Mass Transport Modeling for Turbulent Flow in Saturated Porous Media

This paper presents derivations of mass transport equations for turbulent flow in permeable structures. Equations are developed following two distinct procedures. The first method considers time averaging of the local instantaneous mass transport equation before the volume average operator is applied. The second methodology employs both averaging operators but in a reverse order. This work is intended to demonstrate that both approaches lead to equivalent equations when one takes into account both time fluctuations and spatial deviations of velocity and mass fraction. A modeled form for the final transport equation is presented where turbulent transfer is based on a macroscopic version of the k-ε model.