Representation and effect of mushy zone coefficient on coupled flow and solidification simulation during continuous casting

The mushy zone refers to the region of the solid-liquid system where the temperature is between the liquidus and solidus temperatures. In this zone, the turbulence of the interdendritic flow is reduced by blockage of dendrites. The mushy zone coefficient (A_mush) is an important calculating parameter in the continuous casting numerical simulation process, which strongly affects the prediction of fluid flow and solidification behavior in the mold zone. However, most researchers have neglected the influence of the mushy zone coefficient, and the correct expression of this coefficient is rarely found in the literature. Generally, the lower default value of 1×10⁵ kg·m^-3·s^-1 is used in the model, which leads to unrealistic results. In this study, the relationship between the mushy zone coefficient and permeability was analyzed, and the expression of the mushy zone coefficient was proposed. A coupled flow and solidification numerical model was developed to evaluate the effect of the mushy zone coefficient on the melt flow and solidification phenomena in a bloom continuous casting mold. Results show that the higher the value of the mushy zone coefficient, the stronger the damping becomes, and the faster the velocity drops as melt solidifies. A relatively high value of the mushy zone coefficient generates a "banded" form of mushy zone sandwiched between the solid and liquid phases in the mold zone. When the mushy zone coefficient is at a lower value, a wider mushy zone is obtained and the melt cools down rapidly in the mold region. In addition, the temperature at free surface is relatively low with supercooling, and the solidified shell remelts locally. The model is validated through comparison with measurements of shell thickness on a breakout shell. The value of the mushy zone coefficient ranging from 1×10⁸ to 5×10⁸ kg·m^-3·s^-1 is suggested.