The influence of Reynolds number upon the apparent permeability of spatially periodic arrays of cylinders

D. A. Edwards*, M. Shapiro, P. Bar-Yoseph, M. Shapira

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

120 Scopus citations

Abstract

Flow fields within spatially periodic arrays of cylinders arranged in square and hexagonal lattices are calculated, with microscale Reynolds number ranging between zero and 200, employing a finite element numerical scheme. The terminology of an "apparent permeability" is introduced to establish a relationship existing between mean velocity and macroscopic pressure gradient characterized by a finite Reynolds number flow. In contrast with the low Reynolds number "true" permeability, the apparent permeability is shown here to generally depend upon the direction of the applied pressure gradient, owing to nonlinearities existing within the local fluid motion. The orientation-dependent permeabilities of both square and hexagonal monodisperse arrays are observed to diminish with increasing Reynolds number. Similar behavior is also observed for a bidisperse square array, though the apparent permeability of the latter is shown less sensitive to Darcy velocity orientation at large Reynolds numbers in comparison to the corresponding monodisperse square array, for all cylinder concentrations examined.

Original languageEnglish
Pages (from-to)45-55
Number of pages11
JournalPhysics of fluids. A, Fluid dynamics
Volume2
Issue number1
DOIs
StatePublished - 1990
Externally publishedYes

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