M. H. J. Pedras

Macroscopic turbulence modeling for incompressible flow through undeformable porous media

The literature presents two different methodologies 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 makes use, first, of the Reynolds-averaged equations. These two methodologies lead to distinct set of equations for the k–e model. The present work details a mathematical model for turbulent flow in porous media following the second path, or say, space-integrating the equations for turbulent flow in clear fluid. In order to account for the porous structure, an additional term is included in the sources for k and e. A methodology is followed for determining the additional constant proposed. The equations for the microscopic flow were numerically solved inside a periodic elementary cell. The porous structure was approximated by an infinite array of circular rods. The method SIMPLE and a non-orthogonal boundary-fitted coordinate system were employed. Integrated parameters where compared to the existing data for fully developed homogeneous flow through porous media. Preliminary results are in agreement with numerical experiments presented in the literature.

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.

Recent Mathematical Models for Turbulent Flow in Saturated Rigid Porous Media

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

On the Mathematical Description and Simulation of Turbulent Flow in a Porous Medium Formed by an Array of Elliptic Rods

Many engineering and environmental system analyses can benefit from appropriate modeling of turbulent flow in porous media. Through the volumetric averaging of the microscopic transport equations for the turbulent kinetic energy, k, and its dissipation rate,«, a macroscopic model was proposed for such media (IJHMT, 44(6), 1081-1093, 2001). In that initial work, the medium was simulated as an infinite array of cylindrical rods. As an outcome of the volume averaging process, additional terms appeared in the equations for k and «. These terms were here adjusted assuming now the porous structure to be modeled as an array of elliptic rods instead. Such an adjustment was obtained by numerically solving the microscopic flow governing equations, using a low Reynolds formulation, in the periodic cell composing the medium. Different porosity and Reynolds numbers were investigated. The fine turbulence structure of the flow was computed and integral parameters were presented. The adjusted model constant was compared to similar results for square and cylindrical rods. It is expected that the contribution herein provide some insight to modelers devoted to the analysis of engineering and a environmental systems characterized by a porous structure saturated by a fluid flowing in turbulent regime. @DOI: 10.1115/1.1413244#

SIMULATION OF TURBULENT FLOW IN A POROUS MEDIUM FORMED BY AN INFINITE ARRAY OF ELLIPTIC RODS

Many engineering and environmental system analyses can benefit from appropriate modeling of turbulent flow in porous media. Through the volumetric averaging of the microscopic transport equations for the turbulent kinetic energy, k, and its dissipation rate, epsilon, a macroscopic model was proposed for such media (IJHMT, 44(6), 1081-1093, 2001). In that initial work, the medium was simulated as an infinite array of cylindrical rods. As an outcome of the volume averaging process, additional terms appeared in the equations for k and epsilon. These terms were here adjusted assuming now the porous structure to be modeled as an array of elliptic rods instead. Such an adjustment was obtained by numerically solving the microscopic flow governing equations, using a low Reynolds formulation, in the periodic cell composing the medium. Different porosity and Reynolds numbers were investigated. The fine turbulence structure of the flow was computed and integral parameters were presented. The adjusted model constant was compared to similar results for square and cylindrical rods. It is expected that the contribution herein provide some insight to modelers devoted to the analysis of engineering and environmental systems characterized by a porous structure saturated by a fluid flowing in turbulent regime.