Evaluation of solid-liquid interface profile during continuous casting by a spline based formalism

A numerical framework has been applied which comprises of a,cubic spline based collocation method to determine the solid-liquid interface profile (solidification front) during continuous casting process. The basis function chosen for the collocation algorithm to be employed in this formalism, is a cubic spline interpolation function. An iterative solution methodology has been developed to track the interface profile for copper strand of rectangular transverse section for different casting speeds. It is based on enthalpy conservation criteria at the solidification, interface and the trend is found to be in good agreement with the available information in the literature although a point to point mapping of the profile is not practically realizable. The spline based collocation algorithm is found to be a reasonably efficient tool for solidification front tracking process, as a good spatial derivative approximation can be achieved incorporating simple modelling philosophy which is numerically robust and computationally cost effective.