Abstract : Secondary cooling water control is a core technology of continuous casting production,The slab quality is decided by the result of controlling the Secondary cooling water. On the basis of the mature basic automatic HMI dynamic quadratic equation control, it applies the temperature difference flow it is calculated by aimed slab surface temperature approach control method as the basic flow's supplement, this method operates flexibly, the system is safe and reliable, it has high precision and it is realized easily.
1. Introduction
Secondary cooling water control is a core technology in continuous casting production, and its effectiveness directly affects the quality of the final slab. Currently, the main methods for secondary cooling water control used in steel continuous casting production lines include linear interpolation of secondary cooling water volume, quadratic equation fitting of secondary cooling water volume, and target surface temperature approximation. Linear interpolation of secondary cooling water volume was mostly used in older continuous casting machines. Its advantages are simple algorithm and ease of control, but it has gradually been phased out due to the defect that the difference between the calculated and target water volumes is too large in certain casting speed ranges. The quadratic equation fitting method overcomes the shortcomings of linear interpolation, minimizing the difference between the calculated and target water volumes throughout the casting speed range. The target surface temperature approximation method has become a popular method in recent years. Theoretically, it is the most scientific and accurate method to achieve consistency between the target surface temperature and the actual slab surface temperature by continuously changing the water volume. However, accurately measuring the actual surface temperature of the slab is very difficult, not only due to the accuracy of the measuring instruments but also because of the inherent unpredictable factors in the measurement environment. Currently, the most common application is to indirectly calculate the actual surface temperature based on measurable factors and steel parameters during production, instead of actually measuring the surface temperature of the cast billet.
Combining the advantages and disadvantages of the above three methods, a method combining the quadratic equation fitting method for secondary cooling water volume and the target surface temperature approximation method is selected to achieve accurate and reliable dynamic secondary cooling water control.
2. System Structure
The system architecture mainly consists of hardware network structure and software logic structure.
2.1 Hardware Structure
Based on the characteristics of the combined application of Level 1 HMI and Level 2 model calculations, the hardware configuration is shown in Figure 1:
The primary switch connects the instrument PLC controller and HMI workstation via a 100M Ethernet cable, while the secondary switch connects the model control expert and secondary client via a 100M Ethernet cable. The two switches are also connected via a 100M Ethernet cable.
Figure 1 Hardware network configuration diagram
The instrument PLC analog input port is directly connected to the regulating valve controller in each circuit of the secondary cooling water system, sending commands to adjust the water flow. The HMI workstation runs a dynamic quadratic equation program to control the secondary cooling water flow. Before casting begins, the operator uses the human-machine interface to access the corresponding water meters, calculates the basic water flow based on the average casting speed of each zone, and downloads it to the PLC controller. The model control expert computer runs a temperature field calculation model to obtain the temperature difference compensation water flow. The temperature field calculation results can be monitored and model parameters (such as steel grade thermophysical properties) can be modified on the secondary client machine.
2.2 Software Logical Structure
For dynamic secondary cooling water control in continuous casting production, a control method combining primary basic automation HMI dynamic quadratic equation control with secondary target surface temperature approximation method (temperature field calculation model) for water volume compensation is applied. This not only ensures the accuracy of the final secondary cooling water volume calculation but also guarantees the flexibility and safety of the secondary cooling system control. That is, when the secondary system is in the commissioning phase or experiences a fault, the primary basic automation HMI system continues to operate according to the dynamic quadratic equation control method, without affecting the normal operation of the entire continuous casting production.
Based on the above ideas, dynamic secondary cooling water flow control can be divided into two parts: the basic water flow calculated using a quadratic equation to fit the parameters, and the compensation water flow calculated using a target surface temperature approximation method. The formula is as follows:
Q= Qi +△Q (2-1)
Q represents the total calculated water volume;
Qi is the basic water volume;
△ Qj is the amount of water used to compensate for the difference between the actual surface temperature of the billet and the target surface temperature of the billet in each cooling zone.
