Development method and optimization method of efficient square billet crystallizer heat flow model

Abstract

The invention discloses a development method and an optimization method for a heat flow model of an efficient square billet crystallizer. The method comprises the following steps: acquiring an average heat flow value and a pulling speed parameter of a continuous casting crystallizer; based on the average heat flow value, an instantaneous heat flow distribution function is constructed, and the integral or discrete summation value of the instantaneous heat flow distribution function within the effective height range of the crystallizer and the average heat flow value meet a preset mathematical constraint relation; the average heat flow value calculated by the instantaneous heat flow distribution function is equal to the obtained average heat flow value; determining instantaneous heat flow values at different height positions in the crystallizer according to the instantaneous heat flow distribution function; and inputting the instantaneous heat flow value as a heat boundary condition into a continuous casting solidification heat transfer model for simulating the solidification action of a casting blank in a crystallizer. The high-efficiency square billet crystallizer heat flow model is suitable for the high-pulling-speed working condition, the development of the high-efficiency continuous casting technology is promoted, and the high-productivity, low-cost and green steel production target is achieved in an assisted mode.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of steelmaking continuous casting, and particularly relates to a method for developing a high-efficiency bloom crystallizer heat flow model and an optimization method. BACKGROUND

[0002] High-speed continuous casting is an eternal topic for continuous casting workers, and high-speed casting is one of the core contents. High-speed casting is the basis for realizing high productivity, low equipment cost and low production cost, and is also the main supporting technology for realizing green steel production. At the same time, high-speed casting is a necessary condition for connecting straight sending and straight rolling, headless rolling and other low-energy and near-end production processes. Through years of continuous research, the vibration equipment and process of the crystallizer of the continuous casting machine, the copper pipe form, the protective slag, the secondary cooling equipment and process and the like are improved, the maximum casting speed of 155mm*155mm small bloom is increased to 5.7m / min, the production casting speed is in the range of 4.5-5.0m / min, the maximum casting speed of 160mm*160mm small bloom is increased to more than 6.0m / min, and the existing technology completely has the space for further improving the casting speed. In the high-speed casting research, the heat transfer in the crystallizer is crucial, but when the temperature field simulation is carried out at high speed, it is found that the existing heat flow distribution formula in the crystallizer and the formula given in the existing technology are not completely suitable for the current situation of high-speed casting, and the average heat flow of the crystallizer calculated according to the existing heat flow distribution formula in the crystallizer is smaller than the average heat flow calculated by the actual measured water flow and temperature difference of the crystallizer, which leads to the fact that the total heat transferred from the crystallizer in the model calculation is smaller, and the calculation result must have deviation, which affects the simulation calculation result of the bloom shell thickness and temperature in the crystallizer, and brings influence to the process design and establishment of the crystallizer taper, foot roller water quantity and the like. In addition, the calculated crystallizer heat transfer is smaller than the actual one, and the subsequent calculation of the solidification end position will be delayed, which will bring deviation to the determination of the maximum casting speed, the design of the fire cutting point position and the establishment of the straight sending and straight rolling process. SUMMARY

[0003] In order to overcome the above-mentioned defects of the prior art, the purpose of the present application is to provide a method suitable for model high-speed crystallizer heat flow distribution, which can ensure that the average heat flow in the crystallizer is consistent with the actual measured average heat flow, and can maximize the reliability of the calculation result, so as to solve the problems in the above background art.

[0004] The technical scheme adopted by the present application to solve the technical problems is: a method for developing a high-efficiency bloom crystallizer heat flow model and an optimization method, comprising the following steps:

[0005] S1, obtaining the average heat flow value of the continuous casting crystallizer and the casting speed parameter V;

[0006] S2, constructing a transient heat flux distribution function based on the average heat flux value, wherein an integral or discrete summation value of the transient heat flux distribution function in the effective height range of the crystallizer satisfies a preset mathematical constraint relationship between the average heat flux value, and the average heat flux value calculated by the transient heat flux distribution function is equal to the obtained average heat flux value;

[0007] S3, determining the transient heat flux value at different height positions in the crystallizer according to the transient heat flux distribution function;

[0008] S4, inputting the transient heat flux value as a thermal boundary condition into a continuous casting solidification heat transfer model for simulating the solidification action of the casting blank in the crystallizer.

[0009] As a further improvement of the present application: in the step S2, comprising:

[0010] Discretely setting N grid points in the effective height direction of the crystallizer, and each grid point corresponds to a height h i , i is the grid point number, i = 0, 1, 2,..., N;

[0011] Constructing a transient heat flux distribution function f(h i ) or f(t i ) about height h i or time t i , wherein time t i = h i / V.

