Persistent Link:
http://hdl.handle.net/10150/187235
Title:
Numerical calculation of permeability in dendritic alloys.
Author:
Bhat, Machimale Shankaranarayana.
Issue Date:
1995
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
A new technique of analyzing flows through dendritic microstructures for permeability calculations is presented. The method of applying a Navier-Stokes solver for analyzing flows normal and parallel to columnar dendritic structures and past equiaxed grains is elucidated. The permeability for flow normal to arrays of circular cylinders is first calculated to verify the computational method. Calculated results are extended to volume fraction of liquid as high as 0.98 to achieve relevancy to solidification modeling. The study showed a weak dependence of nondimensional permeability on the Reynolds number(Re), up to Re = 60. Dendritic microstructures, obtained by quenching an alloy during solidification are captured with an image analysis system. Complex solid-liquid dendrite interfaces are then represented in a computer program by retrieving and digitizing the pixel data. A mesh generator is used to subdivide the quenched liquid into quadrilateral finite elements. Using a Navier-Stokes solver, the velocity and pressure at the nodes are calculated at the microstructural level and used to calculate nondimensional permeability. It is found that the calculated results for flows normal to the primary dendrite arms at high liquid volume fractions merge well with the empirical permeabilities obtained at lower volume fractions. The analyses are extended to calculate permeability for flow past equiaxed dendritic grains and past globular grains. A method has been devised to extrapolate results from two-dimensional flows to three-dimensional flows. The results, considering specific surface area as characteristic length, compare to the analytical results for flow through different arrays of spheres. Numerical calculations are also performed to obtain permeabilities for flow parallel to primary dendrites in columnar structures, with high liquid volume fraction (g(L)), where physical experiments fail. For g(L) > 0.6, the results of the present work agree with the permeabilities calculated for fully developed flow parallel to an array of circular cylinders. Also, when the roughness factor is introduced, permeabilities obtained by the present technique merge well with the experimental data. The range in g(L) where the roughness factor should be introduced, however, is yet to be resolved. This merits, therefore, further work involving three-dimensional flow analyses.
Type:
text; Dissertation-Reproduction (electronic)
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Materials Science and Engineering; Graduate College
Degree Grantor:
University of Arizona
Committee Chair:
Poirier, D. R.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleNumerical calculation of permeability in dendritic alloys.en_US
dc.creatorBhat, Machimale Shankaranarayana.en_US
dc.contributor.authorBhat, Machimale Shankaranarayana.en_US
dc.date.issued1995en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractA new technique of analyzing flows through dendritic microstructures for permeability calculations is presented. The method of applying a Navier-Stokes solver for analyzing flows normal and parallel to columnar dendritic structures and past equiaxed grains is elucidated. The permeability for flow normal to arrays of circular cylinders is first calculated to verify the computational method. Calculated results are extended to volume fraction of liquid as high as 0.98 to achieve relevancy to solidification modeling. The study showed a weak dependence of nondimensional permeability on the Reynolds number(Re), up to Re = 60. Dendritic microstructures, obtained by quenching an alloy during solidification are captured with an image analysis system. Complex solid-liquid dendrite interfaces are then represented in a computer program by retrieving and digitizing the pixel data. A mesh generator is used to subdivide the quenched liquid into quadrilateral finite elements. Using a Navier-Stokes solver, the velocity and pressure at the nodes are calculated at the microstructural level and used to calculate nondimensional permeability. It is found that the calculated results for flows normal to the primary dendrite arms at high liquid volume fractions merge well with the empirical permeabilities obtained at lower volume fractions. The analyses are extended to calculate permeability for flow past equiaxed dendritic grains and past globular grains. A method has been devised to extrapolate results from two-dimensional flows to three-dimensional flows. The results, considering specific surface area as characteristic length, compare to the analytical results for flow through different arrays of spheres. Numerical calculations are also performed to obtain permeabilities for flow parallel to primary dendrites in columnar structures, with high liquid volume fraction (g(L)), where physical experiments fail. For g(L) > 0.6, the results of the present work agree with the permeabilities calculated for fully developed flow parallel to an array of circular cylinders. Also, when the roughness factor is introduced, permeabilities obtained by the present technique merge well with the experimental data. The range in g(L) where the roughness factor should be introduced, however, is yet to be resolved. This merits, therefore, further work involving three-dimensional flow analyses.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineMaterials Science and Engineeringen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.chairPoirier, D. R.en_US
dc.contributor.committeememberHeinrich, J. C.en_US
dc.contributor.committeememberDemer, L. J.en_US
dc.contributor.committeememberPeterson, T.en_US
dc.contributor.committeememberOgden, K.en_US
dc.identifier.proquest9603382en_US
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