3. Implementation of the control method
3.1 Fitting Method of Quadratic Equation for Two-Cold Water
The process of fitting the quadratic equation of the secondary cooling water is as follows: First, the steel grade is divided into different steel grade groups according to the carbon equivalent, liquidus temperature and steel grade characteristics of the steel grade. After determining the theoretical superheat and target surface temperature parameters of each cooling zone of each steel grade group, the cooling water flow rate of each secondary cooling zone under a certain casting speed is calculated according to the heat conduction theory and empirical formula, based on the different cross sections of the billet to be cast. However, the functional relationship between the cooling water volume and the casting speed calculated in this way is discrete, which inevitably brings a lot of complex calculation work to the water volume control. Due to the discontinuity of water volume control, the surface quality of the billet will inevitably be affected. Therefore, the secondary cooling water volume under a set casting speed is calculated first, and then the least squares method is used to fit the quadratic equation so that the cooling water volume and the casting speed form a quadratic equation functional relationship, and the quadratic equation coefficients are stored in the form of a water meter. The basic secondary cooling water volume calculated by the quadratic equation can be expressed as: [1]
Qi = (A i *V j 2 + B i *V j + C i ) * k1 ; (3-1)
Qi is the water volume setting value for the i-th loop of the secondary cooling system;
A <sub>i</sub> , B <sub>i</sub> , C<sub> i</sub> are the coefficients of the quadratic equation for water volume corresponding to this loop;
V <sub>j </sub> represents the average casting speed of the j-th cooling zone at time t;
V(j,t) = 12aj+bj2ajbjt1(x,t)bj-aj'> (3-2)
a<sub> j</sub> is the distance from the liquid surface in the crystallizer to the beginning of the cooling zone where the tracking unit is located;
bj represents the cooling zone from the liquid surface of the crystallizer to the location of the tracking unit.
Distance at the end;
t1 (x,t) represents the lifetime of the tracking unit at position x at time t.
k1 is the temperature coefficient of the secondary cooling inlet water;
The primary automation system selects the appropriate water meter based on the current steel grade and billet cross-section. The pulling speed signal collected in real time by the PLC is converted into the average pulling speed of each cooling zone and substituted into formula (3-1) to calculate the basic secondary cooling water volume and download it to the basic automation PLC.
The PLC controller sends the final water volume setpoint, obtained by adding the basic water volume and the temperature difference compensation water volume calculated in the secondary stage, to the regulating valve controllers of each loop in the secondary cooling zone. It also reads the actual flow rate fed back from the flow meters in the secondary cooling loop in real time to form a PID control structure for precise water volume control. Additionally, the user can manually select whether to activate the L2 stage temperature difference compensation water volume calculation. A typical PID water volume control HMI screen is shown in Figure 2.
Figure 2 PID water flow control HMI screen
3.2 Target Surface Temperature Approximation Method
The target surface temperature approximation method calculates the temperature difference compensation water volume based on the temperature difference between the actual surface temperature of each cooling zone and the set target surface temperature, serving as a supplementary correction to the primary basic set water volume. The key to this method lies in the accuracy of the obtained actual surface temperature. This is not only a matter of the precision of the measuring instrument—instruments operating in high-temperature environments for extended periods are prone to damage—but also because there are always unknowable factors that can cause measurement deviations (such as water droplets or mist on the billet surface). Currently, the most common approach is to indirectly calculate the actual surface temperature based on measurable factors and steel grade parameters during production, replacing the actual measured billet surface temperature. Then, the surface temperature calculation model is continuously revised using results obtained from methods such as nail gun measurements, radioactive isotope measurements, and temperature gun point measurements to bring it closer to the true value.
3.2.1 Mathematical Model of Thermal Process in Continuously Cast Slab
Many scholars at home and abroad have studied the mathematical model of heat transfer during secondary cooling and solidification of continuously cast billets. Due to the complexity of the boundary conditions of continuous casting, it is very difficult to accurately solve the general differential equation of heat transfer. In order to simplify the mathematical model and meet the requirements of dynamic calculation speed and reaction time, the following reasonable assumptions are made based on the characteristics of continuously cast billets: [2]
① Ignoring heat transfer in the slab running direction and slab width direction, the heat transfer of the continuously cast slab is simplified to a one-dimensional heat transfer problem.
② Ignoring the fluctuations in the liquid level in the crystallizer, the temperature of the molten steel at the meniscus is the same as the pouring temperature (Tc);
③ The effect of forced convection of molten steel on heat transfer of the billet was considered, and the effect of forced convection was processed into the effective thermal conductivity of molten steel.
④ The latent heat of solidification is evenly included in the specific heat of the two-phase region. That is, the equivalent specific heat C1 is used instead of the specific heat C of steel in the two-phase region.
