Real-time Heat Transfer Model Based on Variable Non-uniform Grid for Dynamic Control of Continuous Casting Billets

Abstract

A real-time heat transfer model has been developed for dynamic control of continuous casting billets. In order to fulfill the real-time requirements for efficiency and accuracy, finite volume method (FVM) and alternating direction implicit algorithm (ADI) have been selected as the efficient numerical solution algorithm. And most important of all, variable non-uniform grid and variable time step have been adopted in the algorithm, accelerating the calculation of heat transfer model by 20–40 times. Further, the algorithm’s discretization parameters including the grid, time step and slice distance have been optimized by error control (< 3°C), improving the relative calculation time to 0.57. The real-time model has been calibrated by surface temperature measurements using a thermal infrared imager, and its online performance has been tested, within ±13°C of the measurements. After the calibration, the model has been applied to the dynamic control of secondary cooling and the dynamic control of the electric current of final electromagnetic stirring (FEMS), providing the surface temperatures and mushy zone radius at the installation position of FEMS. The latter has been validated by shell-thickness measurements using nail-shooting (relative error< 2.3%). The model-based dynamic control systems controlled the surface temperatures and the flow in mushy zone precisely with changing casting conditions, and have improved the billet quality obviously and reduced the fractures of rolling line during wire-drawing to 1/6 times per month in average from 2–3 times before.