone, and has a decisive influence on the quality of the continuous casting ingot. Therefore, determining the heat transfer coefficient of the continuous casting secondary cooling zone is important for formulating a reasonable continuous casting secondary cooling system and producing high-quality ingots.

At present, for the determination method of the heat transfer coefficient of the secondary cooling zone of continuous casting, some studies use "empirical values" for estimation. However, the temperature calculation results obtained by simulation according to the "empirical values" deviate greatly from the actual production. Some researchers also use the laboratory hot test method to heat the steel plate to a certain temperature and spray cool it. The surface temperature change of the steel plate is measured by contact thermocouples to determine the heat transfer coefficient of the spray cooling. The heat transfer coefficient measured in the laboratory is used as the boundary condition of the secondary cooling zone of continuous casting. However, there is a big difference between the spray cooling environment of the secondary cooling zone in actual continuous casting production and the laboratory hot experiment. Therefore, the measured heat transfer coefficient deviates from the actual production continuous casting secondary cooling heat transfer coefficient. Limited by the existing detection methods and technical equipment, it is very difficult to directly measure the material physical parameters, heat transfer coefficient and other calculation parameters under continuous casting production conditions through experimental methods.

The analytic hierarchy process is a multi-objective comprehensive evaluation method that quantitatively describes complex qualitative problems. Its basic idea is to decompose the various indicators of complex system problems into several ordered hierarchical structures according to their mutual subordinate relationships, compare the indicators of each layer in pairs, quantify the subjective judgment into a judgment matrix, and then use a mathematical model to calculate the weight of each indicator in each layer of the judgment matrix relative to the previous layer. Finally, a total ranking is performed to calculate the weight coefficient of all indicators relative to the total goal. At present, the analytic hierarchy process is widely used to determine the weight indicators in various multi-factor comprehensive evaluations.

In the present invention, computer simulation and experimental measurement technology are comprehensively adopted, and the hierarchical analysis method is used to perform a sensitivity analysis on the influence of the empirical parameters in the heat transfer coefficient formula of the secondary cooling zone on the temperature field, and the degree of influence is quantified and ranked; then according to the sensitivity level, combined with the actual measured temperature at the continuous casting production site, the empirical parameters in the heat transfer coefficient formula are optimized in turn, and the boundary conditions of the secondary cooling zone that are more in line with the actual production process are determined, so as to provide support for improving the simulation calculation accuracy of the temperature field in the continuous casting process, optimizing the continuous casting process and the quality control of the ingot.

Summary of the invention

The technical problem to be solved by the present invention is to propose a method for quantifying and determining the sensitivity of the heat transfer coefficient of the secondary cooling zone of continuous casting based on the analytic hierarchy process in view of the deficiencies of the prior art. According to the analytic hierarchy process and parameter optimization, combined with the continuous casting production conditions of a domestic steel plant and the measured surface temperature of the continuous casting billet, a heat transfer coefficient that is more consistent with the actual production process is obtained, the heat transfer boundary conditions of the secondary cooling zone are optimized, and the simulation calculation accuracy of the continuous casting solidification temperature field is improved.

To achieve the above object, the technical solution of the present invention is as follows:

A method for quantifying and determining the sensitivity of the heat transfer coefficient of the secondary cooling zone of continuous casting based on the analytic hierarchy process is divided into two parts. The first part is to use the analytic hierarchy process to analyze and quantify the sensitivity of the empirical parameters in the heat transfer coefficient formula to the temperature field simulation results. The second part is to optimize the empirical parameters with high sensitivity to the temperature field in the continuous casting solidification process based on the measured temperature data of the continuous casting billet in the steel plant, and obtain the heat transfer boundary conditions of the secondary cooling zone that better match the actual production process, so as to achieve the purpose of improving the accuracy of the temperature field simulation calculation. Specifically, it includes the following steps:

Step 1: Sensitivity analysis and quantification of the influence of empirical parameters in the secondary cooling heat transfer coefficient formula of continuous casting billet on temperature field

