Measurement of liquid permeability in the mushy zones of aluminum-copper alloys
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I. INTRODUCTION
THE permeability of interdendritic liquids flowing through dendritic structures is an important parameter needed to predict the level of porosity in castings. The permeability is a component of Darcy’s law, used to estimate the pressure drop due to the resistance to the flow of interdendritic fluid to feed shrinkage. Therefore, much research has focused on measuring the permeability of alloys in the mushy zone.[1–10] The Kozeny–Carman equation for liquid permeability in the mushy zones of alloys may be written as Ks 5
g3L kCS2V
[1]
where gL is the volume fraction of liquid, SV is the specific solid surface area (i.e., surface area of solid in unit volume of sample), and kC is the Kozeny–Carman constant, which takes on various values depending on the characteristics of the porous medium.[11] The first systematic measurement of liquid permeability in the mushy zones of alloys was made by Piwonka and Flemings,[1] who used molten lead to measure the permeability of liquid metal in an Al-4.5 pct Cu alloy. Later, Apelian et al.[2] measured the permeability of water in partially solidified dendritic networks of aluminum-silicon alloys, and Murakami and Okamoto[3] used a transparent borneol-paraffin system to study permeability in equiaxed structures. These studies showed that permeability was proportional to the volume fraction of liquid raised to a power of n (gnL), where n 5 2 to 3.3. While the previous measurements yield valuable estimates
A.J. DUNCAN, formerly Postdoctoral Fellow, Metals and Ceramics Division, Oak Ridge National Laboratory, is Research Staff Member, Savannah River Technology Center, Westinghouse Savannah River Company, Aiken, SC 29808. Q. HAN, Postdoctoral Fellow, and S. VISWANATHAN, Research Staff Member, are with the Metals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6083. Manuscript submitted January 29, 1999. METALLURGICAL AND MATERIALS TRANSACTIONS B
of permeability, the primary disadvantage to these approaches is that the liquid used for the experiment was not the eutectic liquid, and, thus, the result may not be representative of actual castings.[5] To overcome this problem, many studies used eutectic liquid to measure the permeability in both equiaxed[4–9] and columnar[10] dendritic structures. Poirier and Ganesan[6] made measurements on equiaxed structures using eutectic liquid in aluminum-copper alloys and correlated permeability to the alloy microstructure by the Kozeny–Carman relation. The results of this study, together with a more recent study,[8] are compiled in Figure 1. Surprisingly, the scatter on this data spans approximately one and one-half orders of magnitude. This is most likely due to the fact that microstructures undergo coarsening during the test and that the permeability increases with time, since, in these and other measurements, the permeabilty was treated as a constant over time. In this article, a modified approach for calculating permeability from experimental data is presented in which permeability can be determined as
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