Casting billet on-line temperature field prediction method based on cpu+gpu heterogeneous parallelism

Abstract

The application provides a continuous casting billet online temperature field prediction method based on CPU+GPU heterogeneous parallelism, and relates to the technical field of metallurgical continuous casting. The method firstly determines the arrangement positions of rollers and nozzles on a continuous casting machine; records the cooling water supply data of each position displayed by a two-cooling water table; collects the crystallizer thermocouple temperature measurement data under actual working conditions; collects the components and physical property parameters of a steel grade to be produced; then arranges a database on a server side, establishes multiple data tables in the database according to the uses, and inputs the collected data into corresponding data tables; then performs mathematical modeling on the heat transfer and solidification model of the continuous casting billet on the server side, and performs CPU+GPU heterogeneous parallel programming relying on the C++ / CUDA architecture, so that the heat transfer and solidification model can be solved in parallel on the GPU; finally, a client interface is established on the client side in a B / S structure, which is used for realizing continuous casting billet production process parameter display, temperature curve drawing and temperature cloud chart drawing.

Description

Technical Field

[0001] This invention relates to the field of metallurgical continuous casting technology, and in particular to a method for predicting the online temperature field of continuously cast billets based on CPU+GPU heterogeneous parallelism. Background Technology

[0002] Continuous casting (LCC) of steel is essentially a heat transfer and solidification process. Through the synergistic action of the cooling zones in the continuous casting machine, superheat, latent heat, and some sensible heat in the molten steel are removed, gradually solidifying into a continuously cast billet with the desired cross-sectional shape and size. After long-term development, LCC has become a mature and advanced modern steel production process. However, the frequent occurrence of various defects still affects the yield rate and energy-saving and emission-reduction effects of the LCC process. The lack of effective control over heat transfer and solidification behavior during LCC can easily lead to defects such as cracks, segregation, and porosity in the solidified billet shell, and in severe cases, even cause steel leakage accidents. Therefore, a thorough understanding of the macroscopic laws of heat transfer and solidification of the billet, as well as the influence of various process parameters on the heat transfer and solidification of the billet, and the effective online control of the heat transfer and solidification behavior of the billet under unsteady operating conditions, is of great significance for formulating reasonable process conditions, effectively reducing the occurrence of various defects in the billet, and further improving the internal quality of the billet through the use of reduction processes.

[0003] The continuous casting process of steel is a high-temperature and harsh environment. During continuous casting, the billet is often covered by a film of water vapor and iron oxide scale, making it impossible to obtain accurate surface temperature information using traditional temperature measurement methods such as industrial temperature guns, let alone understand key information such as the internal temperature distribution and shell thickness of the billet. Methods such as nail-shot experiments not only require significant manpower and resources but may also cause production delays, making them unsuitable for online control of continuous casting production. To obtain the overall temperature field information of the billet online and intuitively allow on-site personnel and researchers to understand the temperature distribution, it is necessary to use online solidification heat transfer simulation methods to predict the billet temperature field in real time. A software system should then be developed based on this simulation method to provide a realistic basis for real-time adjustment of process parameters during production.

[0004] For online temperature field prediction systems, the core is the online solidification heat transfer model. To enable online numerical simulation, the model's computational speed needs to be equal to or even higher than that of the actual production process to achieve temperature field prediction. Due to this high demand for computational speed, and constrained by the limited computing power of past computers, researchers often heavily simplified the models. This simplification often leads to models that rely excessively on experience and suffer from poor accuracy. Based on the dimensions of heat transfer behavior considered, online heat transfer models can be broadly categorized into one-dimensional, two-dimensional, and three-dimensional models.

[0005] Currently, steel mills commonly use one-dimensional heat transfer models, which only consider one-dimensional heat transfer along the longitudinal section of the billet, ignoring heat transfer in the transverse and drawing directions. This simplification results in excellent real-time performance, but the accuracy of the calculations is questionable, and it cannot provide temperature information for the billet beyond the longitudinal section. To obtain more comprehensive billet temperature information, two-dimensional heat transfer models have been gradually developed. These models consider two-dimensional solidification heat transfer behavior along the billet cross-section, ignoring heat transfer in the drawing direction. Although two-dimensional heat transfer models can obtain relatively comprehensive temperature field information, ignoring heat transfer behavior in the drawing direction can easily lead to instability in high-cooling-intensity regions, such as inside the crystallizer. To achieve accurate and stable predictions, developing three-dimensional solidification heat transfer models is essential. Compared to one-dimensional and two-dimensional solidification heat transfer models, three-dimensional solidification heat transfer models can more comprehensively predict the temperature field distribution of the billet, but the computational load is much larger. With the development of computer graphics processing units (GPUs) and their gradual replacement of central processing units (CPUs) as the main players in general-purpose computing and supercomputers, high-performance three-dimensional online solidification heat transfer models based on GPUs have become possible. Although some methods and systems exist for predicting the three-dimensional temperature field of cast billets, they rarely consider the non-uniform cooling phenomena present in the crystallizer and secondary cooling zone, typically relying on empirical formulas for fitting. However, defects arise precisely from various non-uniform phenomena during continuous casting. Therefore, considering the non-uniform cooling phenomena in the crystallizer and secondary cooling zone and incorporating them into the online solidification heat transfer model using methods that do not affect computational efficiency is of great significance. Thus, based on establishing a complete three-dimensional online solidification heat transfer model using CPU+GPU heterogeneous parallel computing technology, further establishing a server and client system to form a real-time system integrating computation, storage, and display is essential to providing comprehensive temperature information to on-site personnel in real time. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to address the shortcomings of the prior art by providing an online temperature field prediction method for continuous casting billets based on CPU+GPU heterogeneous parallel computing technology. The method uses a three-dimensional online heat transfer model established based on CPU+GPU heterogeneous parallel computing technology to predict the temperature field changes of the billet in real time during the production process.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by this invention is: a method for predicting the online temperature field of continuously cast billets based on CPU+GPU heterogeneous parallelism, involving a database, a server, and a client, including the following steps:

[0008] Step 1: Determine the arrangement of the rollers and nozzles on the continuous casting machine; record the cooling water supply data at each location displayed by the secondary cooling water meter; collect the temperature data measured by the thermocouples of the crystallizer under actual working conditions; collect the composition and physical property parameters of the steel to be produced;

[0009] Step 2: Deploy a database on the server side, create multiple data tables in the database according to the intended use, and input the data collected in Step 1 into the corresponding data tables;

[0010] Step 3: On the server side, perform mathematical modeling of the heat transfer and solidification model of the continuous casting billet, and rely on the C++ / CUDA architecture to perform CPU+GPU heterogeneous parallel programming so that the heat transfer and solidification model can be solved in parallel on the GPU.

[0011] Step 3.1: Using the collected thermocouple temperature data of the crystallizer and numerical calculation software, solve the inverse problem of crystallizer heat transfer based on the interior point method to obtain the overall non-uniform heat flux distribution of the crystallizer that can be directly used in the solidification heat transfer model.

[0012] Step 3.1.1: Establish a forward heat transfer problem model for the crystallizer based on the finite volume method to obtain a two-dimensional steady-state heat conduction model of the wide copper plate of the crystallizer;

[0013] In the finite volume method, the temperature of each control volume is replaced by the temperature at its center point; let P be the node of the control volume to be integrated; W, S, E, and N are the adjacent nodes of node P; w, s, e, and n are the interface positions between nodes W, S, E, and N and node P, respectively; Δx and Δy are the boundary lengths of node P in the x and y directions, respectively; and (δx) w 、(δx) e 、(δy) s And (δy) n These are the distances between node P and its neighboring nodes;

[0014] The calculation area of ​​the wide copper plate of the crystallizer is a two-dimensional steady-state heat conduction, and its governing equation is shown in formula (1);

[0015]

[0016] In the formula, T represents temperature;

[0017] The specific boundary conditions for the calculation region of the wide copper plate of the crystallizer are as follows:

[0018] (1) The boundary condition between the inner side of the wide copper plate of the crystallizer and the cast billet is heat flux:

[0019]

[0020] In the formula, λ is the thermal conductivity of copper; q is the heat flux between the wide copper plate and the casting billet.

[0021] (2) The boundary condition between the outer side of the wide copper plate of the crystallizer and the cooling water is forced convection:

[0022]

[0023] In the formula, h is the forced convection heat transfer coefficient; T k The temperature on the outer side of the wide copper plate of the crystallizer at the thermocouple mounting height; T cool The cooling water temperature at the corresponding height where the thermocouple is installed;

[0024] Integrating the governing equation (1) at node P, we get:

[0025]

[0026] In the formula, V is the volume;

[0027] Equation (4) is further transformed into:

[0028]

[0029] In order to calculate the above equation (5), it is necessary to perform difference on each diffusion term and transform the diffusion term into the form in equation (6);

[0030]

[0031] In the formula, T P T represents the temperature value of node P currently being solved; W T E T N T S These are the temperature values ​​of the adjacent nodes W, E, N, and S to the left, right, top, and bottom of the node P, respectively.