(1.1) Establishing a hierarchical structure: It is mainly to establish the factors involved in the analysis problem and their interrelationships, and decompose the relevant factors into several levels from top to bottom according to different attributes. Factors at the same level are subordinate to the factors at the upper level or have an influence on the factors at the upper level, and at the same time dominate the factors at the lower level or are affected by the factors at the lower level. The hierarchical structure is divided into a target layer (top layer), a criterion layer (middle layer) and an indicator layer (bottom layer). The present invention analyzes the influence of the heat transfer coefficient of the continuous casting secondary cooling on the temperature field. Formula (1) is the empirical formula of the heat transfer coefficient. Based on this, the target layer is designed as the surface temperature T of the specific position of the billet (i.e., the temperature measurement position); the criterion layer is the heat transfer coefficient _h1 of the first zone of the secondary cooling and the heat transfer coefficient _h2 of the second, third, and fourth zones of the secondary cooling; the indicator layer is α, β, γ, δ, ε. Establish a hierarchical model as shown in Figure 1.

Wherein, w is the water flow density, L/(m ² ·s); _Tw is the cooling water temperature, K.

(1.2) Constructing a judgment matrix: In a hierarchical structure, according to certain criteria (usually relying on expert experience or industry standards), for each factor that belongs to or affects the previous level, its importance is compared with other factors at the same level, and a certain value is assigned to the importance, using a 1-9 scale, as shown in Table 1:

Table 1: Judgment matrix scale and meaning

According to the hierarchical model established in step 1.1), the judgment matrix A of surface temperature T for h ₁ and h ₂ , the judgment matrix B of h ₁ for α and β, and the judgment matrix C of h ₂ for γ, δ, and ε are established respectively.

(1.3) Calculate the characteristic weight vector of the judgment matrix: that is, calculate the relative weight of each factor of the judgment matrix for its criteria. The eigenvector of the judgment matrix A corresponds to the maximum eigenvalue λ, which, after normalization, is the ranking weight of the relative importance of the corresponding factor at the same level to a factor at the previous level. The eigenvector of the judgment matrix is solved by the square root method. The specific steps are as follows:

Step 1: Calculate the product of the elements in each row of the matrix. The calculation formula is as follows:

In the formula, _aij represents the influence of i on the previous level relative to j in the judgment matrix A.

Step 2: Calculate the nth root _Bi of _Mi and obtain the new vector B. The calculation formula is as follows:

B＝(B ₁ ,B ₂ ,...B _n ) ^T (4)

Step 3: Normalize each _Bi . The calculation formula is as follows:

The obtained eigenvector is G = (g ₁ , g ₂ , ... g _n ) ^T .

(1.4) Calculate the maximum eigenvalue of the judgment matrix: After obtaining the eigenvector, calculate the maximum eigenvalue λ _max according to the following method. The calculation steps are as follows:

Step 1: Calculate the product of the judgment matrix A and the eigenvector G:

Step 2: Calculate the maximum eigenvalue λ _max :

(1.5) Consistency test: In order to avoid interference from other factors in judgment, the judgment matrix is required to meet the overall consistency in practice, so a consistency test is required. Only when the judgment matrix is logically reasonable through the test can the results be analyzed. The consistency test indicator is the consistency ratio C·R, which is defined as:

In the formula, C·I is the consistency index, and the specific calculation formula is as follows:

Among them, R·I is the average random consistency index, which is related to the matrix order and is calculated according to the values listed in Table 2. The test standard is that when C·R<0.1, the judgment matrix is considered acceptable.

Table 2: Average random consistency index

(1.6) Determine the comprehensive weight of the evaluation factors: According to steps 1.3), 1.4) and 1.5), calculate the comprehensive weight, maximum eigenvalue λ _max , CI, CR and consistency test results of the evaluation factors in the judgment matrix obtained according to step 1.2). Quantify the sensitivity of each evaluation factor (i.e., its comprehensive weight) and rank them, and determine the importance of the temperature field sensitivity according to its weight to determine the evaluation factor that needs to be optimized.

Step 2: Extract measured temperature and calculated temperature at specific locations

(2.1) Collecting the surface temperature of the ingot during the actual continuous casting process: Under stable casting conditions, an infrared thermometer was used to measure the temperature of the center point of the ingot surface at multiple specific positions away from the meniscus (7.75m, 8.926m, and 9.794m away from the meniscus) as the optimization comparison condition.

