Heat transfer process simulation by finite differences for online control of ladle furnaces

Abstract

A numerical method for solving the two-dimensional transient heat conduction equation is presented to determine temperature profiles of ladle furnaces during the casting of special steels. The method is based on an explicit formulation of the heat transfer process in finite differences. In order to improve the efficiency of the method, two auxiliary algorithms are added, one for correcting finite difference results from coarse mesh calculations and the other to perform time extrapolation of the temperature behaviour between furnace batches. The calculated steel temperatures are found to be in good agreement with experimental data, obtained at a Brazilian thin steel casting facility. Currently, about 80% of the ladle batches at this facility come out within their commercial specifications, against 45% previously observed without the use of such a model. With average processing times of the order of 100 s in an AMD K6II 300 MHz computer, the method is suitable for real time thermal tracking of ladles and steel.

An investigation of predictive control for aluminum wheel casting via a virtual process model

“…Shang et al (2003) describe using the high-fidelity model for predicting the optimal set points off-line but not for use as a prediction model in the control solution. Zabadal et al (2004) describe a finite element model (FEM) with simulation times of approximately 100 s that could be used (although not implemented) for online control of a ladle furnace. The best example of integrating a high-fidelity process model in a control solution was where Samaras and Simaan (1997) employed a linearized physical partial differential equation (PDE) model to tune a simple proportional-integral-derivative (PID) controller.…”

“…For example, Hofmann et al (1997) optimized the velocity-withdrawal profile for casting turbine blades through an off-line FE simulation. Zabadal et al (2004) simulated the heat transfer process for a ladle furnace to determine the optimal temperature profile for casting special steels. When implemented, the quality improved from 45% to 80%.…”

High-Performance Prediction of Molten Steel Temperature in Tundish through Gray-Box Model

“…The first-principle models include one dimensional models 2,3) and computational fluid dynamics (CFD) models. [4][5][6][7] In general, one-dimensional models are too simple to predict TD temp precisely, and CFD-based models are too complicated and thus spend much computational time. On the other hand, it is difficult to achieve sufficient estimation accuracy by using statistical models without utilizing process knowledge from limited samples.…”

“…In the past, various models such as first-principle models, [2][3][4][5][6][7] statistical models, 8) and gray-box models 9) have been proposed. The first-principle models include one dimensional models 2,3) and computational fluid dynamics (CFD) models.…”

Prediction of Molten Steel Temperature in Steel Making Process with Uncertainty by Integrating Gray-Box Model and Bootstrap Filter

“…Thus, to predict and control TD temp, various models such as first-principle models (Austin et al, 1992;Xia and Ahokainen, 2001;Zabadal et al, 2004;Jormalainen and Louhenkilpi, 2006;Belkovskii and Kats, 2009), statistical models (Sonoda et al, 2012), and gray-box models (Gupta and Chandra, 2004;Okura et al, 2013;Ahmad et al, 2014) have been proposed. Although deterministic models are dominant in the literature, a stochastic model is preferable to cope with process uncertainties, such as those in temperature measurements, composition and weight of added alloys, the extent of oxidation reactions for removal of impurities, and degradation of ladles.…”