[0032] Substituting equation (6) into the control equation (1), we obtain the discretized control equation for the two-dimensional steady-state heat conduction model of a wide-face copper plate with finite volume, as shown in equation (7).

[0033]

[0034] For the temperature term T at each node in formula (7) P T W T E T N T S By combining like terms and normalizing them, we obtain the general formula (8) for solving the two-dimensional steady-state heat conduction model of the wide copper plate of the crystallizer.

[0035] a P T P =a E T E +a W T W +a N T N +a S T S (8)

[0036] The expression of each coefficient term in general formula (8) is shown in formula (9);

[0037]

[0038] For any node in the discrete region, the calculation is performed using formulas (8) to (9) until the iteration converges;

[0039] Step 3.1.2: Based on the forward heat transfer problem model, the inverse heat transfer problem of the wide copper plate in the crystallizer is solved using the interior point method, including the following steps:

[0040] 1) Construct the objective function and penalty function, and determine the penalty factor and reduction coefficient;

[0041] For the inverse heat transfer problem of the wide copper plate in the crystallizer, the objective function of the interior point method is the least squares function of the calculated temperature value and the actual temperature measured by the thermocouple at the thermocouple installation position in the forward heat transfer problem model described in step 3.1.1, i.e.

[0042]

[0043] Where X is the iteration point in the interior point method iterative process; T e (i) represents the temperature measured by the thermocouple inside the wide copper plate of the crystallizer; T c (i,p) represents the calculated temperature of the forward problem model described in step 3.1.1 at the thermocouple mounting location; n represents the total number of thermocouples mounted on the copper plate; i represents the thermocouple number; and p represents the inversion parameter vector.

[0044] The inequality constraint g(X) of the interior point method is as follows:

[0045]

[0046] Among them, T cool It is the cooling water temperature; T in It is the imported water temperature; T out It is the outlet water temperature;

[0047] The penalty function applied to the iteration point X within the feasible region during the solution of the inverse problem. The expression is:

[0048]

[0049] Where U is the number of inequality constraints g(X); u is the index of the inequality constraint; r (I) The penalty factor is a decreasing sequence of positive numbers, i.e.

[0050] r (0) >r (1) >r(2) >···>r (I) >r (I+1) >···>0 (13)

[0051] The terms in equation (13) satisfy

[0052] 2) Set the initial values ​​of the inversion parameters and substitute them into the forward problem model of heat transfer in the copper plate of the crystallizer to calculate the temperature distribution of the copper plate of the crystallizer;

[0053] 3) Select the calculated temperature value and the measured temperature value corresponding to the thermocouple installation position, calculate the objective function value, and determine whether it converges; if it converges, stop the iteration and return the inversion parameter value; otherwise, proceed to step 4).

[0054] 4) Calculate the penalty function and solve for the extreme points of the penalty function using unconstrained optimization methods;

[0055] 5) Determine whether the iteration has converged based on the convergence conditions. If any one of the convergence conditions is met, the iteration is considered converged and stops; otherwise, return to step 3).

[0056] Step 3.2: Establish a three-dimensional solidification heat transfer model of the billet; take the billet as the modeling object and establish the solidification heat transfer control equation of the billet; read the crystallizer parameter table and use the heat flux distribution obtained by solving the inverse heat transfer problem in the crystallizer as the boundary condition for the solidification heat transfer of the billet; read the roller arrangement table, nozzle arrangement table and secondary cooling water table, and determine the boundary condition for the solidification heat transfer of the billet in the secondary cooling zone and air cooling zone according to the arrangement of nozzles and rollers.

[0057] Step 3.2.1: Establish the solidification heat transfer control equation for the billet;

[0058] The billet is used as the modeling object, and the discrete calculation region of the model is moved along with the billet; the three-dimensional solidification heat transfer control equation of the continuously cast billet is as shown in equation (14).

[0059]

[0060] Where t represents time; T represents the temperature of the control volume; k represents the thermal conductivity; S latent The term represents the latent heat source of solidification in molten steel; ρ is density; c p Specific heat capacity; x, y, and z represent the coordinate axes;

[0061] The stability conditions of the three-dimensional solidification heat transfer model of the continuously cast billet are shown in Equation 15.

[0062]

[0063] In the formula, m iis a binary parameter used to include convective heat transfer in the stability criterion of the boundary node; if the boundary node is located in a position affected by convective heat transfer, then m i =1; otherwise m i =0; Δξ represents the set of characteristic lengths controlling the volume in different directions, Δξ={Δx,Δy,Δz};

[0064] The calculation of the three-dimensional solidification heat transfer model starts at the meniscus of the molten steel in the crystallizer, and the initial conditions are as shown in equation (16).

[0065] T = T c (16)

[0066] In the formula, T c It is the casting temperature;

[0067] Step 3.2.2: Determine the solidification heat transfer boundary conditions of the billet;

[0068] 1. The boundary conditions in the crystallizer adopt the overall non-uniform heat flux distribution of the crystallizer determined in step 3.1;

[0069] 2. In the area of ​​the secondary cooling zone affected by the nozzles, the boundary conditions are determined by convective heat transfer.

[0070] To calculate the convective heat transfer coefficient, it is first necessary to calculate the spray density v of the cooling water on the surface of the billet. w As shown in the formula below:

[0071]

[0072] In the formula, v nozzle It is the water flow velocity at the nozzle; A nozzle It is the cross-sectional area of ​​the nozzle, obtained from the nozzle diameter; A w This is the area of ​​the spray zone. For a circular spray zone, it can be obtained directly from its diameter; for a horizontal spray, the equivalent diameter needs to be taken. The diameter of the circular spray zone is obtained from the nozzle's spray angle and setting height, as shown in the following formula:

[0073]

[0074] In the formula, d nozzle-surf It is the nozzle setting height; Ω nozzle It is the nozzle's firing angle;

[0075] For the approximately rectangular water spray area produced by horizontal jetting, its equivalent diameter is calculated using equation (21):

[0076]

[0077] In the formula, L eLet be the wetted perimeter of the rectangular water spray area; further, using the side lengths a and b of the rectangle to replace the area and wetted perimeter of the water spray area, we get:

[0078]

[0079] Based on the obtained water flow velocity and characteristic dimensions of the spray area, calculate the Reynolds number Re. w And Plantau number Pr w The specific formulas are as follows:

[0080]

[0081]

[0082] If the heat transfer of cooling water on the surface of the billet is considered as plate heat transfer, then the Nusselt number is... w The calculation formula is as follows:

[0083]

[0084] In equations (23) to (25), ρ w μ w c w k w These are the density, viscosity, heat capacity, and thermal conductivity of water, respectively.

[0085] Finally, based on the relationship between the Nusselt number and the convective heat transfer coefficient, the forced convection heat transfer coefficient h of the cooling water is obtained. w As in equation (27):

[0086]

[0087] Among them, L w It is the thickness of the heat transfer layer, i.e., the cooling water film;

[0088] The convective heat transfer flux q generated on the surface of the billet due to cooling water conv for:

[0089] q conv =h w (T w -T surf (25)

[0090] In the formula, T w T represents the temperature of the cooling water ejected from the nozzle. surf The surface temperature of the cast billet;

[0091] 3. For the contact area between the roller and the billet, natural convection and radiation heat transfer boundary conditions are adopted;

[0092] The heat flux between the roller and the billet is considered to be the sum of the convective and radiative heat transfer between the roller and the environment, as shown in the following formula:

[0093]

[0094] In the formula, h roll σ is the convective heat transfer coefficient between the roller and the environment; D is the roller diameter; L is the contact length between the roller and the billet; σ is the Stefan-Boltzmann constant; ε is the emissivity coefficient of the roller; T amb It refers to the ambient temperature; T roll It is the surface temperature of the roller;

[0095] The convective heat transfer coefficient h between the roller and the environment roll The calculation is based on the calorie extraction fraction, as shown in the following formula:

[0096]

[0097] In the formula, f roll This is the heat extraction fraction, representing the roller's contribution to the cooling intensity; h rad-spray h conv h spray These are the radiation heat transfer coefficient, natural convection heat transfer coefficient, and forced convection heat transfer coefficient of the secondary cooling zone, respectively; L spray-pitch L spray L roll-contact These are the length of the water spray area in the secondary cooling zone, the length of the area directly affected by the nozzle, and the length of the contact area with the roller;

[0098] IV. For other areas of the billet surface that are neither affected by the nozzles nor in contact with the rollers, consider the boundary conditions for natural air convection and radiative heat transfer.

