Model for temperature profile estimation in the refractory of a metallurgical ladle
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I.
INTRODUCTION
IN continuous casting, thermal control of liquid steel plays an important role in product quality and ladle refractory life. A small difference between targeted and achieved temperatures on teeming may have very negative consequences for surface quality, cleanliness, tundish flowthrough, nozzles, casting schedules, energy economy, etc. Tapping of a furnace, thereby filling the ladle with molten metal, and emptying the ladle during the casting process are, among foundrymen, referred to by the terms tapping and teeming, respectively. The thermal state of the refractory lining of the ladle upon tapping affects the cooling of the heat (the batch of liquid steel) until teeming. The temperature drop of the heat is mainly caused by convective heat transfer to the ladle refractory and partly from the free surface of the bath. After teeming, when the hot inner walls of the ladle are exposed to the surroundings, the radiative and convective losses from the ladle lining are large. Thus, the heat stored within the inner parts of the refractory when the ladle is filled will be lost to the environment during the period when the ladle is empty. In order to reliably estimate the energy storage in the working lining, it is necessary to know the temperature field in it before and after tapping and teeming. Under industrial conditions, however, temperature measurements are available only occasionally and are often problematic due to high temperatures and a hostile environment. Reliable measurement data on thermal conditions within the ladle refractory are also difficult to produce, as process scheduling and geography move the ladle around in the plant during the casting cycle. Therefore, one has to resort to numerical estimation of needed variables. T.P. FREDMAN, Research Scientist, and H. SAXE´N, Professor, are ˚ bo Akademi University, FINwith the Heat Engineering Laboratory, A ˚ bo, Finland. 20500 A Manuscript submitted February 19, 1997. METALLURGICAL AND MATERIALS TRANSACTIONS B
Calculation of transient heat conduction is mostly done by numerical solution of the heat-conduction equation, especially for more complicated shapes and boundary conditions, although analytical solutions for a number of simple situations have been derived.[1,2] The problem is complicated by the fact that industrial ladle linings consist of several layers, with different material and thermal properties. In addition, it is difficult to quantify the influence on the boundary conditions for the field computation of factors such as wear, sculling, slag attack, and metal penetration into the refractory. The aforementioned circumstances favor a simple model capable of predicting major trends and changes in the heat balance of the ladle refractory. The simplest approach would be to formulate a statistical model for the energy storage in the lining based on measurements of the steel temperature drop for different process conditions. However, such a model cannot be applied outside the original domain of measurements and generally requires extensi
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