Abstract
Abstract A recent asymptotics-based thermomechanical model is adapted and applied to the mould region in the continuous casting of round steel billets, with a view to describing the complex interplay between air-gap formation, mould taper, cooling channel width and cooling water velocity. Although the situation is steady state, the analysis leads to what is mathematically a dual moving-boundary problem for the solid–melt and solid–air interfaces, where the distance from the top of the mould region is the time-like variable in the problem. Moreover, the two interfaces are initiated at different locations. In addition, the thermal and mechanical problems are found to decouple and it is possible to solve the first ahead of the second. The model equations are solved numerically using a finite-difference method, and the approach is subsequently successfully validated against a previous finite-element model and experimental data from temperature measurements taken within the mould.
Highlights
Air-gap formation in the industrial continuous casting of steel has long been recognized as having an adverse effect on process efficiency
The cooling of the steel inevitably causes thermal contraction of the shell, and when the steel shell becomes thick enough to overcome the metallostatic pressure of the molten steel adjacent to it, the shell detaches from the mould wall, allowing air to entrain into the intervening space (Schwerdtfeger et al, 1998)
Our model supposes that molten steel enters the mould region of length L at z = 0 at the liquidus temperature of steel, which we denote by Tmelt; we ignore superheat, we evaluate its effect in appendix A
Summary
Air-gap formation in the industrial continuous casting of steel has long been recognized as having an adverse effect on process efficiency. The model was not for the continuous casting of steel, assumed a fictitious cooling temperature at the outer mould surface and was not validated either against experimental data or the results of any other model; the intention here is to apply those ideas, which were for an axisymmetric geometry, to the continuous casting of steel, with a view to providing validation For this purpose, we will use the experimental results of Dubendorff et al (1983) and the finite-element results of Kelly et al (1988) for the same round steel billet and copper mould geometry; these are rather early references, they contain considerably more detail about the geometry used and the experimental results obtained than almost all newer ones (Lee et al, 1999; Yao et al, 2004; Yin et al, 2006; Guo et al, 2007; Yin & Yao, 2007), and are suitable for validation purposes.
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