Recent Mathematical Models for Turbulent Flow in Saturated Rigid Porous Media

Abstract

Turbulence models proposed for flow through permeable structures depend on the order of application of time and volume average operators. Two developed methodologies, following the two orders of integration, lead to different governing equations for the statistical quantities. The flow turbulence kinetic energy resulting in each case is different. This paper reviews recently published mathematical models developed for such flows. The concept of double decomposition is discussed and models are classified in terms of the order of application of time and volume averaging operators, among other peculiarities. A total of four major classes of models are identified and a general discussion on their main characteristics is carried out. Proposed equations for turbulence kinetic energy following time-space and space-time integration sequences are derived and similar terms are compared. Treatment of the drag coefficient and closure of the interfacial surface integrals are discussed.

From steady to unsteady laminar flow in model porous structures: an investigation of the first Hopf bifurcation

“…For turbulent flow in porous media, many models have been reported [27] and turbulence models, derived 45 from the macroscopic transport equations by time-averaging, have revealed to be quite inaccurate [28]. As an alternative, models where the microscopic transport equations are first time averaged and then up-scaled have been proposed [29,30].…”

Measurements of Transitional and Turbulent Flow in a Randomly Packed Bed of Spheres with Particle Image Velocimetry

“…This will give empirical correlations that can be used to estimate the behavior of porous media and to design special industrial cases such as packed bed reactors (Andrigo et al 1999;Eigenberger 1992). The mathematical set of equations that can be used to provide comprehensive understanding of physical phenomena in a porous bed can also be derived from the Reynolds-averaged Navier-Stokes (RANS) equations according to de Pedras and Lemos (2001):…”

Fundamentals of the double - decomposition concept for turbulent transport in permeable media

“…[17]. A general classification of all proposed models for turbulent flow and heat transfer in porous media has been recently published [39]. Here, a systematic review of this new concept is presented.…”