[0012] As a further improvement of the present application: in the step S2, further comprising:

[0013] Setting a normalization constraint condition for the transient heat flux distribution function, so that the sum of the function values at all grid points is equal to the total number of grid points N, that is, Σf(h i ) = N or Σf(t i ) = N;

[0014] As a further improvement of the present application: in the step S3, comprising:

[0015] Based on the average heat flux value and the transient heat flux distribution function satisfying the normalization constraint condition, the transient heat flux value q i at each grid point is calculated, and the transient heat flux value or

[0016] As a further improvement of the present application: in the step S4, comprising:

[0017] Inputting the calculated transient heat flux value q iAs a thermal boundary condition, the average heat flux value is input into the billet continuous casting solidification heat transfer model for calculation to simulate the solidification process of the billet in the mold.

[0018] As a further improvement of the present application: the step S2 further comprises:

[0019] In the step of constructing the instantaneous heat flux distribution function, the function is a piecewise power function about time ti, and the expression is:

[0020] f(t i )=A, when t i ≤T;

[0021] f(t i )=A*t i n , when t i >T;

[0022] Wherein, A is a normalization coefficient, n is a distribution index, T is a time segmentation point, t i is the time experienced to reach hi.

[0023] As a further improvement of the present application: the normalization coefficient A is obtained by solving the normalization constraint condition, and the specific calculation formula is:

[0024] A=N / Σt i n , and the value of the distribution index n is-0.5.

[0025] As a further improvement of the present application: the average heat flux value is calculated by actually measuring the cooling water flow rate of the mold, the inlet and outlet temperature difference, and the effective heat transfer area, and the calculation formula is:

[0026]

[0027] Wherein, ρ is the density of cooling water, cp is the specific heat capacity of cooling water, Q is the water flow rate, ΔT is the inlet and outlet temperature difference, and Seff is the effective heat transfer area of the mold.

[0028] As a further improvement of the present application: the average heat flux value is calculated by the average heat flux formula , wherein V c is the pulling speed, and a and b are fitting coefficients.

[0029] On the other hand, the present application also provides a continuous casting process parameter optimization method, comprising:

[0030] The heat flux model is developed by using the method according to any one of the above schemes, and the billet shell thickness and / or the billet surface temperature at the mold outlet are obtained by running;

[0031] The thickness of the billet shell and / or the surface temperature of the billet are compared with preset target values;

[0032] Based on the comparison results, adjust one or more continuous casting process parameters, including the crystallizer taper, cooling water volume in the foot roll area, water distribution model in the secondary cooling zone, casting speed setting, or fire cutter position.

[0033] Compared with the prior art, the beneficial effects of the present invention are:

[0034] The method for developing a high-efficiency billet crystallizer heat flow model of the present invention is applicable to high-efficiency billet crystallizer heat flow models under high casting speed conditions. It accurately simulates the heat transfer process within the crystallizer, providing reliable guidance for continuous casting process design and actual production, promoting the development of high-efficiency continuous casting technology, and helping to achieve the goals of high-capacity, low-cost, and green steel production. It also meets the high casting speed requirements of advanced processes such as direct feeding and direct rolling. However, it is necessary to overcome the problem that existing formulas for heat flow distribution within the crystallizer are not applicable at high casting speeds, and to correct the deviation between the calculation results of existing formulas and the actual measurement results. It is crucial to ensure that the average heat flow of the crystallizer calculated by the model is consistent with the measured average heat flow, thereby accurately simulating the billet shell thickness and temperature within the crystallizer, rationally designing process parameters such as crystallizer taper and foot roll water volume, accurately determining the solidification end position, maximum casting speed, and fire cutting point position, and eliminating the impact of heat flow calculation deviations on the formulation of processes such as direct feeding and direct rolling. Attached Figure Description

[0035] Figure 1 This is a schematic diagram of the structure of the present invention; Figure 2 Schematic diagram of average heat flux statistics and measured results; Figure 3 Schematic diagram of high-speed average heat flux fitting; Figure 4 Schematic diagram of instantaneous heat flow distribution inside the crystallizer under different pulling speeds; Figure 5 A schematic diagram comparing the average heat flow calculated according to formula (2) and the measured average heat flow; Figure 6 Comparison of instantaneous heat flow trends Figure 6 A schematic diagram comparing the instantaneous heat flux distribution with different grid numbers; Figure 7 Schematic diagram of instantaneous heat flux distribution with different grid numbers; Figure 8 Based on the measured crystallizer temperature, a regression n-exponential diagram is shown. Figure 9 Based on the literature's schematic diagram of heat flow distribution regression n-index; Figure 10 A schematic diagram of the instantaneous heat flow trend when the exponent n takes different values; Figure 11The temperature field is calculated according to equation (2) for heat flow distribution. Figure 11 A schematic diagram of the temperature field results calculated using the method n=-0.504; Figure 12 A schematic diagram of the temperature field calculated by the method of the present invention with n=-0.504; Figure 13 A schematic diagram of the temperature field calculated by the method in this paper with n=-0.25; Figure 14 A schematic diagram of the temperature field calculation results. Detailed Implementation

