Properties of stochastic permeability
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When modeled at macroscopic length scales, the complex dendritic network in the solid-plus-liquid region of a solidifying alloy (the “mushy zone”) has been modeled as a continuum based on the theory of porous media. The most important property of a porous medium is its permeability, which relates the macroscopic pressure gradient to the throughput of fluid flow. Knowledge of the permeability of the mushy zone as a function of the local volume-fraction of liquid and other morphological parameters is thus essential to successfully modeling the flow of interdendritic liquid during alloy solidification. Permeability is usually treated as a deterministic function of parameters that can be calculated by the model (e.g., local solid fraction, dendrite arm spacing). However, recent results show that the length scales that must be resolved are too small for the assumption of deterministic behavior to be valid, and investigators must confront the stochastic behavior of the permeability field. We describe early work to investigate the spatial structure of the stochastic permeability at these small scales, with a view to develop a comprehensive treatment of stochastic permeability to enable improved modeling.
Keywordsmushy zone permeability fluid flow modelling
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- 1.Flemings M C and Nereo G E, Trans. Metall. Soc. AIME, 239 (1967) 1449.Google Scholar
- 2.Flemings M C, Mehrabian R and Nereo G E, Trans. AIME, 242 (1968) 41.Google Scholar
- 3.Flemings M C and Nereo G E, Trans. Metall. Soc. AIME, 242 (1968) 50.Google Scholar
- 4.Flemings M C, Solidification Processing. McGraw-Hill, New York, NY, (1974).Google Scholar
- 5.Mehrabian R, Keane M and Flemings M C. Metall. Trans., 1 (1970) 1209.Google Scholar
- 7.Frueh C, On the length scale and location of channel nucleation in directional solidification. PhD thesis, The University of Arizona, 2002.Google Scholar
- 13.Erdmann R G. Image-based numerical simulation of Stokes flow in porous media. PhD thesis, The University of Arizona, 2006. http://etd.library.arizona.edu/etd/GetFileServlet?file=file:///data1/pdf/etd/azu_etd_1495_1_m.pdf&type=application/pdf
- 15.Darcy H P G, Les fontaines publiques de la ville de Dijon. Victor Dalmont, Paris, 1856.Google Scholar
- 16.Eric W. Weisstein. MathWorld-A Wolfram Web Resource, 2009. http://mathworld.wolfram.com/Cross-CorrelationTheorem.html
- 17.Wasserman L, All of statistics: a concise course in statistical inference. Springer Verlag, 2004.Google Scholar