Experiments and analyses for flow through partially solidified alloys.

Abstract

The equation for the conservation of momentum in the mushy zone during solidification is derived using the volume averaging technique. The conditions under which the momentum equation reduces to Darcy's law are elucidated. Permeabilities for flow of interdendritic liquid in Al-Cu alloys with equiaxial structures are measured using a simple, cost-effective permeameter. Center-to-center distance between grains (180 μm to 450 μm), specific surface (3.21 x 10⁻² μm⁻¹ to 3.095 x 10⁻¹ μm⁻¹), and volume fraction liquid (0.166 to 0.434) are the structural parameters studied in this investigation. Permeability in Al-Cu alloys with equiaxial grains is structure sensitive. For example, permeabilities for globular structures (nondendritic) are approximately one order of magnitude greater than permeabilities for the dendritic-globular structures, when the volume fraction liquid is approximately 0.3. To better understand the dependence of permeability on structure morphology, structure evolution during the permeability testing was studied in isothermal coarsening experiments. Dimensionless permeabilities based on specific surface, and center-to-center distance between grains are presented along with the theoretical results for flow through different arrays (simple cubic, body-centered cubic and face-centered cubic) of uniform spheres. With dimensionless permeability defined as KSᵥ², where Sᵥ is the specific surface of the solid, the empirical data compare reasonably well with theoretical curves for flow through arrays of uniform spheres. Numerical experiments are performed to obtain permeabilities for flow parallel to primary dendrites in columnar structures with high volume-fraction liquid where physical experiments may fail. The results of numerical experiments are presented along with the analytical results for flow parallel to cylinders arranged in square and triangular packing, analytical results for flow through periodically constricted tubes and the available empirical data. The results indicate that there is a transition in the behavior of permeability in the neighborhood of volume fraction liquid equal to 0.65.