Water Model and CFD-PBM Coupled Model of Gas-Liquid-Slag Three-Phase Flow in Ladle Metallurgy

Modeling of Gas-Steel-Slag Three-Phase Flow in Ladle Metallurgy: Part II. Multi-scale Mathematical Model

“…The present prediction is compared with both the experimental result and that predicted by the Eulerian method coupled with the PBM in our previous work. 7) It is shown that the result of the DBM is a bit larger than that of both the experiment and the PBM in the upper region. The reason may be that the present work ignores the lift force and the bubble breakage which have been considered in the Eulerian PBM.…”

“…15) The results of Klostermann et al 16) showed that VOF is suitable for rising bubble problems where bubbles are much larger than the grid size. Actually, as it is found in the experiment, 7) bubbles injected by porous plug (s) are strongly dispersed in liquid, it is almost impossible to capture the bubble interface for a full-scale simulation. Though the Eulerian discrete fluid model coupled with the PBM provides a valid method for the non-uniform bubble diameter prediction, it still lacks the description of each individual bubble behaviors.…”

“…Details of the observations and the diameter measurements can be found in the authors' previous work. 7) The present work uses the DBM for simulations of bubble transport, except for the bubble-liquid interactions, the bubble-bubble interactions can also be captured. Figure 12 continuously shows the process of bubble coalescence with a time interval of 0.004 s in the condition that the gas flow rate is 70 L/h.…”

“…In an Eulerian way, Li et al 1) and Llanos et al 2) adopted the volume of fluid (VOF) approach to describe the fluid dynamics of all phases in ladle. Numerous works such as Zhang, 3) Bellot et al, 4) Mukhopadhyay et al, 5) Luo and Zhu 6) and Li et al 7) used the Eulerian discrete fluid model with inter-phase interactions to simulate the bubble plume, and the population balance model (PBM) for calculation of non-uniform bubble size is also employed. 5,7) On the other side, Johansen and Boysan, 8) Guo et al 9) and Madan et al 10) early proposed a Lagrangian form of Newton's second law for solution of bubbles in liquid, which is referred to as the discrete phase model (DPM).…”

“…Numerous works such as Zhang, 3) Bellot et al, 4) Mukhopadhyay et al, 5) Luo and Zhu 6) and Li et al 7) used the Eulerian discrete fluid model with inter-phase interactions to simulate the bubble plume, and the population balance model (PBM) for calculation of non-uniform bubble size is also employed. 5,7) On the other side, Johansen and Boysan, 8) Guo et al 9) and Madan et al 10) early proposed a Lagrangian form of Newton's second law for solution of bubbles in liquid, which is referred to as the discrete phase model (DPM). Recently, Liu et al 11) and Cloete et al 12) coupled the VOF and DPM respectively for the immiscible continuous phases and bubbles with the standard k-ε turbulence model.…”