Marcelo J. S. de Lemos

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

Turbulent flow in a channel occupied by a porous layer considering the stress jump at the interface

For hybrid media, involving both a porous structure and a clear flow region, difficulties arise due to the proper mathematical treatment given at the interface. The literature proposes a jump condition in which shear stresses on both sides of the interface are not of the same value. This paper presents numerical solutions for such hybrid medium, considering here a channel partially filled with a porous layer through which fluid flows in turbulent regime. One unique set of transport equations is applied to both regions. Effects of Reynolds number, porosity, permeability and jump coefficient on mean and turbulence fields are investigated. Results indicate that depending on the value of the stress jump parameters, a substantially different structure for the turbulent field is obtained.

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#

Analysis of convective heat transfer for turbulent flow in saturated porous media

Abstract The literature documents two procedures for modeling turbulent heat transport in incompressible flows through homogeneous rigid porous media. The first method considers time averaging of the energy equation before the volume average operator is applied. The second methodology also employs both averaging operators, but in the reverse order. Resulting equations in both cases are different, leading to controversies and interesting discussions in the literature. 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 temperature.

A Correlation for Interfacial Heat Transfer Coefficient for Turbulent Flow Over an Array of Square Rods

Interfacial heat transfer coefficients in a porous medium modeled as a staggered array of square rods are numerically determined. High and low Reynolds k-e turbulence models are used in conjunction of a two-energy equation model, which in chides distinct transport equations for the fluid and the solid phases. The literature has documented proposals for macroscopic energy equation modeling for porous media considering the local thermal equilibrium hypothesis and laminar flow. In addition, two-energy equation models have been proposed for conduction and laminar convection in packed beds. With the aim of contributing to new developments, this work treats turbulent heat transport modeling in porous media under the local thermal nonequilibrium assumption. Macroscopic time-average equations for continuity, momentum, and energy are presented based on the recently established double decomposition concept (spatial deviations and temporal fluctuations of flow properties). The numerical technique employed for discretizing the governing equations is the control volume method. Turbulent flow results for the macroscopic heat transfer coefficient, between the fluid and solid phase in a periodic cell, are presented.

COMPUTATION OF TURBULENT FLOW IN POROUS MEDIA USING A LOW-REYNOLDS K -ε MODELAND AN INFINITE ARRAY OF TRANSVERSALLY DISPLACED ELLIPTIC RODS

Through the volumetric averaging of the microscopic transport equations for the turbulent kinetic energy, k , and its dissipation rate, l , a macroscopic model is proposed for flow in porous media. As an outcome of the volume-averaging process, additional terms appeared in the equations for k and l . These terms are adjusted assuming the porous structure to be modeled as an infinity array of transversally displaced elliptic rods. This adjustment is obtained by solving the microscopic flow governing equations numerically, using a low-Reynolds formulation, in the periodic cell composing the infinite medium. Different porosity and aspect ratios are investigated. The adjusted model is compared with similar results found in the literature. A general view of the effect of the medium morphology on model assumptions is obtained by comparing results for elliptic, cylindrical, and square rods.

NUMERICAL ANALYSIS OF THE STRESS JUMP INTERFACE CONDITION FOR LAMINAR FLOW OVER A POROUS LAYER

A number of natural and engineering systems can be characterized by some sort of porous structure through which a working fluid permeates. Boundary layers over tropical forests and spreading of chemical contaminants through underground water reservoirs are examples of important environmental flows that can benefit form appropriate mathematical treatment. For hybrid media, involving both a porous structure and a clear flow region, difficulties arise due to the proper mathematical treatment given at the interface. The literature proposes a jump condition in which stresses at both sides of the interface are not of the same value. The objective of this article is to present a numerical implementation for solving such a hybrid medium, considering here a channel partially filled with a porous layer through which fluid flows in laminar regime. One unique set of transport equations is applied to both regions. Numerical results are compared with available analytical solutions in the literature for two cases, namely, with and without the nonlinear Forchheimer term. Results are presented for the mean velocity across both the porous structure and the clear region. The influence of medium properties, such as porosity and permeability, is discussed.

Flow and heat transfer in a parallel-plate channel with porous and solid baffles

ABSTRACT Simulations are presented for laminar flow in a channel containing baffles made with solid (impermeable) and porous materials. The equations of mass continuity, momentum and energy are written for an elementary representative volume, yielding a set of equations valid for the entire computational domain. These equations are discretized using the control-volume method and the resulting system of algebraic equations is relaxed with the SIMPLE method. The numerical results for the friction factor f and for the Nusselt number Nu are compared with available data, indicating that results herein differ by less than 5% in relation to published results. Further simulations comparing the effectiveness of the porous material used show that no advantages are obtained when using low-porosity baffles in the laminar flow regime investigated here.