[0036] In order to clearly and completely understand the technical solution, the present invention will be further described in conjunction with the embodiments and accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention. All other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0037] It should be understood that, when used in this specification and the appended claims, the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0038] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0039] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0040] Embodiments of the present invention provide a method for developing a high-efficiency billet crystallizer heat flow model, comprising the following steps:

[0041] S1. Obtain the average heat flux value of the continuous casting mold. and pulling speed parameter V;

[0042] S2. Based on the average heat flux value, construct an instantaneous heat flux distribution function, wherein the integral or discrete summation value of the instantaneous heat flux distribution function within the effective height range of the crystallizer satisfies a preset mathematical constraint relationship with the average heat flux value, and the average heat flux value calculated by the instantaneous heat flux distribution function is equal to the obtained average heat flux value;

[0043] S3. Determine the instantaneous heat flux values ​​at different height positions within the crystallizer based on the instantaneous heat flux distribution function;

[0044] S4. Input the instantaneous heat flow value as a thermal boundary condition into the continuous casting solidification heat transfer model to simulate the solidification action of the billet in the crystallizer.

[0045] As a further improvement of the present invention: step S2 includes:

[0046] N grid points are discretely set along the effective height direction of the crystallizer, and the height corresponding to each grid point is h. i , where i is the grid point index, i = 0, 1, 2, ..., N;

[0047] Construct about height h i or time t i The instantaneous heat flux distribution function f(hi) or f(ti), where time t i =h i / V.

[0048] As a further improvement of the present invention: step S2 further includes:

[0049] A normalization constraint is set on the instantaneous heat flux distribution function such that the sum of the function values ​​at all grid points equals the total number of grid points N, i.e., Σf(h i ) = N or Σf(t) i ) = N;

[0050] As a further improvement of the present invention: step S3 includes:

[0051] Based on the average heat flux value The instantaneous heat flux value q at each grid point is calculated using the instantaneous heat flux distribution function that satisfies the normalization constraint conditions. i The instantaneous heat flux value or

[0052] As a further improvement of the present invention: step S4 includes:

[0053] The instantaneous heat flux value q at each grid point is calculated. i As a thermal boundary condition, it is input into the billet continuous casting solidification heat transfer model for calculation to simulate the billet solidification process in the crystallizer.

[0054] As a further improvement of the present invention: step S2 further includes:

[0055] In the step of constructing the instantaneous heat flux distribution function, the function is a piecewise power function with respect to time ti, and its expression is:

[0056] f(t i ) = A, when t i When ≤T;

[0057] f(t i )=A*t i n When t i >T time;

[0058] Where A is the normalization coefficient, n is the distribution exponent, T is the time segment point, and t is the time interval. i The time taken to reach hi.

[0059] As a further improvement of the present invention: the normalization coefficient A is obtained by solving the normalization constraint conditions, and the specific calculation formula is as follows:

[0060] A = N / Σt i n The distribution index n has a value of -0.5.

[0061] As a further improvement of the present invention: the average heat flux value The calculation formula is obtained by measuring the cooling water flow rate, inlet and outlet temperature difference, and effective heat transfer area of ​​the crystallizer.

[0062]

[0063] Where ρ is the density of cooling water, cp is the specific heat capacity of cooling water, Q is the water flow rate, ΔT is the temperature difference between the inlet and outlet, and Seff is the effective heat transfer area of ​​the crystallizer.

[0064] As a further improvement of the present invention: the average heat flux value Through the average heat flow formula The calculation yields V. c Let be the pulling speed, and a and b be the fitting coefficients.

[0065] On the other hand, the present invention also provides a method for optimizing continuous casting process parameters, comprising:

[0066] Develop a heat flow model using any of the methods described above, and run it to obtain the shell thickness and / or surface temperature of the cast billet at the crystallizer outlet.

[0067] The thickness of the billet shell and / or the surface temperature of the billet are compared with preset target values;

[0068] Based on the comparison results, adjust one or more continuous casting process parameters, including the crystallizer taper, cooling water volume in the foot roll area, water distribution model in the secondary cooling zone, casting speed setting, or fire cutter position.

[0069] Detailed description of the invention:

[0070] 1. Crystallizer heat flow and high-speed production practice

[0071] Evaluating and simulating the heat flux of a crystallizer requires quantitative research on three key characteristics: average heat flux, maximum heat flux, and heat flux distribution. Average heat flux reflects the heat transfer capacity of the crystallizer and can be calculated by measuring the water flow and temperature difference within the crystallizer, or obtained through an inverse problem model using temperature measuring equipment installed on the copper tubes. Maximum heat flux is the peak heat flux at the meniscus of the crystallizer. Heat flux distribution is the instantaneous heat flux distribution along the pulling direction within the crystallizer. Maximum heat flux and heat flux distribution are primarily obtained through temperature measurement and inverse problem models.