(2.2) Simulation calculation of temperature field in continuous casting solidification process: Based on the actual production conditions of a domestic steel plant, taking small square billet continuous casting as the object, a two-dimensional continuous casting billet finite difference heat transfer/solidification numerical calculation model was established based on the basic theory of heat transfer and solidification of continuous casting billets, as shown in Equation (10). The process conditions, boundary conditions, and physical properties of the steel type are input to solve the temperature field, and the center temperature of the billet surface at multiple specific positions away from the meniscus (7.75m, 8.926m, and 9.794m from the meniscus) is extracted as the initial condition for optimization.

—单位时间单位体积物体内部的热生成率(释放的凝固潜热)(J/(m³·s))；ρ为铸坯密度(kg/m³)；c为热容(J/(kg·K))；

为初始浇注温度；n为边界外法线方向余弦，

为给定热流密度(J/(m²·s))；h为对流换热系数；T_a为二冷水温度。Where, k—thermal conductivity (W/(m·K));

—The heat generation rate (released latent heat of solidification) per unit volume per unit time (J/(m ³ ·s)); ρ is the density of the ingot (kg/m ³ ); c is the heat capacity (J/(kg·K));

is the initial pouring temperature; n is the direction cosine of the normal line outside the boundary,

is the given heat flux density (J/(m ² ·s)); h is the convective heat transfer coefficient; _Ta is the secondary cooling water temperature.

Step 3: Optimize the key parameters in the heat transfer coefficient formula of the second cooling zone of the continuous casting billet based on the measured temperature

(3.1) The measured temperatures at multiple specific positions of the ingot (7.75m, 8.926m, and 9.794m from the meniscus) obtained in step 2.1) are used as optimization comparison conditions, and the temperatures at the center points of the surface at multiple specific positions of the ingot obtained in step 2.2) are used as optimization initial conditions. Based on the sensitivity of the evaluation factors quantified in step 1.6), the evaluation factor with the highest sensitivity is first optimized at multiple specific positions (7.75m, 8.926m, and 9.794m from the meniscus) to obtain the optimization results of the evaluation factors, and then the other evaluation factors are optimized in the same way.

与实测温度

的关系，当测温点处铸坯计算温度

与实测温度

符合程度较好时，则认为此时的换热系数值可以反映实际的传热情况；而当测点处计算温度

小于实测温度

时，说明此时的换热系数取值效果大于实际的冷却强度，应减小换热系数取值；反之，增大换热系数取值。(3.2) The optimization of empirical parameters is mainly based on the difference between the calculated value of the billet surface temperature and the target value (actual temperature). The initial calculated temperature at the specific position measurement point extracted in step 3.1) is

The measured temperature

When the temperature of the billet is calculated at the temperature measuring point

The measured temperature

When the degree of conformity is good, it is considered that the heat transfer coefficient value at this time can reflect the actual heat transfer situation; and when the temperature at the measuring point is calculated

Less than the measured temperature

It means that the heat transfer coefficient value at this time is greater than the actual cooling intensity, and the heat transfer coefficient value should be reduced; otherwise, the heat transfer coefficient value should be increased.

(3.3) Continuously adjust the parameters until the calculated temperature of all temperature measurement points is consistent with the measured temperature, and then stop the optimization. At this time, it is considered that the optimized empirical parameters are consistent with the actual working conditions. Use the above method to optimize the empirical parameters that need to be optimized at multiple specific locations in turn.

Step 4: Verification of optimization results of secondary cooling heat transfer coefficient of continuous casting billet

(4.1) Simulation calculation of the continuous casting solidification temperature field after optimizing the parameters: The heat transfer coefficient optimized in step (3) is used as the boundary condition of the second cooling zone, and the heat transfer/solidification model is input to calculate the temperature field of the continuous casting billet to obtain the change of the temperature of the center point of the billet surface with the distance from the meniscus.

(4.2) Temperature comparison before and after optimization: Combined with the measured temperature at the center of the ingot surface at multiple specific locations of the ingot, the temperature variation curves calculated in step (4.1) and step (2.2) over time are compared and analyzed to determine the accuracy of the numerical calculation.

The above-mentioned method of quantifying and determining the sensitivity and numerical value of the secondary cooling heat transfer coefficient of continuous casting based on the hierarchical analysis method makes the simulation parameters adapt to the actual production conditions, improves the calculation accuracy of the continuous casting simulation, provides support for the actual process production of continuous casting, and improves the continuous casting production efficiency.

