5th International Conference on Advances in Solidification Processes (ICASP-5) 5th International Symposium on Cutting Edge of Computer Simulation of Solidification, Casting and Refining (CSSCR-5)

The last decade has witnessed the development of various solidification models based on volume averaging methods. To reduce the calculations cost, the averaging reduces information contained within the mushy zone to a single variable, the solid volume fraction. The solidification rate and the permeability are then calculated with the help of closure laws often based on some semi-empirical correlations. In the present paper it will be shown that beyond the need of sub-grid correlations, some essential mesoscopic features lakes these models. During solidification, natural convection arises from the temperature and concentration gradients. Concentration gradients are caused by the preferential incorporation or rejection of solute element at the solid-liquid interface. In order to catch the smallest solute plumes scale the solidification model simulates directly the envelope of the columnar dendrites with a cellular automaton model. The mushy interior of the dendrite is modelled with a volume averaging method. The dendrites tips are assumed to growth with a modified LGK model to account for the effect of the magnitude and the direction of the flow. Secondary arms are allowed to transform into a primary arm if the curvature of the envelop exceeds a critical value. The competition between grains is well reproduced by the variation between dendrite tips velocities. This model allows the study of the effect of both the grains, and the primary arm spacing on the hydrodynamics. The results given by this model (with primary arms) are compared with the ones predicted with a model using a full volume averaging method (primary arms invisible).