Modeling under-cooling and equiaxed grain growth in continuous casting flow simulations

Electromagnetic stirring in continuous casting is known to increase the amount of equiaxed crystals. The numerical simulation of liquid steel flow and temperature in the strand with and without stirring is an established tool to design stirring tools. Nevertheless, it is difficult to conclude the increase of equiaxed crystals in the cast product from the simulation results: many proposed approaches are either very complex or too simplifying. In a first step, the local super-heat temperature (or under-cooling temperature, if negative) is determined from the temperature field of the strand flow simulation: using the approach of a dimensionless temperature field, the local super-heat temperature can be calculated a posteriori (i.e. without the need to run the simulation again) for arbitrary inflow-super-heat temperatures and concentration-dependent solidus/liquidus temperature intervals resulting from the steel grade phase diagram. The results show that the region of under-cooled steel is probably larger than commonly expected due the huge influence of convective heat transfer. In a second step, a local equiaxed crystal growth velocity for the under-cooled regions is derived based on the local liquid steel temperature. This growth effect can be implemented in the strand simulation as a scalar transport equation for the equiaxed crystal size. A comparison of the simulation of a stirred and a not stirred casting process shows a significant increase of equiaxed grain diameters.