The above method for determining the heat transfer coefficient of the secondary cooling zone of continuous casting is applicable to determining the heat transfer coefficient of the secondary cooling zone of continuous casting billets such as slabs, square billets, round billets, and profiled billets.

The beneficial effects of the present invention are:

(1) The present invention quantifies the sensitivity of the empirical parameters in the heat transfer coefficient formula to the temperature field based on the hierarchical analysis method. The hierarchical analysis method qualitatively judges and quantifies the empirical knowledge based on which the researchers rely, combines the advantages of both qualitative analysis and quantitative analysis, and makes the analysis process more scientific and reasonable; it decomposes complex evaluation problems into hierarchical structures to form a hierarchical structure, making the problem evaluation clearer, more specific, and more hierarchical.

(2) The present invention adjusts and optimizes the evaluation factors with high sensitivity in sequence through parameter optimization, and corrects the estimated values of the empirical parameters in the heat transfer model according to the measured temperature, so as to obtain the heat transfer coefficient of the second cooling zone of continuous casting that matches the actual continuous casting process, and optimizes the boundary conditions of the second cooling zone in the heat transfer calculation, thereby improving the accuracy of the numerical simulation of the temperature field and solidification process of the continuous casting billet.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 shows the hierarchical model;

Figure 2 is a schematic diagram of temperature measurement points;

FIG3 is a flow chart for quantifying and determining the sensitivity of the secondary cooling heat transfer coefficient of continuous casting and its numerical solution;

Figure 4 shows the measured temperature and calculated temperature curve of the surface center during the continuous casting process when the casting speed is 1.5m/min.

DETAILED DESCRIPTION

The present invention will be further described below through specific embodiments with reference to the accompanying drawings:

As shown in Figure 3, the flow chart of solving the main conditions of the continuous casting experiment is shown. First, the sensitivity of each empirical parameter in the heat transfer coefficient formula of the second cooling zone of continuous casting to the temperature field is analyzed and quantified by the hierarchical analysis method; secondly, the empirical parameters are optimized in turn according to the sensitivity by using the temperature data of multiple specific positions measured during the solidification process of the continuous casting billet and the parameter optimization method; finally, the optimized heat transfer coefficient formula is applied to solve the temperature field of the continuous casting billet, and the simulated temperature results are compared and verified in combination with the measured temperature of specific positions to determine the accuracy of the temperature field simulation of the continuous casting process after hierarchical analysis and parameter optimization.

Step 1: Sensitivity analysis and quantification of the influence of empirical parameters in the secondary cooling heat transfer coefficient formula of continuous casting billet on temperature field

(1.1) Establishing a hierarchical structure: Formula (11) is the empirical heat transfer coefficient formula of the continuous casting secondary cooling zone. The target layer is determined as the surface temperature of the ingot at a specific position (temperature measurement position); the quasi-measurement layer is the heat transfer coefficient of the secondary cooling zone ₁ h1 and the heat transfer coefficient of the secondary cooling zones 2, 3, and 4 _h2 ; the indicator layer is the five empirical parameters α, β, γ, δ, and ε. A hierarchical model is established as shown in Figure 1.

Wherein, w is the water flow density, L/(m ² ·s); _Tw is the cooling water temperature, K.

(1.2) Construct a judgment matrix: Based on the hierarchical model established in step 1.1), according to certain criteria, for each factor belonging to (or influencing) the previous level, compare its importance with other factors at the same level, and assign a value to the importance, using a 1-9 scale, as shown in Table 1:

Table 3: Judgment matrix scale and meaning

The judgment matrix of T for h ₁ and h ₂ is as follows:

The judgment matrix of h ₁ for α and β is as follows:

The judgment matrix of h ₂ for γ, δ, and ε is as follows:

When constructing the judgment matrix of T for h ₁ and h ₂ , since the target layer temperature is at the exit of the second cooling zone 4, h ₂ has a more significant effect on the surface temperature T of the ingot than h ₁ , so the judgment matrix shown in formula (12) is constructed; when constructing the judgment matrix of h ₁ for α and β, the importance of α to h ₁ relative to β is judged by keeping β unchanged and when α changes within its empirical value range, the range of h ₁ changes is Δh _1. Similarly, when keeping α unchanged and β changes within its empirical value range, the range of h ₁ changes is Δh′ _1. Compare the relative sizes of Δh ₁ and Δh′ ₁ to determine the importance of α to h ₁ relative to β, so the judgment matrix shown in formula (13) is constructed; when constructing the judgment matrix of h ₂ for γ, δ, and ε, the judgment matrix shown in formula (14) is constructed in the same way as the judgment matrix of h ₁ for α and β.

