Publication de 4 numéros par an
ISSN Imprimer: 2151-4798
ISSN En ligne: 2151-562X
Indexed in
ON THE BRINKMAN EQUATION AND THE CONCEPT OF VISCOUS DISSIPATION IN POROUS MEDIA
RÉSUMÉ
The concept of viscous dissipation in porous media is discussed. It is known that performing upscaling of the momentum equations of fluid continuum moving within porous material results in a set of unclosed system of equations. To get closure to this set of equations can prove very difficult, especially in nonperiodic porous media. Moreover, a set of length scale constraints needs to be satisfied for these equations to be adopted correctly. In this work, the upscaled momentum equation is used to derive an expression for the rate of change of kinetic energy. By slightly relaxing length scale constraints, new term appears that involve the dot product of the porosity gradient vector and velocity gradient tensor. Terms contributing to the conversion of kinetic energy into heat energy are separated and are collected in a single function named the dissipation function. This function is, however, different from that proposed in the literature and hence a resolution to this apparent controversy is needed. It is believed that any attempt to provide an expression for viscous dissipation in porous media should be based on the use of the upscaled equations and not on the semiempirical relationships that involve ad hoc terms.
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