[0099] The heat flux q generated by the boundary conditions of natural air convection and radiation heat transfer air See equation (28):

[0100]

[0101] In the formula, h nat Let be the natural convection coefficient of air, and its expression is as follows:

[0102] h nat =0.84(T) amb -T surf ) 0.333 (29)

[0103] The emissivity coefficient ε is related to the surface temperature of the cast billet, and its relationship is given by equation (32):

[0104]

[0105] Step 3.2.2: Determine the physical property parameters of the three-dimensional solidification heat transfer model; the physical property parameters include solid fraction, effective thermal conductivity, effective specific heat and density;

[0106] The three-dimensional solidification heat transfer model uses the effective thermal conductivity method to calculate the thermal conductivity of the control volume, that is, multiplying the thermal conductivity of the molten steel by a factor to fit the flow enhancement effect, as shown in the following formula:

[0107]

[0108] In the formula, k eff k is the effective thermal conductivity of the calculated control volume. S It is the thermal conductivity of solid steel; k L It is the thermal conductivity of molten steel; K is the multiple used to fit the flow; T S T L These are the solidus temperature and liquidus temperature of molten steel, respectively; f S It is the solid fraction, and its calculation formula is as follows:

[0109]

[0110] In the formula, o is the solid fraction index;

[0111] The three-dimensional solidification heat transfer model uses the equivalent specific heat method to handle the latent heat source term of molten steel, that is, the latent heat source term in the governing equation is expressed by the rate of change of the solid fraction in the control volume with time, as shown in the following formula:

[0112]

[0113] In the formula, L is the latent heat of solidification of steel;

[0114] And because

[0115]

[0116] Substituting equation (35) into the governing equation (16) yields:

[0117]

[0118] The effective specific heat c is extracted from the left side of equation (36). eff The expression is as follows:

[0119]

[0120] Differentiating the solid fraction expression (33) with respect to temperature T and substituting it into the effective specific heat expression (37), we get:

[0121]

[0122] In the three-dimensional solidification heat transfer model, the solidity index σ is taken as 1, therefore we have equation (38):

[0123]

[0124] In the three-dimensional solidification heat transfer model, only the solid and liquid phases are considered, without considering further solid-state phase transformations of the cast billet; therefore, the density controlling the volume is regarded as a piecewise function of the solid fraction:

[0125]

[0126] In the formula, ρ S ρ is the density of solid steel. L The density of molten steel;

[0127] Step 3.3: Implement the modeling of the established three-dimensional solidification heat transfer model of the billet in C++ / CUDA architecture, so that the three-dimensional solidification heat transfer model can start parallel computing on NVIDIA GPU;

[0128] A solution method combining a large time step and a small time step is employed to solve the three-dimensional online solidification heat transfer model. First, the characteristic length Δz in the z-direction of the control volume and the time step Δt1 satisfying the boundary conditions are selected. Then, when the billet moves at a velocity v... cast During runtime, the model is first solved iteratively with a time step of Δt1. This is Δz / (Δt1×v) cast Round down to the nearest integer Q; for the actual movement distance Δt1×v of the billet within Q iterations. cast The difference between ×k and Δz is used to solve the three-dimensional solidification heat transfer model once with a compensation time step Δt2. After all calculations are completed, the calculation region of the three-dimensional solidification heat transfer model is moved by Δz, indicating that the billet has actually moved a distance Δz, thus realizing the thermal tracking design of the calculation region as the billet moves. In order to record the steel composition on each cross section of the calculation region and track the movement of the billet, in order to deal with the situations of mixed casting, the start of casting, and the tailing of the billet, the calculation region is continuously generated layer by layer at the meniscus of the molten steel in the crystallizer as the billet is pulled, and continuously eliminated layer by layer as the billet reaches the end of the continuous casting machine. When the continuous casting production is relatively stable, the size of the calculation region remains unchanged.

[0129] Step 3.4: Based on the configured database, design a server background program to make the model run in a loop. It periodically reads the continuous casting production process parameters stored in the database as the model's solution conditions. After the model solves, it periodically outputs the reading results to the calculation result publishing table for the client to read. The part that periodically reads the continuous casting production process parameter table from the database is separated into an auxiliary thread in the CPU; the part that outputs the model solution results is also separated into an auxiliary thread in the CPU; the main thread is only responsible for calling the CUDA architecture to enable the model solution to be performed on the GPU device.

[0130] Step 4: Establish a client interface using a B / S architecture; the client is used to display continuous casting billet production process parameters, draw temperature curves, and draw temperature cloud maps.

[0131] The beneficial effects of adopting the above technical solution are as follows: The online temperature field prediction method for continuously cast billets based on CPU+GPU heterogeneous parallel computing technology provided by this invention constructs an online-usable three-dimensional solidification heat transfer model for continuously cast billets. Through numerical methods, the three-dimensional temperature field distribution of the billets can be predicted in real time, effectively overcoming the shortcomings of high cost and low accuracy in industrial temperature measurement methods. By solving the inverse heat transfer problem from the measured data of the crystallizer thermocouples and solving the cooling intensity of the nozzle and roller layout of the continuous casting machine, the online predicted three-dimensional temperature field becomes more accurate and effective. Programming using the C++ / CUDA architecture allows the program to be computed on the GPU device, effectively improving computational efficiency and reducing computation time. Attached Figure Description

[0132] Figure 1 A flowchart of the online temperature field prediction method for continuous casting billets based on CPU+GPU heterogeneous parallelism provided in an embodiment of the present invention;

[0133] Figure 2 A diagram showing the distribution of thermocouples on the wide face of a crystallizer provided in an embodiment of the present invention;

[0134] Figure 3 A diagram illustrating the inverse problem model of the wide-face copper plate in a crystallizer, provided in an embodiment of the present invention.

[0135] Figure 4 A flowchart of the interior point method for solving the inverse heat transfer problem provided in this embodiment of the invention;

[0136] Figure 5 A transverse heat flux distribution diagram of the wide face of the crystallizer provided in an embodiment of the present invention;

[0137] Figure 6 This is a diagram showing the overall heat flux distribution across the wide surface of the crystallizer, provided in an embodiment of the present invention.

[0138] Figure 7The diagram shows the characteristic water distribution and nozzle arrangement of a continuous casting machine provided in this embodiment of the invention. In this diagram, (a) is the inner and outer arcs of the second cooling zone 1; (b) is the inner and outer arcs of the second cooling zones 2-4; (c) is the inner and outer arcs of the second cooling zones 5-9; (d) is the narrow surface of the second cooling zone 1; and (e) is the overall water distribution of the inner arc surface.

[0139] Figure 8 This is a schematic diagram of the temperature field of a three-dimensional half-section of a cast billet provided in an embodiment of the present invention;

[0140] Figure 9 This is a schematic diagram of the solidification field of a three-dimensional half-section of a cast billet provided in an embodiment of the present invention;

[0141] Figure 10 This is a flowchart of the solution process for the three-dimensional solidification heat transfer model provided in an embodiment of the present invention;

[0142] Figure 11 A comparison chart of the absolute computation time of the GPU-based three-dimensional solidification heat transfer model and the CPU-based three-dimensional solidification heat transfer model provided in the embodiments of the present invention.

[0143] Figure 12 A comparison chart of the relative computation time between the GPU-based three-dimensional solidification heat transfer model and the CPU-based three-dimensional solidification heat transfer model provided in the embodiments of the present invention.

[0144] Figure 13 This is a diagram of the server-side backend program structure provided in an embodiment of the present invention;

[0145] Figure 14 This is a diagram of the trigger interface provided in an embodiment of the present invention;

[0146] Figure 15 This is a diagram of the client-side temperature curve sub-interface provided in an embodiment of the present invention;

[0147] Figure 16 This is a diagram of the client-side temperature cloud map sub-interface provided in an embodiment of the present invention. Detailed Implementation

[0148] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0149] In this embodiment, the online temperature field prediction method for continuously cast billets based on CPU+GPU heterogeneous parallelism involves a database, a server, and a client, such as... Figure 1 As shown, it includes the following steps:

[0150] Step 1: Analyze and determine the arrangement of rollers and nozzles on the continuous casting machine according to the design drawings; record the cooling water supply data at each position displayed by the secondary cooling water meter; collect the temperature measurement data of the crystallizer thermocouple under actual working conditions; collect the composition and physical property parameters of the steel to be produced, including solid phase density, liquid phase density, solid phase specific heat capacity, liquid phase specific heat capacity, latent heat of solidification, solid phase thermal conductivity, and liquid phase thermal conductivity.

[0151] In this embodiment, the cross-sectional dimensions of the billet are 1550×230mm, and the nozzle and rollers are given in the specific continuous casting machine drawings.

[0152] Thermocouples are distributed on the crystallizer as follows: Figure 2 As shown, the corresponding measured temperature data are shown in Table 1, the steel composition is shown in Table 2, the physical property parameters are shown in Table 3, and the secondary cooling water is shown in Table 4.