(1.3) Calculate the characteristic weight vector of each judgment matrix: that is, calculate the relative weight of each factor of each judgment matrix for its criterion. The eigenvector of the judgment matrix A corresponds to the maximum eigenvalue λ, which, after normalization, is the ranking weight of the relative importance of the corresponding factor at the same level to a factor at the previous level. The judgment matrix is solved by the square root method. The specific steps are as follows, taking matrix A as an example for solution:

Step 1: Calculate the product of the elements in each row of the matrix. The calculation formula is as follows:

In the formula, _aij represents the influence of i relative to j on the previous level in the judgment matrix A.

M2＝3。Then for matrix A,

M2=3.

Step 2: Calculate the nth root _Bi of _Mi and obtain the new vector B. The calculation formula is as follows:

B＝(B ₁ ,B ₂ ,...B _n ) ^T (17)

B＝(0.58,1.73)^T。Then for matrix A,

B＝(0.58,1.73) ^T .

Step 3: Normalize each _Bi . The calculation formula is as follows:

Finally, the eigenvector obtained is W = (w ₁ ,w ₂ ,...w _n ) ^T .

Then for matrix A,

(1.4) Calculate the maximum eigenvalue of the characteristic matrix: After obtaining the eigenvector, calculate the maximum eigenvalue λ _max according to the following method. The calculation steps are as follows:

Step 1: Calculate the product of the discriminant matrix A and the eigenvector G:

For matrix A,

Step 2: Calculate the maximum eigenvalue λ _max :

For the matrix A, λ _max =2.

(1.5) Consistency test: In order to avoid interference from other factors in judgment, the judgment matrix is required to meet the overall consistency in practice, so a consistency test is required. Only when the judgment matrix is logically reasonable through the test can the results be analyzed. The consistency test indicator is the consistency ratio C·R, which is defined as:

In the formula, C·I is the consistency index, and the specific calculation formula is as follows:

R·I is the consistency index, which is related to the matrix order and is calculated according to the values listed in Table 4. The test standard is that when C·R<0.1, the judgment matrix is considered acceptable.

For matrix A, C·I＝0, C·R＝0<0.1, and it is judged that matrix A is acceptable.

Table 4: Average random consistency index

(1.6) Determine the comprehensive weight of the evaluation factors: According to steps 1.3), 1.4) and 1.5), calculate the comprehensive weight, maximum eigenvalue λ _max , CI, CR and consistency test results of each evaluation factor in the judgment matrix B and C obtained according to step 1.2). Table 5 is the weight evaluation of the influencing factors. From the weight evaluation, it can be seen that the sensitivity of each evaluation factor is as follows: γ＞δ＞α＞ε＞β. It can be found that the weights of γ, δ, and α are significantly greater than ε and β. Therefore, the influence of ε and β on temperature T is ignored, and the parameters to be optimized are determined to be γ, δ and α.

Table 5: Weight evaluation of influencing factors

Step 2: Extract measured temperature and calculated temperature at specific locations

(2.1) Collecting the surface temperature of the ingot during the actual continuous casting process: Under stable casting conditions, a high-temperature infrared thermometer was used to measure the temperature of the center point of the ingot surface at multiple specific positions away from the meniscus (7.75m, 8.926m, and 9.794m away from the meniscus) as the optimization comparison condition.

(2.2) Simulation calculation of temperature field during solidification process of continuous casting billet: Based on the actual production status of a domestic steel plant, taking small square billet continuous casting as the object, a two-dimensional continuous casting billet finite difference heat transfer/solidification numerical calculation model was established based on the basic theory of heat transfer and solidification of continuous casting billet, as shown in Equation (23). The process conditions, boundary conditions, and physical properties of steel were input, the temperature field was solved, and the center temperature of the billet surface at multiple specific positions away from the meniscus (7.75m, 8.926m, and 9.794m from the meniscus) was extracted as the initial conditions for optimization.

