Cross-Permeability of the Semisolid Region in Directional Solidification: A Combined Phase-Field and Lattice-Boltzmann Simulation Approach

Based on the results of microstructure simulations, fluid flow through the semisolid region during directional solidification of the technical Ni-base alloy 718 has been studied. Three-dimensional microstructures at different positions in the semisolid region were obtained by using a multicomponent multiphase-field model that was online coupled to a commercial thermodynamic database. For the range of five different primary dendrite distances lambda(1) between 50 mu m and 250 mu m, the flow velocity and the permeability perpendicular to the dendrite growth direction was evaluated by using a proprietary Lattice-Boltzmann model. The commercial CFD software ANSYS FLUENT was alternatively applied for reference. Consistent values of the average flow velocity along the dendrites were obtained for both methods. From the results of the fluid flow simulations, the cross-permeability was evaluated as a function of temperature and fraction liquid for each of the five different primary dendrite distances lambda(1). The obtained permeability values can be approximated by a single analytical function of the fraction liquid and lambda(1) and are discussed and compared with known relations from the literature.