A Mathematical Modeling Study of Tracer Mixing in a Continuous Casting Tundish

A mathematical model based on a water model was developed to study the tracer mixing in a single strand tundish. The mixing behavior of black ink and KCl solution was simulated by a mixed composition fluid model, and the data were validated by water modeling results. In addition, a model that solves the scalar transport equation (STE) without any physical properties of the tracer was studied and the results were compared to predictions using the density-coupled model. Furthermore, the mixing behaviors of different amounts of KCl tracers were investigated. Before the model was established, KCl tracer properties such as the KCl molecule diffusion (KMD), the water molecule self-diffusion (WSD) in KCl solution, and the KCl solution viscosity (KV) were evaluated. The RTD curve of 250 mL KCl for the KMD case was closer to the water modeling results than that of the case implemented with only density. Moreover, the ensemble average deviation of the RTD curves of the cases implemented with KMD + WSD, KMD + KV, and KMD + WSD + KV to the KMD case is less than 0.7 pct. Thus, the water self-diffusion and KV were neglected, while the KCl density and KMD were implemented in the current study. The flow pattern of black ink was similar to the STE result i.e., the fluid flowed upwards toward the top surface and formed a large circulating flow at the outlet nozzle. The flow behavior of the 100, 150, and 250 mL KCl cases exhibited a strong tendency to sink to the tundish bottom, and subsequently flow through the holes in the dam. Thereafter, it propagated toward the outlet nozzle. Regarding the KCl tracer amount, the tracer concentration propagated to the outlet nozzle much faster for the larger amount case than for the smaller amount cases. However, the flow pattern for the 50 mL KCl case was somewhat different. The fluid propagated to the top surface which acted like black ink during the initial injection, and subsequently the fluid flowed throughout the holes at a much slower pace. The breakthrough time and peak concentration of RTD curves of model predictions and water modeling results showed a good agreement (all difference within 12.5 pct) for the 100, 150, and 250 mL KCl cases.