[0153] Table 1 Temperature Data

[0154] Thermocouple serial number Average temperature (°C) Thermocouple serial number Average temperature (°C) 1 210.3 6 155.8 2 204.2 7 153.5 3 191.5 8 148.7 4 198.6 9 151.4 5 208.2 10 156.6

[0155] Table 2 Steel Composition

[0156] Element C Si Mn P S Content (wt%) 0.070 0.100 1.500 0.010 0.001

[0157] Table 3 Physical Properties

[0158]

[0159] Table 4 Secondary Cooling Water

[0160]

[0161]

[0162] In addition, the measured temperature of the intermediate package in this embodiment was 1541℃, and the production speed was 1.40m / min.

[0163] Step 2: Deploy a database on the server side, create multiple data tables in the database according to the purpose of the data, and input the data collected in Step 1 into the corresponding data tables; the data tables include process parameter table, secondary cooling water data table, roller arrangement table, nozzle arrangement table, crystallizer parameter table, and temperature field calculation result release table;

[0164] In this embodiment, a local heat transfer calculation database was built on Microsoft SQL Server 2019. The tables are designed as follows:

[0165] Process parameter table: time, tundish temperature, casting speed, steel grade, steel C content, steel Si content, steel Mn content, steel P content, steel S content;

[0166] Secondary cooling water meter: area, location, water flow rate at 0.80 pull speed, water flow rate at 0.95 pull speed, water flow rate at 1.10 pull speed, water flow rate at 1.25 pull speed, water flow rate at 1.40 pull speed;

[0167] Roller layout table: Roller position (inner / outer arc or side), roller x-coordinate, roller y-coordinate, roller diameter;

[0168] Nozzle layout table: Nozzle position (inner or outer arc or side), nozzle x-coordinate, nozzle y-coordinate, nozzle setting height, nozzle diameter, nozzle firing angle;

[0169] Crystallizer parameter table: Temperature measurement by thermocouple 1, thermocouple 2, thermocouple 3, thermocouple 4, thermocouple 5, thermocouple 6, thermocouple 7, thermocouple 8, thermocouple 9, thermocouple 10;

[0170] The temperature field calculation results are published in the following two tables:

[0171] Temperature profile table: x-value, center temperature of inner arc surface of billet, center temperature of side surface of billet, temperature of inner arc corner of billet, center temperature of billet, solidus, liquidus;

[0172] Three-dimensional temperature field data table: x value, y value, z value, temperature value.

[0173] Step 3: On the server side, perform mathematical modeling of the heat transfer and solidification model of the continuous casting billet, and rely on the C++ / CUDA architecture to perform CPU+GPU heterogeneous parallel programming so that the heat transfer and solidification model can be solved in parallel on the GPU.

[0174] Step 3.1: Using the collected thermocouple temperature data of the crystallizer and MATLAB numerical calculation software, solve the inverse problem of crystallizer heat transfer based on the interior point method to obtain the overall non-uniform heat flux distribution of the crystallizer that can be directly used in the solidification heat transfer model.

[0175] Step 3.1.1: In order to solve the inverse problem, it is first necessary to establish a model of the heat transfer problem of the crystallizer based on the finite volume method, and obtain a two-dimensional steady-state heat conduction model of the wide copper plate of the crystallizer.

[0176] In this embodiment, to solve the inverse problem, it is first necessary to establish a model of the forward problem. The inverse problem model is as follows: Figure 3 As shown, it is necessary to select the effective area of ​​the wide copper plate of the crystallizer at the height corresponding to each row of thermocouples as the research object. The purpose of the inverse problem is to find the distribution of the heat flux q value inside the copper plate.

[0177] A heat transfer analysis was performed on the copper plate. Based on the two-dimensional steady-state heat conduction model, the thickness of the wide copper plate of the crystallizer, which is the research object in this embodiment, is 26 mm, and the effective width is 1550 mm. Taking Δx = 2.5 mm and Δy = 2 mm, the calculation area is uniformly divided into 8060 sub-regions with an area of ​​5 mm2, which is the control volume.

[0178] In the finite volume method, the temperature of each control volume is replaced by the temperature at its center point; let P be the node of the control volume to be integrated; W, S, E, and N are the adjacent nodes of node P; w, s, e, and n are the interface positions between nodes W, S, E, and N and node P, respectively; Δx and Δy are the boundary lengths of node P in the x and y directions, respectively; and (δx) w 、(δx) e 、(δy) s And (δy) n These are the distances between node P and its neighboring nodes;

[0179] The calculation area of ​​the wide copper plate of the crystallizer is a two-dimensional steady-state heat conduction, and its governing equation is shown in formula (1);

[0180]

[0181] In the formula, T represents temperature;

[0182] The specific boundary conditions for the calculation region of the wide copper plate of the crystallizer are as follows:

[0183] (1) The boundary condition between the inner side of the wide copper plate of the crystallizer and the cast billet is heat flux:

[0184]

[0185] In the formula, λ is the thermal conductivity of copper; q is the heat flux between the wide copper plate and the casting billet.

[0186] (2) The boundary condition between the outer side of the wide copper plate of the crystallizer and the cooling water is forced convection:

[0187]

[0188] In the formula, h is the forced convection heat transfer coefficient; T k The temperature on the outer side of the wide copper plate of the crystallizer at the thermocouple mounting height; T cool The cooling water temperature at the corresponding height where the thermocouple is installed;

[0189] Integrating the governing equation (1) at node P, we get:

[0190]

[0191] In the formula, V is the volume;

[0192] Equation (4) is further transformed into:

[0193]

[0194] In order to calculate the above equation (5), it is necessary to perform difference on each diffusion term and transform the diffusion term into the form in equation (6);

[0195]

[0196] In the formula, T P T represents the temperature value of node P currently being solved; W T E T N T S These are the temperature values ​​of the adjacent nodes W, E, N, and S to the left, right, top, and bottom of the node P, respectively.

[0197] Substituting equation (6) into the control equation (1), we obtain the discretized control equation for the two-dimensional steady-state heat conduction model of a wide-face copper plate with finite volume, as shown in equation (7).

[0198]

[0199] For the temperature term T at each node in formula (7) P T W T E T N T S By combining like terms and normalizing them, we obtain the general formula (8) for solving the two-dimensional steady-state heat conduction model of the wide copper plate of the crystallizer.

[0200] a P T P =a E T E +a W T W +a N T N +a S T S (8)

[0201] The expression of each coefficient term in general formula (8) is shown in formula (9);

[0202]

[0203] For any node within the discrete region, formulas (8) to (9) are used for calculation until the iteration converges. Meanwhile, since the forward problem model is a two-dimensional steady-state heat conduction model, iterative solutions are required until convergence.

[0204] Step 3.1.2: Based on the forward heat transfer problem model, the interior point method is used to solve the inverse heat transfer problem of the wide copper plate in the crystallizer;

[0205] The iterative steps of the interior point method are as follows:

[0206] (1) Take the initial penalty factor r (0) =0.1, and the allowable errors ε1 and ε2 are both selected as 0.01;

[0207] (2) Take an initial point X within the feasible region. (0) Let the iteration number I = 1;

[0208] (3) Constructing the penalty function From X (I-1) Starting from a point, solve the penalty function using unconstrained optimization methods. extreme point X * (r (I) );

[0209] (4) Check the iteration termination criterion: If it is satisfied...

[0210] The objective function value is less than the set threshold ε1, that is

[0211] f(X) <e1 (10)

[0212] Or the difference in the objective function is less than the set threshold ε2, i.e.

[0213] ||f(X (I) )-f(X (I-1) )|| <e2 (11)

[0214] Then stop the iterative calculation and use X * (r (I) If f(X) is the constrained optimal solution of the original objective function f(X), then proceed to the next step.

[0215] (5) Take r (I+1) =C·r (I) X (0) =X * (r (I) ), I = I + 1, turn to step (3), where C = 0.1 is the decreasing coefficient;

[0216] In this embodiment, the process of solving the inverse heat transfer problem of the wide copper plate of the crystallizer using the interior point method is as follows: Figure 4 As shown, the specific steps are as follows:

[0217] 1) Construct the objective function and penalty function, and determine the penalty factor and reduction coefficient;

[0218] For the inverse heat transfer problem of the wide copper plate in the crystallizer, the objective function of the interior point method is the least squares function of the calculated temperature value and the actual temperature measured by the thermocouple at the thermocouple installation position in the forward heat transfer problem model described in step 3.1.1, i.e.

[0219]

[0220] Where X is the iteration point in the interior point method iterative process; T e (i) represents the temperature measured by the thermocouple inside the wide copper plate of the crystallizer; T c (i,p) represents the calculated temperature of the forward problem model described in step 3.1.1 at the thermocouple mounting location; n represents the total number of thermocouples mounted on the copper plate; i represents the thermocouple number; and p represents the inversion parameter vector.

