Permeability models for flow in partially solid alloys

Abstract

In order to characterize the flow of interdendritic liquid through the solid-liquid zones of solidifying alloys, it is necessary to have permeability data. Permeability data from five different sources were analyzed by using models based upon the volume fraction of liquid, and the primary and secondary dendrite arm spacings. Three different models were tested, of which two have a physical basis: the Blake-Kozeny model and the Hagen-Poiseuille model; the third model is empirical. Metal as well as nonmetal specimen data were used in this study. The fraction liquid range for all data varied from 0.077 to 0.606, the primary dendrite arm spacing from 28 pm to 420 pm and the secondary dendrite arm spacing from 23 pm to 146 pm. Data for flow parallel as well as perpendicular to the primary dendrite arms were used in order to model the two-dimensional permeability. For parallel flow, the Hagen-Poiseuille model gives the best agreement between calculated and measured permeabilities with an average deviation of 37 percent. However for normal flow, the empirical model gives the best results with an average deviation of 44 percent between calculated and measured permeabilities, and the Blake-Kozeny model correlates almost as well.