# Numerical and asymptotic solutions of vertical continuous casting with and without superheat

Free Boundary Problems and Related Topics

Co-author: Michael Vynnycky (Royal Institute of Technology (Sweden))

In a continuous casting process, such as the strip casting of copper, molten metal first passes through a water-cooled mould region, before being subjected to a high cooling rate further downstream. Consequently, the molten metal solidifies and the solidified metal is withdrawn at a uniform casting speed. Industrialists need to understand the factors influencing product quality and process productivity. Of key significance is the heat transfer that occurs during solidification, particularly the location of the interface between molten metal and solid.

The modelling of the continuous casting of metals is known to involve the complex interaction of non-isothermal fluid and solid mechanics. Typically, the flow in the molten metal is turbulent, and it is generally believed that a computational fluid dynamics (CFD) approach is necessary in order to correctly capture the heat transfer characteristics. However, we can show that an asymptotically reduced version of the CFD -based model, which neglects this turbulence, gives predictions for the pool depth, local temperature profiles and mould wall heat flux that agree very well with results of the original CFD model.

This reduced model can be described as a steady state 2D heat flow Stefan problem, with a degenerate initial condition and non-standard Neumann-type boundary condition. If we assume the incoming metal is at the melt temperature then we obtain a one-phase model but with potentially two stages, depending whether the metal is fully solidified before leaving the mould. However, in reality, the incoming temperature is greater than the melt temperature, termed as including superheat, and this leads to a two-phase model with a pre-solidification stage, where the second phase only first appears after a finite delay.

In this work we highlight some numerical challenges in solving the systems with and without superheat. The Keller box finite-difference scheme is used, along with a boundary immobilisation method.

This talk is part of the Isaac Newton Institute Seminar Series series.

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