On the definition of turbulent kinetic energy for flow in porous media

Abstract

In the literature, there are two distinct approaches for developing turbulent models for flow in a porous medium. The first one starts with the macroscopic equations using the extended Darcy-Forchheimer model. The second method considers first the microscopic balance equations. In both cases, time and volume averaging operators are applied in a different order. The turbulence kinetic energy equation resulting from application of the two averaging operators, following both orders of integration, are different. In this work, a new double-decomposition (time and volume) methodology is suggested and the differences between those two mathematical treatments are highlighted. (c) 2000 Elsevier Science Ltd.In the literature, there are two distinct approaches for developing turbulent models for flow in a porous medium. The first one starts with the macroscopic equations using the extended Darcy-Forchheimer model. The second method considers first the microscopic balance equations. In both cases, time and volume averaging operators are applied in a different order. The turbulence kinetic energy equation resulting from application of the two averaging operators, following both orders of integration, are different. In this work, a new double-decomposition (time and volume) methodology is suggested and the differences between those two mathematical treatments are highlighted.