An examination of effects of solidification parameters on permeability of a mushy zone in castings

A model describing the development of dendritic structure and the resulting gradient of flow resistance to interdendritic liquid is presented. The Hagen–Pousielle version of D’Arcy’s equation for flow through a porous structure is developed as a function of cooling rate and liquid volume fraction. Applied to finite elements in a unidirectionally cooled casting model, permeability gradient, feeding flow-rate required to prevent porosity, and mushy-zone liquid pressure drop at this flow rate are evaluated for the simple Fe–2Cr–0.5C and Al–5Cu castings exhibiting asymptotic and linear temperature profiles, respectively. The model shows permeability of the dendritic structure in the mushy zone dropping sharply, approaching the root of solidification front (solidus). Also shown is the effect of relative magnitude of primary and secondary arm spacing. If secondary dendrite arm spacing approaches primary arm spacing, the permeability for flow normal to primary dendrite arms approaches or even surpasses the permeability for flow parallel to primary dendrite arms.