A Macroscopic Turbulence Model for Flow in a Porous Medium

Abstract

A complete set of macroscopic two-equation turbulence model equations has been established for analyzing turbulent flow and heat transfer within porous media. The volume-averaged transport equations for the mass, momentum, energy, turbulence kinetic energy and its dissipation rate were derived by spatially averaging the Reynolds-averaged set of the governing equations. The additional terms representing production and dissipation of turbulence kinetic energy are modeled introducing two unknown model constants, which are determined from a numerical experiment using a spatially periodic array. In order to investigate the validity of the present macroscopic turbulence model, a macroscopically unidirectional turbulent flow through an infinite array of square rods is considered from both micro- and macroscopic-views. It has been found that the stream-wise variations of the turbulence kinetic energy and its dissipation rate predicted by the present macroscopic turbulence model agree well with those obtained from a large scale microscopic computation over an entire field of saturated porous medium.