A boundary layer model for capture of inclusions by steel–slag interface in a turbulent flow

A boundary layer model was developed to predict the capture of inclusions by steel–slag interface in a turbulent fluid flow, which is based on the detailed analysis of inclusion trajectories. The effective boundary layer for inclusion removal was proposed by a statistical method. It is noticed that the capture of inclusions by steel–slag interface is not only dependent on the diameter of inclusions but also related to the local turbulent conditions. In high turbulent flow fields, the transport of inclusions is mainly dominated by the turbulent flow, and thus, the effective boundary layer thickness is mainly affected by the level of turbulent kinetic energy and is almost independent of the inclusion diameter. The inertia of inclusions gradually takes over the stochastic effect of turbulent flow, and the effect of inclusion diameter on effective boundary layer thickness becomes more noticeable with the decrease in the level of turbulent kinetic energy. Besides, the effective boundary layer thickness is more susceptible to the inclusion diameter for larger inclusions due to its greater inertia under the same turbulent condition while it principally depends on the level of turbulent kinetic energy for smaller inclusions. As the characteristic velocity increases, the time for inclusions transport and interaction with steel–slag interface decreases, and thus, the effective boundary layer thickness decreases. Moreover, the graphical user interface was developed by using the cubic spline interpolation for ease of coupling the current boundary layer model with the macro-scale model of the a turbulent fluid flow in the metallurgical vessel.