—单位时间单位体积物体内部的热生成率(释放的凝固潜热)(J/(m³·s))；ρ为铸坯密度(kg/m³)；c为热容(J/(kg·K))；

为初始浇注温度；n为边界外法线方向余弦，

为给定热流密度(J/(m²·s))；h为对流换热系数；T_a为二冷水温度。Where, k—thermal conductivity (W/(m·K));

—The heat generation rate (released latent heat of solidification) per unit volume per unit time (J/(m ³ ·s)); ρ is the density of the ingot (kg/m ³ ); c is the heat capacity (J/(kg·K));

is the initial pouring temperature; n is the direction cosine of the normal line outside the boundary,

is the given heat flux density (J/(m ² ·s)); h is the convective heat transfer coefficient; _Ta is the secondary cooling water temperature.

Step 3: Optimize the key parameters in the heat transfer coefficient formula of the second cooling zone of the continuous casting billet based on the measured temperature

(3.1) The measured temperatures at multiple specific positions of the ingot (7.75m, 8.926m, and 9.794m from the meniscus) obtained in step 2.1) are used as optimization comparison conditions, and the temperature of the center point of the surface at a specific position of the ingot obtained in step 2.2) is used as the initial optimization condition. Based on the evaluation factors to be optimized determined in step 1.6), the most sensitive evaluation factor γ is first optimized at multiple specific positions (7.75m, 8.926m, and 9.794m from the meniscus) to obtain the optimization result of the evaluation factor γ, and then the other two evaluation factors δ and α are calculated and optimized in the same way.

与实测温度

的关系，当测点处铸坯计算温度

与实测温度

符合程度较好时，则认为此时的换热系数值可以反映实际的传热情况；而当测点处计算温度

小于实测温度

时，说明此时的换热系数取值效果大于实际的冷却强度，应减小换热系数取值；反之，相应的换热系数取值则应增加。(3.2) The optimization of empirical parameters is mainly based on the difference between the calculated value of the billet surface temperature and the target value (actual temperature). The initial calculated temperature at the specific position measurement point extracted in step 3.1) is

The measured temperature

When the temperature of the billet is calculated at the measuring point

The measured temperature

When the degree of conformity is good, it is considered that the heat transfer coefficient value at this time can reflect the actual heat transfer situation; and when the temperature at the measuring point is calculated

Less than the measured temperature

It means that the heat transfer coefficient value at this time is greater than the actual cooling intensity, and the heat transfer coefficient value should be reduced; otherwise, the corresponding heat transfer coefficient value should be increased.

(3.3) Parameters are continuously adjusted until the calculated temperature of all temperature measurement points matches the measured temperature, and then the optimization is stopped. At this time, it is considered that the optimized empirical parameters are consistent with the actual working conditions. The above method is used to optimize γ, δ, and α at multiple measured positions.

Step 4: Verification of optimization results of secondary cooling heat transfer coefficient of continuous casting billet

(4.1) as shown in the following table: Table 6 shows the optimization results of γ, δ, and α at different pulling speeds. It can be seen that as the pulling speed increases, γ, δ, and α all show a decreasing trend.

Table 6: Optimization results of γ, δ, α at different casting speeds

(4.2) Substitute the optimized empirical parameters γ, δ, and α obtained in step 4.1) into the heat transfer coefficient formula, input the optimized heat transfer coefficient formula into the calculation model, calculate the temperature field of the continuous casting process, and output the change of the center temperature of the surface of the ingot with the distance from the meniscus. Compare and analyze the results of the temperature field calculated using the empirical heat transfer coefficient in step 2.1) and step 2.2) to verify the actual measurement of multiple specific position temperatures. As shown in Figure 4, compared with the results of the simulation calculation using the empirical heat transfer coefficient, the temperature data obtained by the optimized heat transfer coefficient calculation is more consistent with the actual temperature data. It is proved that the key condition sensitivity analysis and quantification based on the hierarchical analysis method can accurately find out the main reasons for the change of the temperature field of the continuous casting ingot. At the same time, the optimized heat transfer coefficient is more in line with the actual production conditions, and the calculated temperature field is more accurate.

