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This paper investigates the different possible behaviours of a recent asymptotic model for oscillation-mark formation in the continuous casting of steel, with particular focus on how the results obtained vary when the heat transfer coefficient (R-mf), the thermal resistance (mu(f)) and the dependence of the viscosity of the flux powder as a function of temperature, are changed. It turns out that three different outcomes are possible: (I) the flux remains in molten state and no solid flux ever forms; (II) both molten and solid flux are present, and the profile of the oscillation mark is continuous with respect to the space variable in the casting direction; (III) both molten and solid flux are present, and the profile of the oscillation mark is discontinuous with respect to the space variable in the casting direction. Although (I) gave good agreement with experimental data, it suffered the drawback that solid flux is typically observed during actual continuous casting; this has been rectified in this work via alternative (II). On the other hand, alternative (III) can occur as a result of hysteresis-type phenomenon that is encountered in other flows that involve temperature-dependent viscosity; in the present case, this manifests itself via the possibility of multiple states for the oscillation-mark profile at the instants in time when solid flux begins to form and when it ceases to form., QC 20200623

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., QC 20170627

We develop a coupled thermomechanical model, that includes mould taper, for the formation of air gaps in the vertical continuous casting of round billets. The system is very sensitive to the small width of the air gap. Mould tapers are used to mitigate the contraction of the solidified shell during cooling. We apply numerical and perturbation methods to show that a small mould taper significantly reduces the insulating effect of the air gap. The analysis is presented in a more transparent and less computationally expensive way than earlier, fully numerical models. We also consider a theoretical ideal taper, which eliminates the air gap altogether. The air gap is found to be quite robust; increasing the size of the taper does not constitute an equal reduction in the air gap size. Sample computations are carried out using parameters for the continuous casting of a pure metal (copper), although the framework can easily be extended to the continuous casting of alloys., QC 20151104