Darcy's law for flow in a periodic thin porous medium confined between two parallel plates

Fabricius, John (author): Luleå tekniska universitet,Matematiska vetenskaper

Hellström, Gunnar (author): Luleå tekniska universitet,Strömningslära och experimentell mekanik

Lundström, Staffan (author): Luleå tekniska universitet,Strömningslära och experimentell mekanik

Miroshnikova, Elena (author): Luleå tekniska universitet,Matematiska vetenskaper

(creator_code:org_t)

2016-05-12
2016
English.
In: Transport in Porous Media. - : Springer Science and Business Media LLC. - 0169-3913 .- 1573-1634. ; 115:3, s. 473-493

Related links:: https://ltu.diva-por... (primary) (Raw object); show more...; https://link.springe...; https://urn.kb.se/re...; https://doi.org/10.1...; show less...

Abstract Subject headings

We study stationary incompressible fluid flow in a thin periodic porous medium. The medium under consideration is a bounded perforated 3D-domain confined between two parallel plates. The distance between the plates is \(\delta \), and the perforation consists of \(\varepsilon \)-periodically distributed solid cylinders which connect the plates in perpendicular direction. Both parameters \(\varepsilon \), \(\delta \) are assumed to be small in comparison with the planar dimensions of the plates. By constructing asymptotic expansions, three cases are analysed: (1) \(\varepsilon \ll \delta \), (2) \(\delta /\varepsilon \sim \text {constant}\) and (3) \(\varepsilon \gg \delta \). For each case, a permeability tensor is obtained by solving local problems. In the intermediate case, the cell problems are 3D, whereas they are 2D in the other cases, which is a considerable simplification. The dimensional reduction can be used for a wide range of \(\varepsilon \) and \(\delta \) with maintained accuracy. This is illustrated by some numerical examples.

TEKNIK OCH TEKNOLOGIER -- Maskinteknik -- Strömningsmekanik och akustik (hsv//swe)
ENGINEERING AND TECHNOLOGY -- Mechanical Engineering -- Fluid Mechanics and Acoustics (hsv//eng)
NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)

By the author/editor: Fabricius, John; Hellström, Gunna ...; Lundström, Staff ...; Miroshnikova, El ...; Wall, Peter

About the subject

ENGINEERING AND TECHNOLOGY: ENGINEERING AND ...; and Mechanical Engin ...; and Fluid Mechanics ...

NATURAL SCIENCES: NATURAL SCIENCES; and Mathematics; and Mathematical Ana ...

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