8 - Modeling turbulence in porous media

Abstract

This chapter reviews four available methodologies for developing macroscopic turbulence models for incompressible single-phase flow in rigid, fully saturated porous media. The first method, known as the Antohe-Lage (A-L) method, starts with the closed volume-averaged equations, which are then averaged in time to produce the turbulence equations. The second method known as the Nakayama-Kuwahara (N-K) makes use of the closed time-averaged and volume-averaging equations for deriving the turbulence equation. These two methodologies lead to distinct sets of turbulence equations because of the different averaging order, that is, space-time and time-space, respectively. The third method, based on double-decomposition, is called the Pedras-de Lemos (P-dL) method. In this method, the momentum equation is closed by using the Hazen-Dupuit-Darcy model for the total drag effect only after the space-time averaging (or time-space averaging) is performed. Although for the P-dL method the averaging order is immaterial when deriving the turbulence momentum equation, the difference between space-time and time-space averaging remains in the k-e equations. The detailed experimental model validation is tremendously challenging because of the need to obtain time-averaged and volume averaged quantities simultaneously in order to compare experimental and analytical (numerical) results directly. The Travkin-Catton (T-C) morphology method is discussed briefly.