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Forchheimer law derived by homogenization of gas flow in turbomachines

Authors
Journal
Journal of Computational and Applied Mathematics
0377-0427
Publisher
Elsevier
Publication Date
Volume
215
Issue
2
Identifiers
DOI: 10.1016/j.cam.2006.03.049
Keywords
  • Homogenization
  • Porous Media
  • Mixed Stabilized Finite Elements

Abstract

Abstract A general formulation of the homogenization problem of compressible fluid flow through a periodic porous material in turbomachines is presented here. This formulation is able to derive a Forchheimer law with a mean velocity dependent permeability as equivalent macroscopic behavior. To specify this permeability, additional flow problems are defined on the unit cell and solved by a mixed stabilized finite element discretization. The application of the Galerkin least-square (GLS) method requires the introduction of two stabilization terms with appropriate parameters. The mixed finite element discretization of these unit cell problems is finally outlined.

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