Knowledge of gas-liquid multiphase flow behavior in the Rheinsahl-Heraeus (RH) system is of great significance to clarify the circulation flow rate, decarburization, and inclusion removal with a reliable description. Thus, based on the separate model of injecting gas behavior, a novel mathematical model of multiphase flow has been developed to give the distribution of gas holdup in the RH system. The numerical results show that the predicted circulation flow rates, the predicted flow velocities, and the predicted mixing times agree with the measured results in a water model and that the predicted tracer concentration curve agrees with the results obtained in an actual RH system. With a lower lifting gas flow rate, the rising gas bubbles are concentrated near the wall; with a higher lifting gas flow rate, gas bubbles can reach the center of the up-snorkel. A critical lifting gas flow rate is used to obtain the maximum circulation flow rate.

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Numerical simulation is a powerful tool to investigate inclusion behavior in the molten steel. Although many mathematical models have been developed to predict inclusion collision-growth behavior in different metallurgical reactors, the inclusion size distribution had to be obtained by experiment or assumption. Thus, a general nucleation-growth model, which involves in chemical reaction, homogeneous nucleation and growth kinetics, is developed to investigate the inclusion nucleation, Ostwald ripening, Brownian collisiongrowth, Stokes collision-growth and turbulent collision-growth. In order to speed up the calculation, the deoxidation products are divided into two parts. The first part only consists of embryos, and directly numerical simulation is used to solve the differential equations. The second part only consists of inclusion particles, and particle-size-grouping method is introduced to solve the related equations. Numerical results showed that the predicted inclusion size distributions are consistent with previous experimental data. With the increasing diffusion coefficient, the peak-value diameter keeps unchanged and the maximum number density decreases. With the increasing turbulent energy dissipation rate, the peak-value diameter and the maximum number density decrease under the assumption on floating-out of larger inclusions.

A numerical method has been employed to investigate the flow field and mixing characteristic in the Rheinsahl-Heraeus (RH) degasser with side-bottom blowing. The numerical results showed that stream flows in the up snorkel, the vacuum chamber, the down snorkel and the ladle form a large rectangular circulation zone in the RH degasser with side-bottom blowing, which can enhance the circulation flow rate effectively. For an RH with side-bottom blowing, when the included angle of the line between bottom blowing location and ladle centre and the line between two snorkels is zero, the circulation flow rate increases initially with increasing dimensionless distance between the bottom blowing location and the ladle centre and then decreases, while the mixing time increases with increasing dimensionless distance. On the other hand, when the dimensionless distance is 0?2, both the circulation flow rate and the mixing time decrease with the increasing included angle initially, reach their minimum value and then increase. The optimum values for the dimensionless distance and the included angle to achieve large circulation flow rate and small mixing time are 0?2 and p/4 in the present work.

Because of the high heating efficiency, channel type induction heating is utilized in the tundish in order to reduce the temperature fluctuations of the molten steel in the process of continuous casting. In order to have a deep insight into the complex MHD (magneto hydrodynamic) process in the tundish with channel type induction heating, water model and mathematical model are performed to describe the fluid flow and the heat transfer in the tundish. A non-isothermal water model with channel heater is built to investigate the thermal convection in the tundish. The electromagnetic force and Joule heating are introduced into the momentum equations and the energy conservation equation as a source term, and the coupled flow and temperature field are solved by the finite volume method. The results show that the predicted flow field and temperature field agree with the experimental data. In the case of channel type induction heating, there are two spiral flow in the channel due to electromagnetic force, and the temperature difference of molten steel is 12 C between the inlet and the outlet of the channel due to Joule heating.

Based on the two-phase fluid (Eulerian-Eulerian) model, a mathematical model about the gas-liquid flow and mixing behavior was developed to investigate the effect of the offset of dual plugs, the included angle of dual plugs with a center point, and gas flow rate on the mixing time in a ladle with dual plugs. Numerical results indicate that two types of recirculation zones exist in the ladle. One is the middle recirculation between gas and liquid plumes, and the other is the sidewall recirculation between plumes and the ladle sidewall. The correction shows that the mixing time is in proportion to −0.2676 power of gas flow rate. There is a unique optimum offset of dual plugs with a particular included angle, in turn, a unique optimum included angle of dual plugs exits with a particular offset.

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...

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