Extension of the k-ε model for the numerical simulation of the melt flow in induction crucible furnaces

Checking the calculations of turbulent melt flow in induction crucible furnaces that were carried out with various modifications of the two-dimensional (2-D)k-ε model using experimental findings has shown basic differences in the distributions of the specific generation of the turbulent energy and the kinetic energy of the turbulence. The discrepancies are explained by the distinctive three-dimensional (3-D) character of the pulsations and the low-frequency fluctuations of the macroscopic toroidal eddy; these are not taken into account in the numerical methods mentioned. With the aid of this 3-D model, the additional component of turbulent kinetic energy involved is estimated, and an approximation formula for the low-frequency component of the specific generation of turbulence is given. This results in an extension of the 2-D k-ε model for a recirculated flow with several toroidal eddies, leading to good qualitative agreement of the characteristics of turbulent flow with the experimental findings. Since the numerical simulation-in agreement with industrial practice and the experiments carried out-demonstrates good effective mixing of the entire flow region, there is thus a possibility for the simulation of aterial transport in the melt of induction crucible furnaces as part of the widespread 2-D computation methods.