(4.3) Table 7 shows the error between the measured temperature results at 7.75m, 8.926m, and 9.794m from the meniscus at different pulling speeds and the temperature results calculated by the model before optimization. It can be found that the average error is 13-20°C. Table 8 shows the error between the measured temperature results at 7.75m, 8.926m, and 9.794m from the meniscus at different pulling speeds and the temperature results calculated by the optimized model. The average error is 3-5°C. It also verifies that the optimized heat transfer coefficient is used as the boundary condition of the second cooling zone. The calculation results of the temperature field are more accurate and more in line with the actual production conditions.

Table 7: Error between calculated temperature results before optimization and actual temperature measurement results

Table 8: Error between calculated temperature results after optimization and actual temperature measurement results

The above-described embodiments merely express the implementation methods of the present invention, but they cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims (5)

1. A method for quantifying and determining the sensitivity of the heat transfer coefficient of the secondary cooling zone of continuous casting based on the hierarchical analysis method, characterized in that the method is divided into two parts. One is to use the hierarchical analysis method to analyze and quantify the sensitivity of the empirical parameters in the heat transfer coefficient formula to the temperature field simulation results; the other is to optimize the empirical parameters with high sensitivity to the temperature field in the continuous casting solidification process based on the measured temperature data of the continuous casting billet in the steel plant, so as to obtain the heat transfer boundary conditions of the secondary cooling zone that better match the actual production process, thereby achieving the purpose of improving the accuracy of temperature field simulation calculation. 2. The method for quantifying and determining the sensitivity of the heat transfer coefficient of the secondary cooling of continuous casting based on the analytic hierarchy process according to claim 1, characterized in that it comprises the following steps: Step 1: Sensitivity analysis and quantification of the influence of empirical parameters in the secondary cooling heat transfer coefficient formula of continuous casting billet on temperature field (1.1) Establishing a hierarchical structure: Analyze the influence of the heat transfer coefficient of the continuous casting secondary cooling on the temperature field, and obtain the empirical formula of the heat transfer coefficient as shown in formula (1). Based on this, the design target layer is the surface temperature T of the specific position of the billet; the criterion layer is the heat transfer coefficient of the secondary cooling zone ₁ h1 and the heat transfer coefficient of the secondary cooling zone ₂ h2; the indicator layer is α, β, γ, δ, ε; establish a hierarchical model;

Wherein, w is the water flow density, L/(m ² ·s); _Tw is the cooling water temperature, K; (1.2) Construct a judgment matrix: Use a 1-9 scale, as shown in Table 1: Table 1: Judgment matrix scale and meaning

According to the hierarchical model established in step 1.1), the judgment matrix A of surface temperature T for h ₁ and h ₂ , the judgment matrix B of h ₁ for α and β, and the judgment matrix C of h ₂ for γ, δ, and ε are established respectively; (1.3) Calculate the eigenweight vector of the judgment matrix: that is, calculate the relative weight of each factor of the judgment matrix with respect to its criterion; the eigenvector of the judgment matrix A corresponding to the maximum eigenvalue λ, after normalization, is the ranking weight of the relative importance of the corresponding factor at the same level to a factor at the previous level; (1.4) Calculate the maximum eigenvalue of the judgment matrix: After obtaining the eigenvector, calculate the maximum eigenvalue λ _max ; (1.5) Consistency test: The consistency test indicator is the consistency ratio C·R, which is defined as:

In the formula, C·I is the consistency index, and the specific calculation formula is as follows:

Among them, R·I is the average random consistency index, which is related to the matrix order and is calculated according to the values listed in Table 2; the test standard is that when C·R<0.1, the judgment matrix is considered acceptable; Table 2: Average random consistency index