[0221] The inequality constraint g(X) of the interior point method is as follows:

[0222]

[0223] Among them, T cool It is the cooling water temperature; T in It is the imported water temperature; T out It is the outlet water temperature;

[0224] The penalty function applied to the iteration point X within the feasible region during the solution of the inverse problem. The expression is:

[0225]

[0226] Where U is the number of inequality constraints g(X), and in this embodiment, as shown in equation (13), there are two inequality constraints; u is the sequence number of the inequality constraint; r (I) The penalty factor is a decreasing sequence of positive numbers, i.e.

[0227] r (0) >r (1) >r (2) >···>r (I) >r (I+1) >···>0 (15)

[0228] The terms in equation (13) satisfy Take r (I) =0.1, 0.01, 0.001, ...

[0229] 2) Make assumptions about the inversion parameters as initial values ​​and substitute them into the forward problem model of heat transfer in the copper plate of the crystallizer to calculate the temperature distribution of the copper plate of the crystallizer;

[0230] 3) Select the calculated temperature value and the measured temperature value corresponding to the thermocouple installation position, calculate the objective function value, and determine whether it converges; if it converges, stop the iteration and return the inversion parameter value; otherwise, proceed to step 4).

[0231] 4) Calculate the penalty function and solve for the extreme points of the penalty function using unconstrained optimization methods;

[0232] 5) Determine whether the iteration has converged based on the convergence conditions. If any one of the convergence conditions is met, the iteration is considered converged and stops; otherwise, return to step 3).

[0233] Through the above steps, Figure 2 The lateral heat flux distribution of the crystallizer at the corresponding height, obtained by solving the inverse problem using the two rows of thermocouples shown, is as follows: Figure 5 As shown. For Figure 5 The results shown were further fitted longitudinally at x = 0, 0.2, 0.4, ..., 1.4, 1.55 m to obtain the overall heat flux distribution at the wide copper plate of the crystallizer, as shown below. Figure 6 As shown.

[0234] Step 3.2: Establish a three-dimensional solidification heat transfer model of the billet; take the billet as the modeling object and establish the solidification heat transfer control equation of the billet; read the crystallizer parameter table and use the heat flux distribution obtained by solving the inverse heat transfer problem in the crystallizer as the boundary condition for the solidification heat transfer of the billet; read the roller arrangement table, nozzle arrangement table and secondary cooling water table, and determine the boundary condition for the solidification heat transfer of the billet in the secondary cooling zone and air cooling zone according to the arrangement of nozzles and rollers.

[0235] Step 3.2.1: Establish the solidification heat transfer control equation for the billet;

[0236] The billet is used as the modeling object, and the discrete calculation region of the model is moved along with the billet; the three-dimensional solidification heat transfer control equation of the continuous casting billet is as shown in equation (16).

[0237]

[0238] Where t represents time; T represents the temperature of the control volume; k represents the thermal conductivity; S latent The term represents the latent heat source of solidification in molten steel; ρ is density; c p Specific heat capacity; x, y, z represent the coordinate axes; in a very short time, density ρ and c p Specific heat c p These two items can be treated as constants.

[0239] The stability condition of the three-dimensional solidification heat transfer model of the continuously cast billet is given by equation (17).

[0240]

[0241] In the formula, m i is a binary parameter used to include convective heat transfer in the stability criterion of the boundary node; if the boundary node is located in a position affected by convective heat transfer, then m i =1; otherwise m i =0; Δξ represents the set of characteristic lengths controlling the volume in different directions, Δξ={Δx,Δy,Δz};

[0242] The calculation of the three-dimensional solidification heat transfer model starts at the meniscus of the molten steel in the crystallizer, and the initial conditions are as shown in equation (18).

[0243] T = T c (18)

[0244] In the formula, T c It is the casting temperature;

[0245] Step 3.2.2: Determine the solidification heat transfer boundary conditions of the billet;

[0246] I. The boundary conditions in the crystallizer are as determined in step 3.1, such as... Figure 6 The crystallizer shown has a non-uniform heat flux distribution.

[0247] 2. In the area of ​​the secondary cooling zone affected by the nozzles, the boundary conditions are determined by convective heat transfer.

[0248] To calculate the convective heat transfer coefficient, it is first necessary to calculate the spray density v of the cooling water on the surface of the billet. w As shown in the formula below:

[0249]

[0250] In the formula, v nozzle The water flow velocity at the nozzle can be obtained from the secondary cooling water meter feed rate recorded in step 1; A nozzle It is the cross-sectional area of ​​the nozzle, obtained from the nozzle diameter; A w This is the area of ​​the spray zone. For a circular spray zone, it can be obtained directly from its diameter; for a horizontal spray, the equivalent diameter needs to be taken. The diameter of the circular spray zone is obtained from the nozzle's spray angle and setting height, as shown in the following formula:

[0251]

[0252] In the formula, d nozzle-surf It is the nozzle setting height; Ω nozzle It is the nozzle's firing angle;

[0253] For the approximately rectangular water spray area produced by horizontal jetting, its equivalent diameter is calculated using equation (21):

[0254]

[0255] In the formula, L e Let be the wetted perimeter of the rectangular water spray area; further, using the side lengths a and b of the rectangle to replace the area and wetted perimeter of the water spray area, we get:

[0256]

[0257] Based on the obtained water flow velocity and characteristic dimensions of the spray area, calculate the Reynolds number Re. w And the Plantl number (Pr) w The specific formulas are as follows:

[0258]

[0259]

[0260] If the heat transfer of cooling water on the surface of the billet is considered as plate heat transfer, then the Nusselt number is... w The calculation formula is as follows:

[0261]

[0262] In equations (23) to (25), ρ w μ w c w k w These are the density, viscosity, heat capacity, and thermal conductivity of water, respectively.

[0263] Finally, based on the relationship between the Nusselt number and the convective heat transfer coefficient, the forced convection heat transfer coefficient h of the cooling water is obtained. w As in equation (26):

[0264]

[0265] Among them, L w It refers to the thickness of the heat transfer layer, i.e., the cooling water film. In this embodiment, L w Set to 0.002m;

[0266] The convective heat transfer flux q generated on the surface of the billet due to cooling water conv for:

[0267] q conv =h w (T w -T surf (27)

[0268] In the formula, T w T represents the temperature of the cooling water ejected from the nozzle.surf The surface temperature of the cast billet;

[0269] 3. For the contact area between the roller and the billet, natural convection and radiation heat transfer boundary conditions are adopted;

[0270] The rollers primarily transfer heat from the surface of the cast billet through inter-solid heat conduction. Under relatively stable continuous casting conditions, the temperature of the rollers themselves remains relatively stable. Therefore, the heat flux between the rollers and the cast billet can be considered equivalent to the sum of convective and radiative heat transfer between the rollers and the environment, as shown in the following formula:

[0271]

[0272] In the formula, h roll σ is the convective heat transfer coefficient between the roller and the environment; D is the roller diameter; L is the contact length between the roller and the billet; σ is the Stefan-Boltzmann constant; ε is the emissivity of the roller; T amb It refers to the ambient temperature; T roll It is the surface temperature of the roller;

[0273] The convective heat transfer coefficient h between the roller and the environment roll The calculation is based on the calorie extraction fraction, as shown in the following formula:

[0274]

[0275] In the formula, f roll This is the heat extraction fraction, representing the roller's contribution to the cooling intensity; h rad-spray h conv h spray These are the radiation heat transfer coefficient, natural convection heat transfer coefficient, and forced convection heat transfer coefficient of the secondary cooling zone, respectively; L spray-pitch L spray L roll-contact These are the length of the water spray area in the secondary cooling zone, the length of the area directly affected by the nozzle, and the length of the contact area with the roller;

[0276] IV. For other areas of the billet surface that are neither affected by the nozzles nor in contact with the rollers, consider the boundary conditions for natural air convection and radiative heat transfer.

[0277] The heat flux q generated by the boundary conditions of natural air convection and radiation heat transfer air See equation (30):

[0278]

[0279] In the formula, h nat Let be the natural convection coefficient of air, and its expression is as follows:

[0280] h nat =0.84(T) amb -T surf ) 0.333 (31)

[0281] The emissivity coefficient ε is related to the surface temperature of the cast billet, and its relationship is given by equation (32):

[0282]

[0283] Step 3.2.2: Determine the physical property parameters of the three-dimensional solidification heat transfer model; the physical property parameters include solid fraction, effective thermal conductivity, effective specific heat and density;

[0284] For the physical properties parameters of the three-dimensional solidification heat transfer model, the effects of composition and temperature are considered. The thermal conductivity of the billet is related to temperature and composition. Simultaneously, molten steel flows within the liquid cavity during continuous casting. This flow also enhances the thermal conductivity within the liquid cavity and the two-phase region. To comprehensively consider the enhancing effect of flow on thermal conductivity without increasing additional computational load, the three-dimensional solidification heat transfer model uses the effective thermal conductivity method to calculate the thermal conductivity of the control volume. This involves multiplying the thermal conductivity of the molten steel by a factor to fit the enhancing effect of flow, as shown in the following formula:

[0285]

[0286] In the formula, k eff k is the effective thermal conductivity of the calculated control volume. S It is the thermal conductivity of solid steel; k L is the thermal conductivity of the molten steel; K is the multiple used for fitting the flow, in this embodiment K = 5.0; T S T L These are the solidus temperature and liquidus temperature of molten steel, respectively; f S It is the solid fraction, and its calculation formula is as follows:

[0287]

[0288] In the formula, o is the solid fraction exponent, and the solid fraction f is the solid fraction. S This indicates the fraction of solids within the control volume.

