Experimental difficulties associated with permeability measurements in aluminum alloys
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I. INTRODUCTION
THE Kozeny–Carman relation, along with more recent theory,[1] are in fairly good agreement with the permeability measurements of equiaxed aluminum alloys presented in the literature.[2] However, because the existing data are scarce, there is still a need for validation of these relations for a large range of alloys and morphologies. The permeability measurements have been presented with little or no discussion about the considerable experimental difficulties associated with the experiments.[2–5] Therefore, it can be difficult for others to reproduce these measurements and to use the suggested experimental methods to measure the permeability for other alloys and morphologies. In the present article, we will discuss some of the experimental difficulties associated with the measurement of mushy-zone permeability in aluminum alloys, based on the experience gained through the work with the development of the experiment presented in Reference 2. General experimental principles are discussed. Furthermore, the concept of a flux material is described, and the influence of the permeameter design and the experimental procedure on grain detachment, preferred-flow channel formation, and coarsening is revealed through microstructural images. II. EXPERIMENTAL PRINCIPLES The interdendritic liquid flow through a mushy zone with a rigid or “coherent” solid phase is commonly described by Darcy’s law. In differential form, this law can be written as ¹p 5 2
mlV 1 rl g K
[1]
where p is the local liquid pressure, V is the superficial liquid velocity (local-volume-averaged liquid velocity times the liquid fraction), and K is the permeability. The quantities
ØYVIND NIELSEN, formerly Doctoral Student, Department of Materials Technology and Electrochemistry, Norwegian University of Science and Technology, is Research Scientist, SINTEF, N-0314 Oslo, Norway. LARS ARNBERG, Professor, is with the Department of Materials Technology and Electrochemistry, Norwegian University of Science and Technology, 7491 Trondheim, Norway. Manuscript submitted April 3, 2000. METALLURGICAL AND MATERIALS TRANSACTIONS A
ml and rl are the viscosity and the density of the interdendritic liquid, respectively, and g is the acceleration due to gravity. For a homogeneous mushy sample in a cylindrical container (Figure 1), integration of the one-dimensional version of Eq. [1] from top (x 5 0) to bottom (x 5 L) yields pext 5
mlVL mlVL 2 rlgL or K 5 K pext 1 rlgL
[2]
where pext is an applied pressure, L is the length of the mushy sample, and V 5 .V..* Figure 1, along with Eq. [2], *If the cylinder is horizontally aligned, the terms containing g in Eq. [2] disappear.
reveals the principle of a permeameter: if we set up a pressure difference over a one-dimensional mushy zone and measure the resulting superficial liquid velocity, we can calculate the permeability from Eq. [2]. Measurement of the superficial liquid velocity in a permeameter requires a finite displacement of the liquid relative to the coherent solid phase. Thus, a pressurized fluid, a fl
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