[0072] The average heat flux of the crystallizer, combined with the measured results of high-speed production of small billets in this application, is statistically analyzed and measured as follows: Figure 1 As shown. The measured average heat flow of the crystallizer in this application is calculated according to formula (1). The specific conditions are as follows: the cross-section is a small square billet of 155mm×155mm, the effective height of the crystallizer is 900mm, the steel grade is HRB400E (composition: w(C)=0.22%, w(Si)=0.4%, w(Mn)=1.27%, w(S)=0.02%, w(P)=0.03%, w(V)=0.004%, w(Nb)=0.008%), protective slag lubrication is used, the superheat is 10~20℃, the crystallizer water flow rate is 18~21m / s, the crystallization inlet water temperature is about 32℃, the crystallizer water temperature difference is 8~10℃, the crystallizer electric agitator is used (current 300A, frequency 3.5Hz), and the crystallizer lower opening size is 159mm×159mm.

[0073]

[0074] In the formula: ρ is the density of cooling water, kg / m³ 3 cp is the specific heat capacity of cooling water, 4.182 kJ / (kg·℃); Q is the flow rate of water in the crystallizer, m³ / s. 3 / s; ΔT is the water temperature difference, K; Seff is the effective heat transfer area of ​​the crystallizer, m² 2 .Depend on Figure 1It can be seen that due to the many factors affecting heat transfer in the crystallizer and the differences in existing testing conditions, the data range fluctuates significantly. However, overall, they all reflect a clear trend of increasing average heat flux in the crystallizer with increasing casting speed. From the oil and protective slag lubrication formulas derived from Wolf regression, it can be seen that oil lubrication is better than protective slag in heat transfer. However, compared with the actual test results, the formula results for protective slag are obviously too small, while those for lubricating oil are more consistent with the current test results. This may be due to the application of different copper tubes in the crystallizer or the advancement of protective slag technology. The LORENTO formula is the fitting result for a 700mm long crystallizer. Among all the formulas, it has the largest average heat flux, which conforms to the basic rule: for the same casting speed, as the crystallizer length increases, the decrease in instantaneous heat flux becomes more significant, thus lowering the average heat flux. Based on the comparison with the measured average heat flux, the Wolf oil lubrication, Li, and Lorento regression formulas are recommended as reference formulas for calculating the average heat flux of small billets at high casting speeds.

[0075] For the crystallizer with an effective length of 900 mm in this application, the measured data is located in the middle of the fitted data of LI and LORENTO. Therefore, the average data of the two is used to refit the average heat flow fitting formula that is more suitable for the measured data of this application, as follows: Figure 2 As shown, the specific average heat flux fitting formula is 1.34·V. c 0.502 (Extraction speed V) c (m / min). CHOW's experimental results show that the heat transfer of the crystallizer in high-carbon steel is greater than that in low-carbon steel. However, the average heat flow of the crystallizer in this application was obtained on low-carbon steel. Therefore, the average heat flow of high-carbon steel is likely to be greater than the existing measurement results. Thus, the average heat flow formula recommended above may not be suitable and needs to be refitted based on the experimental results.

[0076] The maximum heat flux, also known as the peak heat transfer at the meniscus of the crystallizer, is influenced by more complex factors and varies more drastically, ranging from 3.0 to 9.0 MW / m². 2 The data is quite divergent. The maximum heat flux results are as follows: Figure 2 As shown, the measured results indicate that the maximum heat flux is 5.6 MW / m at a pulling speed of 3.0 m / min. 2 In thin strip continuous casting, the maximum heat flux can reach 10.0–20.0 MW / m²; when the casting speed reaches approximately 20.0 m / min, it is recommended that the maximum heat flux be 12.4 MW / m². 2 Even at the same moment, the maximum heat flux on the four sides of the crystallizer can differ by 3.0 to 4.0 MW / m. 2For model calculations, LI recommends taking the maximum heat flux as 5.0 MW / m² at high drawing speeds. This is comparable to the average of the maximum heat flux measured by CHOW on the four surfaces, and can be used as a reference for the model's maximum heat flux. In principle, the peak value of the maximum heat flux can be evaluated by calculating the hot-side temperature of the copper tubes using the cold-side water temperature and the thickness of the crystallizer copper tubes. The calculated hot-side temperature should not exceed the withstand temperature of the copper tube's hot-side material; otherwise, the copper tubes will be burned and damaged, rendering them unusable. Maximum heat fluxes within this range are considered reasonable.

