A mathematical model has been developed to predict the collision and aggregation among inclusions in the ladle with different porous plug configurations. The numerical results showed that the porous plug configuration has a profound effect on the inclusion removal process in ladle. The eccentric bottom blowing is better than the central bottom blowing. The terminal inclusion removal efficiency decreases with the increasing porous plugs. The inclusions captured by the top slag accounts for the majority of the removed inclusions, inclusion adhesion to the sidle wall is the minor manner, and inclusions adhered to the ladle bottom wall can be negligible. In order to avoid newly generated large inclusions to be remained in the liquid steel after about 16 min of treatment, it is necessary to prolong the treating time on the condition of one porous plug configuration.KEY WORDS: mathematical model; ladle; porous plug; turbulent collision; Stokes collision; aggregation; bubble; inclusion removal.
1597© 2010 ISIJ gas is injected through one plug placed centrally, one plug placed eccentrically at half radius, two and three plugs placed at half radius, as shown in Fig. 1. And the position of main plane in the following figures is also shown in Fig. 1.
Mathematical ModelThe mathematical model for fluid flow and inclusion removal is based on the following assumptions:(a) The fluids in both the gas and liquid phases are Newtonian, viscous and incompressible, and the fluid flow is at the steady state.(b) The effect of top slag on fluid flow is neglected and the free surface is thought to be flat.(c) The gas bubbles are spherical and the interaction among bubbles is not considered.(d) The fluid flow in the ladle is assumed to be an isothermal process.(e) The effect of inclusion movement on fluid flow is neglected.(f) Inclusions are spherical and each inclusion moves independently before the collision occurs.(g) The fractional inclusion number density has an exponential relationship with the inclusion radius and can be expressed as [15][16][17][18][19] :Thus, the inclusion characteristic number density, concentration and radius can be expressed as:and r* 3 ø -6/B, respectively. Furthermore, C* can also be expressed as the function of N* and r* : C*ϭN* · (4/3)pr* 3 . In order to give a basic idea of the mathematical model, a schematic of the model has been shown in Fig. 2. First of all, an Eulerian-Eulerian model was employed to simulate the two-phase flow in the ladle. Then the transient transport equations for inclusion characteristic number density and concentration, which consider different inclusion removal approaches and collision mechanisms, have been solved to investigate the variations of inclusion characteristic parameters with space and time. In the calculation, new values of N* and C* at each grid point during the whole process are obtained by each iteration and the values of A and B can also be derived, which indicate new inclusion size distribution of inclusions at each grid point.
Theory of Multiphase FlowThe multip...