Analysis of high-speed continuous casting with inverse finite elements

Abstract

A recently proposed inverse isotherm finite element method is further extended in order to account for processes with distorted isotherms. With this method a variety of problems can be solved which require the explicit calculation of characteristic material lines along with the common field of unknowns in transport phenomena. The method is applied to high-speed metal casting, where the location and shape of the extensive solidification front is calculated simultaneously with the primary unknowns, the velocity and the pressure, whereas the temperature is fixed at the moving nodes of the finite element tessellation. This is achieved by solving the energy equation inversely along with the rest of the conservation equations, i.e. the temperature field is fixed and its location is calculated. Empirical correlations may be derived which give the shape of the solidification front as a function of the process parameters. This may be used to improve the control means of metal casting, which is currently based on one-dimensional approximate analyses.