[0077] To calculate the heat flow distribution in the solidification heat transfer model of the billet within the crystallizer, it is necessary to know the heat flow distribution within the crystallizer. The maximum heat flow is only one important value in the heat flow distribution. This application compares various heat flow distribution laws, including the heat flow distribution formula used in the self-developed billet temperature field calculation program. It was found that the average heat flow in the crystallizer calculated according to the existing heat flow distribution is smaller than the actual measurement. That is, the heat released in the crystallizer calculated by the model is less than the actual situation, which leads to the calculation results of the temperature inside the crystallizer and the billet shell being inconsistent with the actual situation. Related designs based on this will inevitably have large errors. LI et al. gave a heat flow distribution formula, as shown in equation (2). The heat flow distribution in the crystallizer calculated directly according to this formula is as follows: Figure 3 As shown, this formula linearizes the heat transfer at the meniscus of the crystallizer, providing the instantaneous heat flow distribution at different locations under different drawing speeds. The maximum instantaneous heat flow at the meniscus does not change with the drawing speed. Subsequently, as the drawing speed decreases, the overall heat flow decreases, which is consistent with the actual law. As the drawing speed decreases, the thickness of the billet shell inside the crystallizer increases, and the rate of heat transfer decreases, so the instantaneous heat flow will decrease.

[0078] q = 5 - 0.2444t, t ≤ 1.0

[0079] q=4.7556t-0.504, t>1.0, (2)

[0080] In the formula: q represents the heat flux at different heights, W / m 2 t represents time, in seconds.

[0081] This heat flow distribution formula is quite suitable for high-speed continuous casting, but there is still a phenomenon where the average heat flow obtained according to the given heat flow distribution formula is less than the given (or measured) average heat flow. The instantaneous heat flow is calculated according to formula (2), the curve is integrated and averaged (discrete method: sum the instantaneous heat flows at different heights and then divide by the number) to obtain the average heat flow value; simultaneously, the program is loaded according to formula (2) to determine the instantaneous heat flow, which can also yield the average heat flow. The obtained average heat flow is as follows: Figure 8 As shown. From Figure 4It can be seen that the final average heat flow is less than the measured value and also less than the result obtained by the average heat flow formula of self-regression. It is about 0.5 MW / m2 smaller than the measured result. That is, the total heat output from the crystallizer calculated by the heat flow distribution formula (2) will be less than the given heat.

[0082] 2. Derivation of the heat flow distribution formula

[0083] The instantaneous heat flow distribution law is difficult to obtain through actual measurement, but it must be given for the temperature field calculation model. Therefore, it needs to be constructed, as in the form of equation (2). However, for the calculation model, after the instantaneous heat flow distribution is fixed, the average heat flow obtained from this distribution must be close to or equal to the given average heat flow in order to ensure that the calculation results are reasonable and reliable. This should be the premise for constructing the heat flow distribution law. Based on this, this application explores a method for constructing the heat flow distribution. When constructing the instantaneous heat flow distribution law, the average heat flow is given as a known condition. The average heat flow can be obtained in two ways: calculated by equation (1) based on the measured water volume and temperature difference of the crystallizer; or calculated according to the average heat flow formula recommended earlier in this application. Assume that the instantaneous heat flow distribution law along the height direction of the crystallizer is f(h i If ), then the instantaneous heat flow can be set as shown in equation (3).

[0084]

[0085] In the formula: q i For heat flow at different heights, W / m 2 ; The average heat flux is W / m 2 ; i represents different discrete heights in the height direction.

[0086] Equation (4) can be obtained from the prerequisite that the average instantaneous heat flux at height must be equal to the average heat flux.

[0087]

[0088] In the formula: N is the number of grids discrete along the height. Substituting equation (3) into equation (4), equation (5) can be derived.

[0089] ∑f(h i )=N,(5)

[0090] Equation (5) is the condition that must be met to construct the instantaneous heat flow distribution. Only when this condition is met can the average heat flow obtained according to this distribution law be exactly the same as the measured average heat flow, ensuring that the total heat output from the crystallizer is consistent with the actual situation.

[0091] Assuming that the instantaneous heat flux is distributed in a power form, while avoiding the occurrence of a maximum value on the meniscus, and that the constant can be solved, the expression of equation (6) is set as a piecewise function like equation (2).

[0092] f(h i ) = A, t i ≤1.0

[0093] f(h i )=A·t i n , ti>1.0, (6)

[0094] In the formula: A is a constant; n is a power; ti is the time taken to reach hi, in seconds; assuming the pulling speed is V, in m / min;

[0095] Obviously t i =h i / V, (7)

[0096] Substituting equation (6) into equation (5), we can obtain equation (8).

