Persistent Link:
http://hdl.handle.net/10150/195724
Title:
Image-Based Numerical Simulation of Stokes Flow in Porous Media
Author:
Erdmann, Robert Gerald
Issue Date:
2006
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:
Numerical models for the simulation of longitudinal and transverse Stokes flow in cylindrical periodic porous media are presented. The models, which are based on a finite-volume formulation in primitive variables, utilize digital image representations of the geometries to simulate, making them particularly well-suited for the rapid automated analysis of creeping flow in porous media with complex morphologies. Complete details of the model formulations are given, including extensive treatment of the pressure boundary conditions at the solid-liquid interface needed to guarantee convergence with all possible geometries. The convergence behavior of both models is tested, and the models are shown to be second-order accurate.The models are used to simulate flow over the whole range of volume fractions of liquid in several regular geometries. The longitudinal model is used to simulate flow in square arrays of circular and square ducts, and both models are used to simulate flow in square and hexagonal arrays of circular cylinders and square arrays of square cylinders rotated by varying amounts. For each of the geometries, accurate empirical expressions for the Darcy permeability as a function of volume fraction solid are presented. Where applicable, model predictions of permeability are compared to existing analytical results.Subsequently, the models are used to simulate Stokes flow in random domains over a wide range of fractions liquid. The sequential random packing algorithm is used to generate 1,000 random packings of circular cylinders at each of 14 fractions of liquid, and longitudinal and transverse flow simulations are performed for each geometry. Histograms and summary statistics are computed for the permeability for each fraction liquid, and empirical expressions for mean permeability as a function of fraction liquid are given. The autocorrelation structure of the geometry and of the fluid velocity is analyzed, and an analysis of the scaling of longitudinal permeability variance is presented. In transverse flow at high packing densities, it is found that lightning-like patterns emerge in the fluid velocity. It is also found that the details of flows in such geometries are strongly sensitive to the placement of individual solid obstacles.
Type:
text; Electronic Dissertation
Keywords:
porous media; permeability; Stokes flow; creeping flow; Darcy's Law; computational fluid dynamics
Degree Name:
PhD
Degree Level:
doctoral
Degree Program:
Materials Science & Engineering; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Poirier, David R.
Committee Chair:
Poirier, David R.

Full metadata record

DC FieldValue Language
dc.language.isoENen_US
dc.titleImage-Based Numerical Simulation of Stokes Flow in Porous Mediaen_US
dc.creatorErdmann, Robert Geralden_US
dc.contributor.authorErdmann, Robert Geralden_US
dc.date.issued2006en_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.abstractNumerical models for the simulation of longitudinal and transverse Stokes flow in cylindrical periodic porous media are presented. The models, which are based on a finite-volume formulation in primitive variables, utilize digital image representations of the geometries to simulate, making them particularly well-suited for the rapid automated analysis of creeping flow in porous media with complex morphologies. Complete details of the model formulations are given, including extensive treatment of the pressure boundary conditions at the solid-liquid interface needed to guarantee convergence with all possible geometries. The convergence behavior of both models is tested, and the models are shown to be second-order accurate.The models are used to simulate flow over the whole range of volume fractions of liquid in several regular geometries. The longitudinal model is used to simulate flow in square arrays of circular and square ducts, and both models are used to simulate flow in square and hexagonal arrays of circular cylinders and square arrays of square cylinders rotated by varying amounts. For each of the geometries, accurate empirical expressions for the Darcy permeability as a function of volume fraction solid are presented. Where applicable, model predictions of permeability are compared to existing analytical results.Subsequently, the models are used to simulate Stokes flow in random domains over a wide range of fractions liquid. The sequential random packing algorithm is used to generate 1,000 random packings of circular cylinders at each of 14 fractions of liquid, and longitudinal and transverse flow simulations are performed for each geometry. Histograms and summary statistics are computed for the permeability for each fraction liquid, and empirical expressions for mean permeability as a function of fraction liquid are given. The autocorrelation structure of the geometry and of the fluid velocity is analyzed, and an analysis of the scaling of longitudinal permeability variance is presented. In transverse flow at high packing densities, it is found that lightning-like patterns emerge in the fluid velocity. It is also found that the details of flows in such geometries are strongly sensitive to the placement of individual solid obstacles.en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.subjectporous mediaen_US
dc.subjectpermeabilityen_US
dc.subjectStokes flowen_US
dc.subjectcreeping flowen_US
dc.subjectDarcy's Lawen_US
dc.subjectcomputational fluid dynamicsen_US
thesis.degree.namePhDen_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineMaterials Science & Engineeringen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorPoirier, David R.en_US
dc.contributor.chairPoirier, David R.en_US
dc.contributor.committeememberHeinrich, Juan C.en_US
dc.contributor.committeememberDavenport, William G.en_US
dc.contributor.committeememberNikravesh, Parviz E.en_US
dc.identifier.proquest1495en_US
dc.identifier.oclc137355822en_US
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