Permeability in the mushy zone

R. G. Erdmann, David R Poirier, A. G. Hendrick

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

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. In current continuum models, the permeability of the mushy zone is given as a deterministic function of (1) the local volume fraction of liquid and (2) a characteristic length scale such as the primary dendrite arm spacing or the reciprocal of the specific surface area of the solid-liquid interface. Here we first provide a broad overview of the experimental data, mesoscale numerical flow simulations, and resulting correlations for the deterministic permeability of both equiaxed and columnar mushy zones. A extended view of permeability in mushy zones which includes the stochastic nature of permeability is discussed. This viewpoint is the result of performing extensive numerical simulations of creeping flow through random microstructures. The permeabilities obtained from these simulations are random functions with spatial autocorrelation structures, and variations in the local permeability are shown to have dramatic effects on the flow patterns observed in such microstructures. Specifically, it is found that "lightning-like" patterns emerge in the fluid velocity and that the flows in such geometries are strongly sensitive to small variations in the solid structure. We conclude with a comparison of deterministic and stochastic permeabilities which suggests the importance of incorporating stochastic descriptions of the permeability of the mushy zone in solidification modeling.

Original languageEnglish (US)
Title of host publicationMaterials Science Forum
Pages399-408
Number of pages10
Volume649
DOIs
Publication statusPublished - 2010
Event5th International Conference on Solidification and Gravity - Miskolc-Lillafured, Hungary
Duration: Sep 4 2008Sep 5 2008

Publication series

NameMaterials Science Forum
Volume649
ISSN (Print)02555476

Other

Other5th International Conference on Solidification and Gravity
CountryHungary
CityMiskolc-Lillafured
Period9/4/089/5/08

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ASJC Scopus subject areas

  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanical Engineering
  • Mechanics of Materials

Cite this

Erdmann, R. G., Poirier, D. R., & Hendrick, A. G. (2010). Permeability in the mushy zone. In Materials Science Forum (Vol. 649, pp. 399-408). (Materials Science Forum; Vol. 649). https://doi.org/10.4028/www.scientific.net/MSF.649.399