[0097] A = N / ∑t i n (8)

[0098] Once the instantaneous heat flow distribution trend *n* and the pulling speed are known, *A* can be calculated using equation (8). Based on the average heat flow and distribution formulas, the instantaneous heat flow distribution law can be obtained. Clearly, by constructing a calculation model based on this heat flow distribution formula for the crystallizer heat flow distribution calculation, the average heat flow obtained from the calculated heat flow distribution is equal to the measured average heat flow, thus ensuring the rationality and reliability of the model calculation. Simultaneously, as the pulling speed changes, while ensuring the distribution form remains constant, *A* changes, and the maximum heat flow and heat flow distribution will also change, which is more consistent with the actual situation.

[0099] 3. Operational verification

[0100] The heat flow distribution at high drawing speeds is constructed according to the heat flow distribution formula of this application. The process is as follows: determine the drawing speed and the grid along the drawing direction in the crystallizer, calculate A, determine the average heat flow, and obtain the heat flow distribution corresponding to the given drawing speed. In the case of high drawing speed in this application, the effective height of the crystallizer is 900mm, n is taken as -0.504 in formula (2), and the crystallizer is divided into 65 grids along the drawing direction. Table 1 shows the characteristic parameters obtained according to the method of this application. Among them, "average heat flow according to the method of this application" is obtained by summing and averaging all nodes according to the heat flow distribution formula, and "average heat flow according to formula (2)" is obtained by summing and averaging all nodes according to the heat flow distribution obtained according to formula (2). Figure 5 The table shows the heat flow distribution at each node (i.e., at different locations) under different pulling speeds for two heat flow distribution methods. Evaluation parameters for heat flow distribution patterns are shown in Table 1, and instantaneous heat flow trends are compared as follows: Figure 9 As shown in Table 1 and Figure 9It can be seen that: the average heat flow obtained by the method of this application is consistent with the measured average heat flow, ensuring that the total heat output from the crystallizer is the same as the measured value, while the average heat flow obtained by the instantaneous heat flow distribution result obtained by equation (2) is smaller; the instantaneous heat flow distribution obtained by the method of this application is generally larger than that of equation (2); in the instantaneous heat flow processing near the meniscus of the crystallizer, equation (2) adopts linear processing, while in the method of this application, equivalent processing is performed in order to obtain the solution of the constant A; the maximum instantaneous heat flow at the meniscus in equation (2) does not change with the drawing speed, while the maximum instantaneous heat flow in the method of this application changes appropriately with the drawing speed. As the drawing speed increases, the thickness of the billet shell in the area near the meniscus will inevitably tend to decrease, so the instantaneous heat flow increasing with the drawing speed is more in line with the actual situation.

[0101] Table 1 Evaluation parameters of heat flow distribution law in this application

[0102]

[0103] The effect of the number of grids N on the instantaneous heat flux distribution under a pulling speed of 5.0 m / min with different values ​​of the number of grids N is as follows: Figure 6 As shown, except for the area near the piecewise function (around 1.0s) due to the different number of data points, there are slight differences in heat flux at the same node position. This is to ensure that the average heat flux must be equal to the given value. The instantaneous heat flux corresponding to different grid numbers is adjusted overall. Although different grid numbers have a certain impact on heat flux distribution, it ensures that the average heat flux obtained from the heat flux distribution results under different grid numbers is absolutely equal to the given average heat flux, ensuring that the total heat output from the crystallizer is consistent with the actual situation. 3.3 The distribution index n studies the heat flux distribution method, ensuring that the average heat flux under the instantaneous heat flux distribution results is the same as the measured value, that is, ensuring that the total heat output from the crystallizer is the same as the actual value. Based on this, the distribution expression will affect the instantaneous heat flux distribution, thereby affecting the temperature distribution and the shell thickness distribution within the crystallizer, which needs to be studied. There are two methods to study the distribution index n. One approach is to theoretically derive the correlation between heat flow and billet shell distribution in the crystallizer, so n is taken as -0.5 or -0.504. The other approach is to refer to existing technologies that measure the temperature or instantaneous heat flow changes in the crystallizer along the casting direction and regress the n-index. The n-index regressed from the crystallizer temperature changes in existing technologies is as follows: Figure 7 As shown, the n-exponent, regressed from the instantaneous heat flux change measured in existing technologies, is as follows: Figure 12 As shown in the figure, the scatter plot data represents existing technology data, and the lines corresponding to different linearities and widths represent the results of power-law fitting of the data.

