http://lcft.mec.ita.br/articles/JA_Pedras&deLemos_IJHMT.44(6).1081.2001.pdf

Macroscopic turbulence modeling for incompressible flow through undeformable porous media

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.

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

http://lcft.mec.ita.br/articles/ja_pedras&delemos_jfe.123(4).941.2001.pdf

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

Thermal dispersion in porous media as a function of the solid-fluid conductivity ratio

Four available methodologies for developing macroscopic turbulence models for incompressible single-phase flow in rigid, fully saturated porous media are reviewed. The first method, known as the Antohe–age (A–) method, starts with the closed volume-averaged equations, which are then averaged in time to produce the turbulence equations. The second, known as the Nakayama–uwahara (N–) method, makes use, first, of the closed time-averaged equations, and then proceeds with volume-averaging for deriving the turbulence equations. These two methodologies lead, in general, to distinct sets of turbulence equations because of the different averaging order, i.e., space–ime and time–pace, respectively. A third, and probably the most consistent method, based on double-decomposition, is the Pedras–e Lemos (P–L) method. In this method, the momentum equation is closed by using the Hazen–upuit–Darcy model for the total drag effect only after the space-time averaging (or time-space averaging) is performed. Although for the P–dL method the averaging order is immaterial when deriving the turbulence momentum equation, the difference between space-time and time-space averaging remains in the k–e equations. Unfortunately, detailed experimental model validation, which remains to be seen, is tremendously challenging because of the need to obtain time-averaged and volume-averaged quantities simultaneously in order to compare experimental and analytical (numerical) results directly. A fourth method, the Travkin–Catton (T–C) morphology method, is discussed only briefly because it follows the N–K method (time-space integrating order) and no closure to the final equations is yet available.

Modeling Turbulence in Porous Media

We propose a new turbulence model which is modified from the low-Reynolds-number k-e model developed by Nagano and Tagawa. The main improvement is made by the introduction of the Kolmogorov velocity scale, ue≡(νe)1/4, instead of the friction velocity uτ, to account for the nearwall and low-Reynolds-number effects. We have also reevaluated the model constants in the transport equations of the turbulent energy and its dissipation rate. With these modifications, it is shown that the present model predicts quite successfully a diffuser flow with a strong adverse pressure gradient and the separating and reattaching flows downstream of a backward-facing step.

https://www.jstage.jst.go.jp/article/kikaib1979/58/554/58_554_3003/_pdf

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Papers

はく離・再付着を伴う乱流場への適用を考慮したk-εモデル

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Papers

はく離・再付着を伴う乱流場への適用を考慮したk-εモデル

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