Mathematical model for cluster-inclusion's collision-growth in inclusion cloud at continuous casting mold

Abstract

The inclusion's morphology and size play a strong role in the steel product quality, so it is very important to have a deep insight into the inclusion's collision-growth in the continuous caster. In order to describe the formation of the cluster-inclusion, a mathematical model and the related source code are developed to trace the inclusion's movement and collision-growth in the inclusion cloud. Such a model includes two sub-models. Firstly, the spatial distribution of turbulent flow and the inclusion's number density and the characteristic radius after Stokes collision and turbulent collision are obtained by Eulerian approach. Secondly, the inclusion's trajectory and the related inclusion fractal growth are predicted by Lagrangian approach. Numerical results show that the spatial distributions of the inclusion volumetric concentration, number density and characteristic radius have some features of the upper and lower recirculation zone due to the fluid flow. For an inclusion particle, the bigger inclusion has more chances to catch other inclusions and forms a more complex cluster-structure. Among the forces acting on the inclusion, the pressure gradient force, Basset history force, the visual mass force, the gravitational force and the buoyancy force should be considered in order to describe the inclusion's exact motion. Furthermore, the pressure gradient force, the Basset force, the visual mass force follow the same variation rule along with the inclusion's trajectory. © 2014 ISIJ.