[0104] Figure 7The n-index values ​​of (3) to (6) are relatively small, while those of (1), (2), (7), and (8) are relatively large. This may be due to the complex influence of heat flow distribution within the crystallizer, and may also be related to testing and data processing. Existing technologies [3] and [4] are the results of tests conducted by the same team, while existing technology

[18] is the result of tests conducted by a different team. From the results of existing technologies [3] and [4], the average n-index value is around -0.5, which is not directly related to the pulling speed. The n-coefficient obtained by regression of heat flow distribution from existing technologies is as follows: Figure 12 As shown, the conclusion is clearer: the n-exponent of the measured heat flux distribution is basically around -0.5, and has no correlation with the casting speed. Therefore, the n-exponent regressed from the temperature and instantaneous heat flux distribution measured using existing technology is consistent with the theoretically understood heat flux distribution and billet shell distribution patterns.

[0105] Figure 8 The figure shows the instantaneous heat flux distribution trends obtained according to the allocation formula of this application under two n-index conditions. It can be seen that the value of the n-index significantly affects the instantaneous heat flux distribution pattern. The smaller the n-index, the flatter the instantaneous heat flux distribution; the larger the n-index, the steeper the instantaneous heat flux distribution, and the greater the difference between the maximum and minimum heat flux. The maximum heat flux is within a reasonable range. Clearly, when the index n is -0.504, the maximum and minimum heat fluxes are more consistent. Figure 12 The measured heat flow variation trend is observed. Therefore, it is recommended that the n-index be chosen to be consistent with the distribution law of the billet shell, and the value should be around -0.5.

[0106] The temperature field calculation results under different instantaneous heat flux distributions are as follows: Figures 10-12 As shown, where Figure 10 The calculation results are based on the heat flow distribution formula in equation (2). Figure 11 To achieve n = -0.504 according to the method described in this application, Figure 12 The calculation results are based on the method described in this application, with n set to -0.25. Table 2 shows the shell thickness and surface center temperature at the crystallizer outlet from the statistically analyzed calculation results. Figures 10-12 As can be seen from the results in Table 2;

[0107] (1) The heat flow distribution in the crystallizer will significantly affect the results of the billet temperature field calculation program. Different heat flow distributions not only affect the temperature distribution inside the crystallizer, but also affect the temperature distribution at the crystallizer outlet and the billet shell thickness.

[0108] (2) Due to the heat flow distribution according to formula (2), the total heat released in the crystallizer is smaller than the actual heat. Therefore, compared with the method of this application, the surface temperature of the crystallizer is greater than that of this application, and the thickness of the billet shell is smaller than that of this application. As shown in Table 2, the temperature at the outlet of the crystallizer is about 120°C higher than that of the method of this application with n = -0.504, and the thickness of the billet shell is about 1.3 mm smaller.

[0109] (3) In the method of this application, different values ​​of n represent different heat flow distribution trends, such as Figure 11 and Figure 12 As shown, the changes in surface temperature and billet thickness inside the crystallizer are significantly different; when n is -0.25, the temperature change inside the crystallizer is basically linear, which is obviously unreasonable; moreover, even if the total heat output inside the crystallizer is the same (the average heat flow is the same), the surface temperature and billet thickness at the crystallizer outlet still differ depending on the value of n.

[0110] This clearly demonstrates that the heat flow distribution within the crystallizer has a decisive impact on the calculation results for temperature field calculation models. Therefore, it is more appropriate to determine the heat flow distribution based on the thickness of the billet shell, and it is recommended that the value of n be around -0.5.

[0111] Table 2 Comparison of Feature Calculation Results

[0112]

[0113] The method and formula (2) of this application are used to calculate the temperature field of the entire billet, which affects the heat transfer treatment of the crystallizer. Under the condition that the post-crystallizer process and heat exchange treatment are exactly the same, the calculated billet temperature field results are as follows: Figure 13 As shown, the drawing speed was 4.97 m / min, the steel grade was HRB400, and the tundish temperature was 1520℃. From Figure 13 As can be seen, due to the different instantaneous heat flow distribution patterns in different crystallizers, the average heat flow is different, and the total heat carried away from the crystallizer is different. The temperature inside the crystallizer is significantly different under the two different treatment methods. At the same time, it also has a great influence on the position of the solidification end. The solidification end positions under the two treatment methods are 28.41m and 29.13m, respectively, which is 0.72m apart.

[0114] Based on a comparative analysis of the average heat flux under high-speed conditions and the measured heat flux in this paper, a suitable fitting formula for the average heat flux under high-speed conditions is suggested as 1.34·vc. 0.502 (vc, m / min). The Wolf oil lubrication, Li and Lorento regression formulas can also be used as reference formulas for calculating the average heat flux of small billets at high drawing speeds.

[0115] The process for constructing the heat flux distribution law in this invention is as follows: determine the calculation speed and the grid along the pulling direction in the model crystallizer, and calculate A; obtain the average heat flux, and determine the heat flux distribution corresponding to this pulling speed. The heat flux distribution method in this paper ensures that the average heat flux obtained from the heat flux distribution used in the crystallizer calculation is equal to the measured average heat flux, thereby ensuring the rationality and reliability of the model calculation.

