Quantitative model to determine permeability for columnar dendritic structures

Abstract

A new model that can quantitatively evaluate the permeability for columnar dendritic structures was developed by modifying the Kozeny constant in Kozeny-Carman's equation. The modified Kozeny constant consists of two terms: one accounting for the flow direction for primary arms of columnar dendrites and the other accounting for the tortuosity of channels in the dendritic structures. The permeability calculated by this new model was compared with that obtained in our previous simulations [Y. Natsume et al.: Tetsuto-Hagané, 99 (2013), 117] and from experiments other researchers [K. Murakami et al.: Acta metall., 31 (1983), 1417, 32 (1984), 1423, Liu et al.: Mater. Sci. Tech., 5 (1989), 1148] and the values were found to be in fairly good agreement with the compared values. In addition, we investigated the obtained quantitative model to determine permeability for use in computational studies of macrosegregation. To evaluate the permeability quantitatively using Kozeny-Carman's equation, the value of the specific surface area for dendrites is required. We introduced an assumption that the inverse of the specific surface area for columnar dendrites is proportional to the secondary arm spacing. By using this assumption in our modified model, the permeability can be determined using only the dendrite arm spacing and liquid volume fraction. © 2013 ISIJ.