Based on the above simplification, the basic differential equation for heat transfer during solidification in slab continuous casting can be obtained as follows:
12鈭?:v/m:t>T鈭俴onts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/>=1蟻.c=1鈭?/m:t>鈭倄位鈭俆鈭倄'> (3-3)
Because the cross-sectional shape of the continuously cast billet is regular, and the dynamic model has high requirements for speed and reaction time, the finite difference method is used to solve this model. The temperature equations of the tracking elements are discretized in the casting speed direction. For the temperature field distribution of each tracking element, the one-dimensional unsteady heat transfer equation can be used to solve for the nodal temperature of the billet surface:
T <sub>i </sub>k+1 = T <sub>i</sub> k + 12 2.螖tal="["/>位1 Ti+1k-Tik-q.螖x蟻.c1.(螖x)2'>
(3-4)
In the formula: λ1 is the weighted average of the effective thermal conductivity at temperatures Tik and Ti -1k ; λ2 is the weighted average of the effective thermal conductivity at temperatures Tik and Ti +1k ; c1 is the equivalent specific heat; ρ is the density; Δx is the spatial step size in the thickness direction of the slab; Δt is the time step size; and q is the average heat flux density of a certain secondary cooling zone.
3.2.2 Parameters and processing methods suitable for real-time temperature field calculation models
(1) Density, specific heat, and thermal conductivity change linearly with temperature. The formula for these changes needs to be selected according to different steel grades. For example, for general low-carbon steel, it can be taken as:
ρ= 128.6*103-T, T>1200 t/m:t>8.0*103-0.5*T, T<sub>200 t/m:t>'> (3-5)
12C=544.1106+9.5011x10-2*'>(3-6) (3-7)
(2) Latent heat of solidification
The latent heat of solidification varies depending on the steel grade, but the difference is not significant, and it is generally taken as 270 kJ/kg.
(3) Other parameters
The specific heat of water, C <sub>w</sub> , is 4187.0 J/(kg·℃); the Boltzmann constant, D, is 4.88; and the emissivity, E, is 0.8.
(4) Heat transfer boundary conditions in the secondary cooling zone
The thermal conductivity inside the cast billet is always associated with various heat transfer phenomena at the boundary, such as convective heat transfer and radiative heat transfer. Therefore, the boundary conditions can be divided into three types:
① Convective heat transfer boundary conditions
When the surface of a cast billet is cooled by fluids such as water or air, convective heat transfer can be used as the boundary condition, specifically expressed by heat flux density:
q <sub>convection</sub> = h(T <sub>W </sub> - T<sub> 0</sub> ) (3-8)
q <sub>convection </sub>—convective heat flux density at the billet boundary, W/m <sup>2</sup>;
h—convective heat transfer coefficient, W/(m² ; ℃);
TW — Surface temperature of the billet, °C;
T0 — Cooling fluid temperature, °C.
② Radiative heat transfer boundary conditions
When the surface of the cast billet is cooled by air, in addition to natural convection heat transfer, heat is mainly transferred outward by radiation. Radiation heat transfer can be used as a partial boundary condition, expressed in terms of heat flux density:
q_radiation = εC_0 [( T_W / 100) _4 - ( T_1 / 100) _4 ] (3-9)
ε—Surface emissivity of the billet shell, 0.7~0.8;
C <sub>0</sub> — Blackbody radiation coefficient, W/(m<sup> 2 </sup>.k<sup> 4</sup> )
TW — Blank surface temperature, K;
T1 — Ambient air temperature, kJ
③ Conductive heat transfer boundary conditions
When the billet comes into contact with the rollers, some heat is transferred outwards through conduction. Of the total heat released by the billet during solidification, radiation accounts for 25% and conduction accounts for 17%. Therefore:
q -conduction = 0.17/0.25 * q- radiation
=0.68 * q radiation (3-10)
Based on the temperature of each unit billet calculated by the heat transfer model, the average surface temperature of each cooling zone billet is further calculated, and the dynamic compensation water volume of the secondary cooling basic water volume can be obtained by equation (3-11).
△Q j =G j * (T j - T j aim ) (3-11)
T<sub> j</sub> represents the actual surface temperature of the cast billet.
T<sub> j </sub>a<sub>im</sub> is the target surface temperature of the cast billet;
Gj is the temperature difference gain value.
Of course, the actual surface temperature Tj of the billet calculated using the temperature field model needs to be continuously corrected by using methods such as nailing, radioactive isotope measurement, and temperature gun point measurement, so that the calculated surface temperature of the billet in each cooling zone is close to the true value.
4. Conclusion
The dynamic secondary cooling water control in continuous casting production is based on the already mature first-level basic automation HMI dynamic quadratic equation control method, combined with the second-level target surface temperature approximation method (temperature field calculation model) as a control method for precise water replenishment. In practical applications, it is flexible in operation, safe and reliable in system, has high calculation accuracy, and is easy to implement.
