A New Constitutive Relation for Describing the Flow through Porous Media with Unsaturated–Saturated Transition

Author:

Martins-Costa Maria Laura1ORCID,Cunha da Silva Daniel1,Cunha da Silva Michele2,Martins Saldanha da Gama Rogério2

Affiliation:

1. Laboratory of Theoretical and Applied Mechanics (LMTA) Mechanical Engineering Graduate Program (TEM-PGMEC), Universidade Federal Fluminense, Rua Passo da Pátria, No. 156, 24210-240 Niterói, RJ, Brazil

2. Mechanical Engineering Graduate Program (FEN), Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier, No. 524, 20550-013 Rio de Janeiro, Brazil

Abstract

The present work proposes an adequate constitutive relation to treat the process of filling with a fluid porous medium. This relation assures the problem to remain hyperbolic when the porous medium is saturated by the fluid. When the fluid fraction reaches porosity, the proposed constitutive relation increases the porous matrix resistance to more fluid inlet due to an important feature: it is a continuous and differentiable function with first derivative being also an increasing function. This allows assuring that the fluid fraction may exceed the porosity only by a very small value, making the constitutive relation realistic. Some examples compare this new constitutive relation with previous ones, highlighting its advantages.

Funder

Conselho Nacional de Desenvolvimento Científico e Tecnológico

Publisher

Hindawi Limited

Subject

General Engineering,General Mathematics

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