[0289] The three-dimensional solidification heat transfer model uses the equivalent specific heat method to handle the latent heat source term of molten steel, that is, the latent heat source term in the governing equation is expressed by the rate of change of the solid fraction in the control volume with time, as shown in the following formula:

[0290]

[0291] In the formula, L is the latent heat of solidification of steel;

[0292] And because

[0293]

[0294] Substituting equation (35) into the governing equation (16) yields:

[0295]

[0296] The effective specific heat c is extracted from the left side of equation (36). eff The expression is as follows:

[0297]

[0298] Differentiating the solid fraction expression (33) with respect to temperature T and substituting it into the effective specific heat expression (37), we get:

[0299]

[0300] In the three-dimensional solidification heat transfer model, the solidity index σ is taken as 1, therefore we have equation (39):

[0301]

[0302] In the three-dimensional solidification heat transfer model, only the solid and liquid phases are considered, without considering further solid-state phase transformations of the cast billet; therefore, the density controlling the volume is regarded as a piecewise function of the solid fraction:

[0303]

[0304] In the formula, ρ S ρ is the density of solid steel. L The density of molten steel;

[0305] In this embodiment, the characteristic surface water distribution of the cast billet, the three-dimensional temperature field (half-section) and the three-dimensional solidification field (half-section) at different casting speeds were obtained. After generating cloud maps using the visualization software Tecplot, they are shown below. Figure 7 , Figure 8 and Figure 9 As shown.

[0306] Step 3.3: Implement the modeling of the established three-dimensional solidification heat transfer model of the billet in C++ / CUDA architecture, so that the model can start parallel computing on NVIDIA GPU;

[0307] A solution method combining a large time step and a small time step is employed to solve the three-dimensional online solidification heat transfer model. First, the characteristic length Δz in the z-direction of the control volume and the time step Δt1 satisfying the boundary conditions are selected. Then, when the billet moves at a velocity v... cast During runtime, the model is first solved iteratively with a time step of Δt1. This is Δz / (Δt1×v) cast Round down to the nearest integer Q; for the actual movement distance Δt1×v of the billet within Q iterations. cast The difference between ×k and Δz is used to solve the three-dimensional solidification heat transfer model once with a compensation time step Δt2. After all calculations are completed, the calculation region of the three-dimensional solidification heat transfer model is moved by Δz, indicating that the billet has actually moved a distance Δz, thus realizing the thermal tracking design of the calculation region as the billet moves. In order to record the steel composition on each cross section of the calculation region and track the movement of the billet, in order to deal with the situations of mixed casting, the start of casting, and the tailing of the billet, the calculation region is continuously generated layer by layer at the meniscus of the molten steel in the crystallizer as the billet is pulled, and continuously eliminated layer by layer as the billet reaches the end of the continuous casting machine. When the continuous casting production is relatively stable, the size of the calculation region remains unchanged.

[0308] This embodiment uses C++ / CUDA as the programming platform for CPU+GPU heterogeneous parallel programs. To fully leverage the advantages of both the CPU and GPU, appropriate tasks need to be assigned to them. In a CUDA program, the CPU and GPU are referred to as the host and device, respectively. The parts of the program that require computation on the GPU are called kernel functions, which are called by the host, i.e., the CPU. Within the kernel function, relatively independent computational processes can be distributed across CUDA cores using parallel thread indexes. The CPU, in this process, only plays the roles of control logic, memory allocation, and kernel function invocation. The task allocation for solving the three-dimensional solidification heat transfer model is as follows: Figure 10 As shown.

[0309] To ensure the computational efficiency of the three-dimensional online heat transfer prediction method established in this invention is sufficiently high, the following benchmark tests are conducted in this embodiment. The tests use two computation times to evaluate the computational performance between the proposed GPU-based model and a traditional CPU-based model:

[0310] (1) Absolute computation time: The actual time required for the model to complete a single simulation;

[0311] (2) Relative calculation time: The dimensionless ratio of the absolute calculation time to the actual continuous casting process time;

[0312] The absolute computation time for simulating the same continuous casting process at a casting speed of 1.4 m / min using a heat transfer model based on CPU and GPU is as follows: Figure 11 As shown. Figure 11 Plotted on a logarithmic scale, it shows that GPU parallel computing technology greatly accelerates the computation of the model.

[0313] The relative computation time of a 3D solidification heat transfer model is a key metric for its real-time usability. A comparison of the relative computation times for CPU- and GPU-based 3D solidification heat transfer models is provided below. Figure 12 As shown. This model is designed for real-time control of the casting process, and its relative computation time must be much less than 1. From Figure 12 It is evident that the developed GPU-based model provides robust support for real-time control. Therefore, this method for predicting the three-dimensional temperature field of continuously cast billets effectively meets the real-time requirements of the field.

[0314] Step 3.4: Based on the configured database, design a server background program to make the model run in a loop, periodically reading the continuous casting production process parameters stored in the database as the model solution conditions. After the model solution is completed, periodically output the reading results to the calculation result publishing table for the client to read. In the method of this invention, the part of periodically reading the continuous casting production process parameter table in the database is separated as an auxiliary thread in the CPU; the part of outputting the model solution results is also separated as an auxiliary thread; the main thread is only responsible for calling the CUDA architecture to enable the model solution to be performed on the GPU device.

[0315] In this embodiment, to reduce the computational burden on the model, the periodic reading of the database parameter table is separated into an auxiliary thread within the CPU; the model solution output is also separated into an auxiliary thread; the main thread is only responsible for calling the CUDA architecture to enable model solving on the GPU device. The server-side background program architecture is as follows: Figure 13 As shown.

[0316] In this embodiment, to predict the temperature field offline, a B / S (Browser / Server) architecture is adopted on the server side, and triggers are built using Spring Boot, Mybatis, and Java languages ​​combined with the Eclipse compilation environment. The triggers input parameters such as continuous casting speed, tundish temperature, steel composition, steel grade, casting length, casting width, casting thickness, secondary cooling water meter reading, and crystallizer water volume into the database in real time for the model to solve. Through the construction of the triggers, offline adjustments can be achieved in a non-field environment via analog signal input. Under field conditions, this trigger can also be replaced by signals from the field control system.

[0317] In this embodiment, the constructed trigger is as follows: Figure 14As shown. Open the trigger in Chrome or Edge browser. The left side displays the current time and casting machine status console; clicking it switches the current casting machine status. The middle section is the casting machine process parameter monitoring console, including plotting curves for casting speed, tundish temperature, and casting length. The right side is the process parameter input console, where process parameters can be changed at any time. After making a change, clicking "Status Modification" will input the change into the database, enabling communication with the server-side backend program.

[0318] Step 4: On the client side, adopt a B / S architecture and use Spring Boot, Mybatis, and Java languages ​​in conjunction with the Eclipse compilation environment to build the client interface; use Maven to implement version control management; the client includes: basic production process parameter display, temperature curve drawing, and temperature cloud map drawing functions.

[0319] In this embodiment, the two sub-interfaces in the constructed client are respectively as follows: Figure 15 and Figure 16 As shown. Open the trigger in the Chrome or Edge browser, where Figure 15 It is a temperature curve plotting platform for key locations of the billet, responsible for reading the model calculation results in the calculation result storage table in real time and plotting the curves in real time so that production personnel can intuitively understand the temperature distribution at key locations of the billet, mainly including the billet center temperature, billet surface temperature, billet corner temperature, solidus line and liquidus line. Figure 16 This is a billet cross-section temperature contour plotting platform, allowing users to freely adjust the positions of the horizontal and vertical cross-sections for plotting. The platform reads the calculation results from the storage table in real time and uses bilinear interpolation to interpolate and display the RGB values ​​of each point on the canvas, thus achieving the purpose of plotting the contour map. In addition, the client includes functions such as overview, historical data display, secondary cooling water meter display, and crystallizer parameter display, implemented in their respective sub-interfaces. Through the separate construction of triggers, client, and server-side backend programs, the goal of real-time temperature field prediction and visualization of calculation results is achieved.

