On volume and time averaging of transport equations for turbulent flow in porous media

Abstract

In the literature, turbulence models proposed for porous media follow two contradictory approaches. In the first one, governing equations for the mean and turbulent fields are obtained by time-averaging the volume-averaged equations. In the second method, volume averaging is applied to the time-averaged equations. The two different approaches lead to different governing equations and, ultimately, to contradicting overall conclusions. In this work, a new double-decomposition (time and volume) methodology is suggested and the differences between those two mathematical treatments are highlighted.