Two-phase modelling of equiaxed crystal sedimentation and thermomechanic stress development in the sedimented packed bed

During many industrial solidification processes equiaxed crystals form, grow and move. When those crystals are small they are carried by the melt, whereas when getting larger they sediment. As long as the volume fraction of crystals is below the packing limit, they are able to move relatively free. Crystals being backed in a so called packed bed form a semi-solid slurry, which may behave like a visco-plastic material. In addition, cooling-induced density increase of both, liquid and solid phases might lead to shrinkage of the whole casting domain. So deformation happens and gaps between casting and mold occur. In the present work, a two-phase Eulerian-Eulerian volume averaging model for describing the motion of equiaxed crystals in the melt is combined with a similar two-phase model for describing the dynamic of the packed bed. As constitutive equation for the solid skeleton in the packed bed Norton-Hoff law is applied. Shrinkage induced by density changes in the liquid or the solid phase is explicitly taken into account and handled by remeshing the calculation domain accordantly.