[0320] On one hand, in this embodiment, a parallel program for the continuous casting three-dimensional online heat transfer model was written on the server side using a C++ / CUDA architecture. Running the program and visualizing the results, a comparison revealed that the three-dimensional temperature field prediction method of this invention has good accuracy, especially in accurately considering the cooling non-uniformity of the billet surface. Furthermore, this embodiment evaluated the real-time performance of this prediction method. Through measurement and comparison of absolute and relative computation time, it was found that this prediction method has higher computational efficiency and excellent real-time performance compared to traditional methods. This demonstrates that this method is suitable for online prediction of the billet temperature field and can provide accurate billet temperature field information for on-site applications.

[0321] On the other hand, to build an application platform for this prediction method, this embodiment also establishes two interfaces through a B / S architecture: a trigger and a client. The SQL Server database serves as the communication platform between the server-side background program, the trigger, and the client. The trigger simulates on-site signal input and transmits information to the server-side background program in real time through the database. The server-side background program predicts the billet temperature using the temperature field prediction method and outputs the results. The client uses multiple sub-interfaces to visualize the results, allowing on-site personnel to intuitively understand the temperature distribution of the billet. In this embodiment, a temperature field prediction system is constructed using the server, trigger, and client. The establishment of this system demonstrates that the method of this invention is applicable to the field and possesses good efficiency, stability, and feasibility.

[0322] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the claims of the present invention.

Claims

1. A method for predicting the online temperature field of continuously cast billets based on CPU+GPU heterogeneous parallelism, characterized in that: Includes the following steps: Step 1: Determine the arrangement of the rollers and nozzles on the continuous casting machine; Record the cooling water supply data at each location displayed on the secondary cooling water meter; collect the temperature data measured by the thermocouples of the crystallizer under actual operating conditions; Collect the composition and physical property parameters of the steel grade to be produced; Step 2: Deploy a database on the server side, create multiple data tables in the database according to the intended use, and input the data collected in Step 1 into the corresponding data tables; Step 3: On the server side, perform mathematical modeling of the heat transfer and solidification model of the continuous casting billet, and rely on the C++ / CUDA architecture to perform CPU+GPU heterogeneous parallel programming so that the heat transfer and solidification model can be solved in parallel on the GPU. Step 4: Establish a client interface using a B / S architecture; the client is used to display continuous casting billet production process parameters, draw temperature curves, and draw temperature cloud maps. Step 3 is achieved through the following steps: Step 3.1: Using the collected thermocouple temperature data of the crystallizer and numerical calculation software, solve the inverse problem of crystallizer heat transfer based on the interior point method to obtain the overall non-uniform heat flux distribution of the crystallizer that can be directly used in the solidification heat transfer model. Step 3.2: Establish a three-dimensional solidification heat transfer model of the billet; take the billet as the modeling object and establish the solidification heat transfer control equation of the billet; read the crystallizer parameter table and use the heat flux distribution obtained by solving the inverse heat transfer problem in the crystallizer as the boundary condition for the solidification heat transfer of the billet; read the roller arrangement table, nozzle arrangement table and secondary cooling water table, and determine the boundary condition for the solidification heat transfer of the billet in the secondary cooling zone and air cooling zone according to the arrangement of nozzles and rollers. Step 3.3: Implement the established three-dimensional solidification heat transfer model of the billet in C++ / CUDA architecture, so that the three-dimensional solidification heat transfer model can be solved in parallel on NVIDIA GPU; Step 3.4: Based on the configured database, design a server background program to make the model run in a loop, periodically read the continuous casting production process parameters stored in the database as the model solution conditions, and after the model solution is completed, output the reading results to the calculation result publishing table periodically for the client to read. The part that periodically reads the continuous casting production process parameter table from the database is separated into an auxiliary thread in the CPU; the part that outputs the model solution results is also separated into an auxiliary thread in the CPU; the main thread is only responsible for calling the CUDA architecture to enable the model solution to be performed on the GPU device.

2. The method for predicting the online temperature field of continuously cast billets based on CPU+GPU heterogeneous parallelism according to claim 1, characterized in that: Step 3.1 is achieved through the following two steps: Step 3.1.1: Establish a forward heat transfer problem model for the crystallizer based on the finite volume method to obtain a two-dimensional steady-state heat conduction model of the wide copper plate of the crystallizer; Step 3.1.2: Based on the forward heat transfer problem model, the interior point method is used to solve the inverse heat transfer problem of the wide copper plate of the crystallizer.

3. The method for predicting the online temperature field of continuously cast billets based on CPU+GPU heterogeneous parallelism according to claim 2, characterized in that: The specific method for step 3.1.1 is as follows: In the finite volume method, the temperature of each control volume is replaced by the temperature at its center point; let P be the node of the control volume to be integrated; W, S, E, and N are the adjacent nodes of node P; w, s, e, and n are the interface positions between nodes W, S, E, and N and node P, respectively; Δx and Δy are the boundary lengths of node P in the x and y directions, respectively; and (δx) w 、(δx) e 、(δy) s And (δy) n These are the distances between node P and its neighboring nodes; The calculation area of ​​the wide copper plate of the crystallizer is a two-dimensional steady-state heat conduction, and its governing equation is shown in formula (1); (1)； In the formula, T represents temperature; The specific boundary conditions for the calculation region of the wide copper plate of the crystallizer are as follows: I. The boundary condition between the inner side of the wide copper plate of the crystallizer and the cast billet is heat flux: (2)； In the formula, λ is the thermal conductivity of copper; q is the heat flux between the wide copper plate and the casting billet. II. The boundary condition between the outer side of the wide copper plate of the crystallizer and the cooling water is forced convection: (3)； In the formula, h is the forced convection heat transfer coefficient; T k The temperature on the outer side of the wide copper plate of the crystallizer at the thermocouple mounting height; T cool The cooling water temperature at the corresponding height where the thermocouple is installed; Integrating the governing equation (1) at node P, we get: (4)； In the formula, V is the volume; Equation (4) is further transformed into: (5)； In order to calculate the above equation (5), it is necessary to perform difference on each diffusion term and transform the diffusion term into the form in equation (6); (6)； In the formula, T P T represents the temperature value of node P currently being solved; W T E T N T S These are the temperature values ​​of the adjacent nodes W, E, N, and S to the left, right, top, and bottom of the node P, respectively. Substituting equation (6) into the control equation (1), we obtain the discretized control equation for the two-dimensional steady-state heat conduction model of a wide-face copper plate with finite volume, as shown in equation (7). (7)； For the temperature term T at each node in formula (7) P T W T E T N T S By combining like terms and normalizing them, we obtain the general formula (8) for solving the two-dimensional steady-state heat conduction model of the wide copper plate of the crystallizer. (8)； The expression of each coefficient term in general formula (8) is shown in formula (9); (9)； For any node in the discrete region, the calculation is performed using formulas (8) to (9) until the iteration converges.

4. The method for predicting the online temperature field of continuously cast billets based on CPU+GPU heterogeneous parallelism according to claim 3, characterized in that: The implementation process of step 3.1.2 is as follows: 1) Construct the objective function and penalty function, and determine the penalty factor and reduction coefficient; For the inverse heat transfer problem of the wide copper plate in the crystallizer, the objective function of the interior point method is the least squares function of the calculated temperature value and the actual temperature measured by the thermocouple at the thermocouple installation position in the forward heat transfer problem model described in step 3.1.1, that is: (10)； Where X is the iteration point in the interior point method iterative process; T e (i) represents the temperature measured by the thermocouple inside the wide copper plate of the crystallizer; T c (i,p) represents the calculated temperature of the forward problem model described in step 3.1.1 at the thermocouple mounting location; n represents the total number of thermocouples mounted on the copper plate; i represents the thermocouple number; and p represents the inversion parameter vector. The inequality constraint g(X) of the interior point method is as follows: (11)； Among them, T cool It is the cooling water temperature; T in It is the imported water temperature; T out It is the outlet water temperature; For the inverse problem solution process, the penalty function φ(X, r) applied to the iteration point X within the feasible region. (I) The expression for ) is: (12)； Where U is the number of inequality constraints g(X); u is the index of the inequality constraint; r (I) The penalty factor is a decreasing sequence of positive numbers, i.e.: (13)； The terms in equation (13) satisfy ; 2) Set the initial values ​​of the inversion parameters and substitute them into the forward problem model of heat transfer in the copper plate of the crystallizer to calculate the temperature distribution of the copper plate of the crystallizer; 3) Select the calculated temperature value and the measured temperature value corresponding to the thermocouple installation position, calculate the objective function value, and determine whether it converges; if it converges, stop the iteration and return the inversion parameter value; otherwise, proceed to step 4). 4) Calculate the penalty function and solve for the extreme points of the penalty function using unconstrained optimization methods; 5) Determine whether the iteration has converged based on the convergence conditions. If any one of the convergence conditions is met, the iteration is considered converged and stops; otherwise, return to step 3).