(1.6) Determine the comprehensive weight of the evaluation factors: According to steps 1.3), 1.4) and 1.5), calculate the comprehensive weight, maximum eigenvalue λ _max , CI, CR and consistency test results of the evaluation factors in the judgment matrix obtained according to step 1.2); quantify the sensitivity of each evaluation factor and rank them, and determine the importance of the sensitivity to the temperature field according to its weight to determine the evaluation factor that needs to be optimized; Step 2: Extract measured temperature and calculated temperature at specific locations (2.1) Collecting the surface temperature of the ingot during the actual continuous casting process: Under stable casting conditions, use an infrared thermometer to measure the temperature of the center point of the ingot surface at multiple specific locations away from the meniscus as the optimization comparison condition; (2.2) Simulation calculation of temperature field in continuous casting and solidification process: Based on the actual production conditions of a domestic steel plant, taking small square billet continuous casting as the object, and based on the basic theory of heat transfer and solidification of continuous casting billets, a two-dimensional continuous casting billet finite difference heat transfer/solidification numerical calculation model was established. The process conditions, boundary conditions, and steel grade physical properties were input to solve the temperature field, and the center temperature of the billet surface at multiple specific positions away from the meniscus was extracted as the initial condition for optimization; Step 3: Optimize the key parameters in the heat transfer coefficient formula of the second cooling zone of the continuous casting billet based on the measured temperature (3.1) The measured temperatures at multiple specific positions of the ingot obtained in step 2.1) are used as optimization comparison conditions, and the temperatures at the center points of the surface at multiple specific positions of the ingot obtained in step 2.2) are used as optimization initial conditions. Based on the sensitivity of the evaluation factors quantified in step 1.6), the evaluation factor with the highest sensitivity is first optimized at multiple specific positions to obtain the optimization results of the evaluation factors, and then the other two evaluation factors are optimized in turn in the same manner; (3.2) The optimization of empirical parameters is mainly based on the difference between the calculated value of the billet surface temperature and the target value, where the target value is the measured temperature; (3.3) Continuously adjust the parameters until the calculated temperature of all temperature measurement points is consistent with the measured temperature, and then stop the optimization. At this time, it is considered that the optimized empirical parameters are consistent with the actual working conditions; use the above method to optimize the empirical parameters that need to be optimized at multiple specific locations in turn; Step 4: Verification of optimization results of secondary cooling heat transfer coefficient of continuous casting billet (4.1) Simulation calculation of continuous casting solidification temperature field after optimizing parameters: The heat transfer coefficient optimized in step (3) is used as the boundary condition of the secondary cooling zone, input into the heat transfer/solidification model, and the temperature field of the continuous casting billet is calculated to obtain the variation of the temperature at the center point of the billet surface with the distance from the meniscus; (4.2) Temperature comparison before and after optimization: Combined with the measured temperature at the center of the ingot surface at multiple specific locations of the ingot, the temperature variation curves calculated in step (4.1) and step (2.2) over time are compared and analyzed to determine the accuracy of the numerical calculation. 3. The method for quantifying and determining the sensitivity of the heat transfer coefficient of the continuous casting secondary cooling system based on the analytic hierarchy process according to claim 2 is characterized in that, in the step (1.3), the judgment matrix is solved for its eigenvector by the square root method, and the specific steps are as follows: 1.3.1) Calculate the product of the elements in each row of the matrix. The calculation formula is as follows:

In the formula, a _ij represents the influence of i on the previous level relative to j in the judgment matrix A; 1.3.2) Calculate the nth root _Bi of _Mi and obtain the new vector B. The calculation formula is as follows:

B＝(B ₁ ,B ₂ ,…B _n ) ^T (4 1.3.3) Normalize each _Bi ; the calculation formula is as follows:

The obtained eigenvector is G = (g ₁ , g ₂ , … g _n ) ^T . 4. A method for quantifying and determining the sensitivity of heat transfer coefficient of continuous casting secondary cooling based on hierarchical analysis method according to claim 2, characterized in that the specific process of optimization of step (3.2) is: according to the relationship between the initial calculated ^{temperature TjC} _and the measured temperature _TjM at the specific position measuring point extracted in step 3.1), when the calculated temperature _TjC of the casting at the measuring ^point is consistent with the measured temperature ^TjM to a good extent, it is considered that the heat transfer ^coefficient value at this time can reflect the actual heat transfer situation; and when ^{the calculated temperature TjC} _{at the measuring point is less than the measured temperature TjM ,} ^it _means that the heat transfer coefficient value effect at this time is greater than the actual cooling intensity, and the heat transfer coefficient value should be reduced; otherwise, the heat transfer coefficient value should be increased. 5. A method for quantifying and determining the sensitivity of the secondary cooling heat transfer coefficient of continuous casting based on the hierarchical analysis method according to any one of claims 1-4, characterized in that the method is applicable to the quantification and determination of the sensitivity of the secondary cooling heat transfer coefficient of slabs, square billets, round billets, special-shaped billets or other continuous casting billets.

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