[0116] Based on comparison and theoretical analysis, it is recommended that the value be around -0.5 in this method to maintain consistency with the distribution pattern of the billet shell.

[0117] By implementing the above methods, the real-time heat flux at high drawing speeds can be theoretically calculated, providing technical support for the development of high drawing speeds.

[0118] In summary, after reading this invention document, those skilled in the art can make various other corresponding modifications to the technical solutions and concepts based on this invention without creative mental effort, and all of these modifications fall within the scope of protection of this invention.

Claims

1. A method for developing a high-efficiency billet crystallizer heat flow model, characterized in that, Includes the following steps: S1. Obtain the average heat flux value of the continuous casting mold. and pulling speed parameter V; S2. Based on the average heat flux value, construct an instantaneous heat flux distribution function, wherein the integral or discrete summation value of the instantaneous heat flux distribution function within the effective height range of the crystallizer satisfies a preset mathematical constraint relationship with the average heat flux value, and the average heat flux value calculated by the instantaneous heat flux distribution function is equal to the obtained average heat flux value; S3. Determine the instantaneous heat flux values ​​at different height positions within the crystallizer based on the instantaneous heat flux distribution function; S4. Input the instantaneous heat flow value as a thermal boundary condition into the continuous casting solidification heat transfer model to simulate the solidification action of the billet in the crystallizer.

2. The method for developing a high-efficiency billet crystallizer heat flow model according to claim 1, characterized in that, Step S2 includes: N grid points are discretely set along the effective height direction of the crystallizer, and the height corresponding to each grid point is h. i , where i is the grid point index, i = 0, 1, 2, ..., N; Construct about height h i or time t i The instantaneous heat flux distribution function f(hi) or f(ti), where time t i =h i / V.

3. The method for developing a high-efficiency billet crystallizer heat flow model according to claim 2, characterized in that, Step S2 further includes: A normalization constraint is set on the instantaneous heat flux distribution function such that the sum of the function values ​​at all grid points equals the total number of grid points N, i.e., Σf(h i ) = N or Σf(t) i ) = N; 4. The method for developing a high-efficiency billet crystallizer heat flow model according to claim 3, characterized in that, Step S3 includes: Based on the average heat flux value The instantaneous heat flux value q at each grid point is calculated using the instantaneous heat flux distribution function that satisfies the normalization constraint conditions. i The instantaneous heat flux value or 5. The method for developing a high-efficiency billet crystallizer heat flow model according to claim 4, characterized in that, Step S4 includes: The instantaneous heat flux value q at each grid point is calculated. i As a thermal boundary condition, it is input into the billet continuous casting solidification heat transfer model for calculation to simulate the billet solidification process in the crystallizer.

6. The method for developing a high-efficiency billet crystallizer heat flow model according to claim 5, characterized in that, Step S2 further includes: In the step of constructing the instantaneous heat flux distribution function, the function is a piecewise power function with respect to time ti, and its expression is: f(t i ) = A, when t i When ≤T; f(t i )=A*t i n When t i >T time; Where A is the normalization coefficient, n is the distribution exponent, T is the time segment point, and t is the time interval. i The time taken to reach hi.

7. The method for developing a high-efficiency billet crystallizer heat flow model according to claim 6, characterized in that, The normalization coefficient A is obtained by solving the normalization constraint conditions, and the specific calculation formula is as follows: A = N / Σt i n The distribution index n has a value of -0.

5.

8. The method for developing a high-efficiency billet crystallizer heat flow model according to claim 7, characterized in that, The average heat flux value The calculation formula is obtained by measuring the cooling water flow rate, inlet and outlet temperature difference, and effective heat transfer area of ​​the crystallizer. Where ρ is the density of cooling water, cp is the specific heat capacity of cooling water, Q is the water flow rate, ΔT is the temperature difference between the inlet and outlet, and Seff is the effective heat transfer area of ​​the crystallizer.

9. The method for developing a high-efficiency billet crystallizer heat flow model according to claim 8, characterized in that, The average heat flux value Through the average heat flow formula The calculation yields V. c Let be the pulling speed, and a and b be the fitting coefficients.

10. A method for optimizing continuous casting process parameters, characterized in that... include: A heat flow model was developed using the method described in any one of claims 1-9, and run to obtain the shell thickness and / or surface temperature of the billet at the crystallizer outlet. The thickness of the billet shell and / or the surface temperature of the billet are compared with preset target values; Based on the comparison results, adjust one or more continuous casting process parameters, including the crystallizer taper, cooling water volume in the foot roll area, water distribution model in the secondary cooling zone, casting speed setting, or fire cutter position.

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