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.

Review on Modeling and Simulation of Continuous Casting

“…When accurate pyrometer measurements are available, an inverse model can be applied to match the predicted surface temperature profile with the peaks of those measurements, to overcome dips caused by intermittent scale . Finally, the shell thickness predictions near final solidification of several models have been successfully validated with nail shooting measurements …”

“…[12] Finally, the shell thickness predictions near final solidification of several models have been successfully validated with nail shooting measurements. [12,[25][26][27][28] Once validated, simple heat transfer solidification models have a wide range of powerful practical applications, which have had great impact on improving the process in commercial practice. For example, post-mortem analysis of the location and cause of internal hot-tear cracks can be inferred from model predictions of the location of the critical temperature range near the solidification front.…”

“…In addition to finding the maximum casting speed to avoid whale formation, [24] such models can be used to help choose the best position of soft reduction equipment [27,29] or final electro-magnetic stirring equipment. [12,25,26,28] for the mitigation of centerline defects.…”

Real‐Time Heat Transfer Model Based on Distributed Thermophysical Property Calculation for the Continuous Casting Process

“…Although the offline heat transfer model could predict solidification ends with different casting conditions, it is difficult to real‐time predict the solidification end of strand in industry production process due to the huge calculation cost, especially under conditions of the unsteady continuous casting. Therefore, many real‐time heat transfer models were developed to calculate the solidification end efficiently . Voest‐Alpine Industieanlaenbau(VAI) developed a real‐time cooling control and heat transfer calculation model, named Dynacs @ (Dynamic Strand Cooling Management System), which could determine the solidification end with the specific condition of steel grade, casting speed, and casting temperature.…”

Calculation of Solidification‐Related Thermophysical Properties of Steels Based on Fe‐C Pseudobinary Phase Diagram

“…Nowadays, real-time heat transfer models are gradually applied as fundamental part for studying the solidification process and even for online applications in continuous casting process of steel, such as secondary cooling, soft reduction and electromagnetic stirring, with the purpose to improve the quality of products. [1][2][3][4][5][6][7] In these heat transfer models, accurate thermophysical properties are essential for their reliability. However, it is not always possible to find data for a certain steel grade, although thermophysical data of a great number of steels has been measured.…”