Derivation of the Forchheimer law via homogenization

Citation
Zx. Chen et al., Derivation of the Forchheimer law via homogenization, TRANS POR M, 44(2), 2001, pp. 325-335
Citations number
23
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Chemical Engineering
Journal title
TRANSPORT IN POROUS MEDIA
ISSN journal
0169-3913 → ACNP
Volume
44
Issue
2
Year of publication
2001
Pages
325 - 335
Database
ISI
SICI code
0169-3913(200108)44:2<325:DOTFLV>2.0.ZU;2-4
Abstract
In this paper we derive the Forchheimer law via the theory of homogenizatio n. In particular, we study the nonlinear correction to Darcy's law due to i nertial effects on the flow of a Newtonian fluid in rigid porous media. A g eneral formula for this correction term is derived directly from the Navier -Stokes equation via homogenization. Unlike other studies based on the same approach that concluded for the nonlinear correction to be cubic in veloci ty for isotropic media, the present work shows that the nonlinear correctio n is quadratic. An example is constructed to illustrate our theory. In this example, the analytic solution to the Navier-Stokes equation is obtained a nd is utilized to show the validity of the quadratic correction. Both incom pressible and compressible fluids are considered.