Research And Application Of Analytical Solution For Temperature Field In Accelerated Cooling Process Of Plate

Automation control system for accelerated cooling process of plate is essential for controlled cooling technology to put into practice effectively, stably and accurately. Specifically, accuracy of temperature control for cooling process is subject to mathematical models. With the development of computer technology, numerical solutions have been applied widely. At present, the model based on finite difference method has been used on line to calculate temperature evolution, which increased accuracy of temperature control significantly. Due to the complexity of actual accelerated cooling process, analytical solution can be exactly solved only by simplifying conditions of the problem, which has limited its application in industrial practice. However, analytical solutions have irreplaceable theoretical value. They play very important roles in understanding essence of the problems, analyzing physical relation between different variables and acting as standard solutions to verify and develop numerical solutions. Therefore, concentrating on accelerated cooling process of plate, and commencing on the study of analytical solution for temperature field under the simplified conditions, the regularities of temperature distribution is researched in detail. In combination with the practical cooling process, the relation of surface, center and average temperatures is discussed. Based on the researches in this dissertation, improved projects for on-line temperature calculation model and off-line simulation model are put forward. The main progresses are as follows:(1) To obtain the temperature field for accelerated cooling process of plate, the solving methods consisting of one, two and three dimensional analytical solutions, as well as finite difference solutions including one-dimensional explicit, implicit and C-N (Crank-Nicolson) scheme, two-dimensional explicit and ADI (Alternating Direction Implicit) scheme, and three-dimensional explicit scheme are researched in detail. Computer programs of all these solutions are developed, and the results of them are good agreement under identical computational conditions. Then, compared with analytical solution, the computational stability and truncation error of different finite difference schemes with various step-sizes are investigated. The scheme of finite difference method adequate for on-line calculation with appropriate spacing and time step is discussed. The conclusion provides significant reference for analyzing the accuracy and real-time performance of on-line temperature model based on finite difference method.(2) Through analyzing the characteristic of temperature field in regular regime of unsteady heat conduction process, the concept of regular solution is defined. Regular solution depends on surface temperature and Bi number, and it is analytical solution in regular regime. Regular regime will be indicated by the calculation deviation of regular solution within the accepted tolerances. And Fo_m number, namely, the dimensionless time is defined as the dividing point between initial regime and regular regime. It is obtained that Fo_m is not a fixed value corresponding to same calculation deviation but depends on Bi number and the initial value of calculation deviation of regular solution.(3) In consideration of the actual variations of boundary conditions and thermophysical properties, the concept of approximate regular regime is defined. Approximate regular regime will also be indicated by the calculation deviation of regular solution within the accepted tolerances or by Fo_m. In approximate regular regime, regular solution is approximate to actual temperature field. It is proved that approximate regular regime exists in two air cooling processes which before and after water cooling process. And the regular solution of air-cooling in this regime is lower limit of the actual temperature field. In particular, it is drawn that the time of surface temperature recovery finishing after water-cooling can be considered as the sign of arriving in approximate regular regime instead of Fo_m .(4) Combined with the regularities of temperature distribution described by analytical solution, the mechanism of temperature recovery after water-cooling is introduced. The position of surface temperature recovery finishing is obtained by simulated calculation given different thickness, steel grade and cooling conditions, which provides reference for the control of finish cooling temperature and the location of pyrometers. And the reference values of stay time for thicker plates before leveling are presented. Furthermore, the position where the value of temperature equals to average temperature is analyzed according to temperature recovery process after water-cooling. It shows that the region of X = 0.57～1 is the distinct area of temperature recovery which will provide reference data to discuss the influence of temperature recovery on the structure and performance of plate. In addition, the difference between center and surface temperatures and that between average and surface temperatures in the water-cooling process and temperature recovery process after that are researched. The conclusion will provide theoretical direction to establish cooling strategies and estimate the difference between center and surface temperatures and that between average and surface temperatures after temperature recovery finishing.(5) The improved projects of process control system for accelerated cooling of plate are presented. Surface temperature measured by the pyrometer which close to the position of temperature recovery finishing will be the basis of finishing cooling temperature control. The regular solution is applied into on-line model, and provides reliable temperature distribution and average temperature to the preset model and self-learning model to increase the preset accuracy essentially. Three new functions can be extended into off-line model to promote the control accuracy of on-line model, which involve analysis of temperature recovery process after water-cooling, estimate of the difference between center and surface temperatures and that between average and surface temperatures, as well as research on the calculation deviation of regular solution.The researches on analytical solution for temperature field are of great theoretical significance to improve accuracy of temperature control in accelerated cooling of plate. The regular solution defined in this dissertation creates a reliable calculation method for real-time acquiring temperature distribution of things, which exhibiting significant utility value. In plate mills, holding process of inter-slab between rough rolling and finish rolling and cooling process of plate on cooling bed, etc., both meet conditions to apply regular solution to calculate temperature distribution. Application of the regular solution is more meaningful for thicker plate.