5. The method for predicting the online temperature field of continuously cast billets based on CPU+GPU heterogeneous parallelism according to claim 4, characterized in that: Step 3.2 is achieved through the following steps: Step 3.2.1: Establish the solidification heat transfer control equation for the billet; Step 3.2.2: Determine the solidification heat transfer boundary conditions of the billet; Step 3.2.3: Determine the physical property parameters of the three-dimensional solidification heat transfer model; the physical property parameters include solid fraction, effective thermal conductivity, effective specific heat and density.

6. The method for predicting the online temperature field of continuously cast billets based on CPU+GPU heterogeneous parallelism according to claim 5, characterized in that: The specific method for establishing the solidification heat transfer control equation of the billet in step 3.2.1 is as follows: The billet is used as the modeling object, and the discrete calculation region of the model is moved along with the billet; the three-dimensional solidification heat transfer control equation of the continuously cast billet is as shown in equation (14). (14)； Where t represents time; T represents the temperature of the control volume; k represents the thermal conductivity; S latent The term represents the latent heat source of solidification in molten steel; ρ is density; c p Specific heat capacity; x, y, and z represent the coordinate axes; The stability conditions of the three-dimensional solidification heat transfer model of the continuously cast billet are shown in Equation 15. (15)； In the formula, m i is a binary parameter used to include convective heat transfer in the stability criterion of the boundary node; if the boundary node is located in a position affected by convective heat transfer, then m i = 1; otherwise m i = 0; Δξ represents the set of characteristic lengths controlling the volume in different directions, Δξ = {Δx, Δy, Δz}; The calculation of the three-dimensional solidification heat transfer model starts at the meniscus of the molten steel in the crystallizer, and the initial conditions are as shown in equation (16). (16)； In the formula, T c It refers to the casting temperature.

7. The method for predicting the online temperature field of continuously cast billets based on CPU+GPU heterogeneous parallelism according to claim 6, characterized in that: The specific method for step 3.2.2 is as follows:

1. The boundary conditions in the crystallizer adopt the overall non-uniform heat flux distribution of the crystallizer determined in step 3.1; 2. In the area of ​​the secondary cooling zone affected by the nozzles, the boundary conditions are determined by convective heat transfer. To calculate the convective heat transfer coefficient, it is first necessary to calculate the spray density v of the cooling water on the surface of the billet. w As shown in the formula below: (17)； In the formula, v nozzle It is the water flow velocity at the nozzle; A nozzle It is the cross-sectional area of ​​the nozzle, obtained from the nozzle diameter; A w This is the area of ​​the spray zone. For a circular spray zone, it can be obtained directly from its diameter; for a horizontal spray, the equivalent diameter needs to be taken. The diameter of the circular spray zone is obtained from the nozzle's spray angle and setting height, as shown in the following formula: (18)； In the formula, d nozzle-surf It is the nozzle setting height; Ω nozzle It is the nozzle's firing angle; For the approximately rectangular water spray area produced by horizontal jetting, its equivalent diameter is calculated using equation (21): (19)； In the formula, L e The wetted perimeter of the rectangular water spray area; Further, using the side lengths a and b of the rectangle to replace the area and wetted perimeter of the spray area, we get: (20)； Based on the obtained water flow velocity and characteristic dimensions of the spray area, calculate the Reynolds number Re. w And Plantau number Pr w The specific formulas are as follows: (21)； (22)； If the heat transfer of cooling water on the surface of the billet is considered as plate heat transfer, then the Nusselt number... The calculation formula is as follows: (23)； In equations (23) to (25), ρ w μ w c w k w These are the density, viscosity, heat capacity, and thermal conductivity of water, respectively. Finally, based on the relationship between the Nusselt number and the convective heat transfer coefficient, the forced convection heat transfer coefficient h of the cooling water is obtained. w As in equation (27): (24)； Among them, L w It is the thickness of the heat transfer layer, i.e., the cooling water film; The convective heat transfer flux q generated on the surface of the billet due to cooling water conv for: (25)； In the formula, T w T represents the temperature of the cooling water ejected from the nozzle. surf The surface temperature of the cast billet; 3. For the contact area between the roller and the billet, natural convection and radiation heat transfer boundary conditions are adopted; The heat flux between the roller and the billet is considered to be the sum of the convective and radiative heat transfer between the roller and the environment, as shown in the following formula: (26)； In the formula, h roll σ is the convective heat transfer coefficient between the roller and the environment; D is the roller diameter; L is the contact length between the roller and the billet; σ is the Stefan-Boltzmann constant; ε is the emissivity coefficient of the roller; T amb It refers to the ambient temperature; T roll It is the surface temperature of the roller; The convective heat transfer coefficient h between the roller and the environment roll The calculation is based on the calorie extraction fraction, as shown in the following formula: (27)； In the formula, f roll This is the heat extraction fraction, representing the roller's contribution to the cooling intensity; h rad-spray h conv h spray These are the radiation heat transfer coefficient, natural convection heat transfer coefficient, and forced convection heat transfer coefficient of the secondary cooling zone, respectively; L spray-pitch L spray L roll-contact These are the length of the water spray area in the secondary cooling zone, the length of the area directly affected by the nozzle, and the length of the contact area with the roller; IV. For other areas of the billet surface that are neither affected by the nozzles nor in contact with the rollers, consider the boundary conditions for natural air convection and radiative heat transfer. The heat flux q generated by the boundary conditions of natural air convection and radiation heat transfer air As shown in the formula below: (28)； In the formula, h nat Let be the natural convection coefficient of air, and its expression is as follows: (29)； The emissivity coefficient ε is related to the surface temperature of the cast billet, as shown in the following formula: (30)。 8. The method for predicting the online temperature field of continuously cast billets based on CPU+GPU heterogeneous parallelism according to claim 7, characterized in that: The specific method for determining the various physical property parameters of the three-dimensional solidification heat transfer model in step 3.2.3 is as follows: The three-dimensional solidification heat transfer model uses the effective thermal conductivity method to calculate the thermal conductivity of the control volume, that is, multiplying the thermal conductivity of the molten steel by a factor to fit the flow enhancement effect, as shown in the following formula: (31)； In the formula, k eff k is the effective thermal conductivity of the calculated control volume. S It is the thermal conductivity of solid steel; k L It is the thermal conductivity of molten steel; K is the multiple used to fit the flow; T S T L These are the solidus temperature and liquidus temperature of molten steel, respectively; f S It is the solid fraction, and its calculation formula is as follows: (32)； In the formula, o is the solid fraction index; The three-dimensional solidification heat transfer model uses the equivalent specific heat method to handle the latent heat source term of molten steel, that is, the latent heat source term in the governing equation is expressed by the rate of change of the solid fraction in the control volume with time, as shown in the following formula: (33)； In the formula, L is the latent heat of solidification of steel; And because: (34)； Substituting equation (35) into the governing equation (16) yields: (35)； The effective specific heat c is extracted from the left side of equation (36). eff The expression is as follows: (36)； Differentiating the solid fraction expression (33) with respect to temperature T and substituting it into the effective specific heat expression (37), we get: (37)； In the three-dimensional solidification heat transfer model, the solidity index σ is taken as 1, therefore we have equation (38): (38)； In the three-dimensional solidification heat transfer model, only the solid and liquid phases are considered, without considering further solid-state phase transformations of the cast billet; therefore, the density controlling the volume is regarded as a piecewise function of the solid fraction: (39)； In the formula, ρ S ρ is the density of solid steel. L This is the density of the molten steel.

9. The method for predicting the online temperature field of continuously cast billets based on CPU+GPU heterogeneous parallelism as described in claim 8, characterized in that: Step 3.3 employs a "large time step + small time step" solution method to solve the three-dimensional online solidification heat transfer model, as follows: First, select the characteristic length Δz in the z-direction of the control volume and the time step Δt1 that satisfies the boundary condition; when the billet is cast at a speed v cast During runtime, the model is first solved iteratively with a time step of Δt1. Next, that is Round down to the nearest integer Q; for the actual movement distance Δt1×v of the billet within Q iterations. cast The difference between ×k and Δz is used to solve the three-dimensional solidification heat transfer model once with a compensation time step Δt2. After all calculations are completed, the calculation area of ​​the three-dimensional solidification heat transfer model is moved by Δz, indicating that the billet has actually moved a distance Δz, thereby realizing the thermal tracking design of the calculation area as the billet moves. In order to record the steel composition on each cross section of the calculation area and track the movement of the billet, in order to deal with the situations of mixed casting, the start of casting and the tailing of the billet, the calculation area is continuously generated layer by layer at the meniscus of the molten steel in the crystallizer as the billet is pulled, and continuously disappears layer by layer as the billet reaches the end of the continuous casting machine. When the continuous casting production is relatively stable, the size of the calculation area remains unchanged.

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