Abstract
Asymptotic methods are employed to revisit an earlier model for oscillation-mark formation in the continuous casting of steel. A systematic non-dimensionalization of the governing equations, which was not carried out previously, leads to a model with 12 dimensionless parameters. Analysis is provided in the same parameter regime as for the earlier model, and surprisingly simple analytical solutions are found for the oscillation-mark profiles; these are found to agree reasonably well with the numerical solution in the earlier model and very well with fold-type oscillation marks that have been obtained in more recent experimental work. The benefits of this approach, when compared with time-consuming numerical simulations, are discussed in the context of auxiliary models for macrosegregation and thermomechanical stresses and strains.
Highlights
Mould oscillation has been implemented for a long time in the continuous casting of steel in order to avoid sticking of the solid shell to the mould walls if there is insufficient lubrication
It is evident that the results are both qualitatively similar, in that periodically spaced marks are obtained; we have treated the governing equations differently, we obtain the pitch to be given by 2π Vcast/ω
In contrast with that model, where reductions were made in an ad hoc fashion, we began with a non-dimensionalization of the governing equations, to determine which reductions can be justified on an order-of-magnitude basis, and which are made for the sake of convenience to enable tractability
Summary
Mould oscillation has been implemented for a long time in the continuous casting of steel in order to avoid sticking of the solid shell to the mould walls if there is insufficient lubrication. A schematic of the situation is shown in figure 1. The nature of these marks has long been a subject of modelling in the continuous casting literature [2]; a recent and comprehensive literature review is given in [3] and is, not repeated here.
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