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.

[1]  C. L. Tien,et al.  Boundary and inertia effects on flow and heat transfer in porous media , 1981 .

[2]  Marcelo J.S. de Lemos,et al.  Recent Mathematical Models for Turbulent Flow in Saturated Rigid Porous Media , 2001 .

[3]  SIMULATION OF TURBULENT FLOW IN POROUS MEDIA USING A SPATIALLY PERIODIC ARRAY AND A LOW RE TWO-EQUATION CLOSURE , 2001 .

[4]  I. F. Macdonald,et al.  Flow through Porous Media-the Ergun Equation Revisited , 1979 .

[5]  Marcos H. J. Pedras,et al.  Simulation of Turbulent Flow Through Hybrid Porous Medium: Clear Fluid Domains , 2000, Heat Transfer: Volume 5.

[6]  A. Nakayama,et al.  Numerical Modeling of Non-Darcy Convective Flow in a Porous Medium , 1998 .

[7]  I. Catton,et al.  Porous media transport descriptions - non-local, linear and non-linear against effective thermal/fluid properties , 1998 .

[8]  Marcelo J.S. de Lemos,et al.  Analysis of convective heat transfer for turbulent flow in saturated porous media , 2000 .

[9]  靖尚 長野,et al.  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 , 1992 .

[10]  Marcelo J.S. de Lemos,et al.  Macroscopic turbulence modeling for incompressible flow through undeformable porous media , 2001 .

[11]  Eugene S. Takle,et al.  Boundary-layer flow and turbulence near porous obstacles , 1995 .

[12]  J. L. Lage,et al.  A general two-equation macroscopic turbulence model for incompressible flow in porous media , 1997 .

[13]  Marcelo J.S. de Lemos,et al.  On the definition of turbulent kinetic energy for flow in porous media , 2000 .

[14]  J. L. Lage,et al.  A modified form of the κ–ε model for turbulent flows of an incompressible fluid in porous media , 2000 .

[15]  Marcelo J.S. de Lemos,et al.  On the Mathematical Description and Simulation of Turbulent Flow in a Porous Medium Formed by an Array of Elliptic Rods , 2001 .

[16]  J. Ward,et al.  Turbulent Flow in Porous Media , 1964 .

[17]  H. Brinkman.  A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles , 1949 .

[18]  A. Nakayama,et al.  Numerical Modeling of Turbulent Flow in Porous Media Using a Spatially Periodic Array , 1998 .

[19]  J. L. Lage.  THE FUNDAMENTAL THEORY OF FLOW THROUGH PERMEABLE MEDIA FROM DARCY TO TURBULENCE , 1998 .

[20]  Akira Nakayama,et al.  A Macroscopic Turbulence Model for Flow in a Porous Medium , 1999 .

[21]  I. Kececioglu,et al.  Flow Through Porous Media of Packed Spheres Saturated With Water , 1994 .

[22]  Shirley Dex,et al.  JR 旅客販売総合システム（マルス）における運用及び管理について , 1991 .

[23]  I. Catton,et al.  A Two-Temperature Model for Turbulent Flow and Heat Transfer in a Porous Layer , 1995 .

[24]  Kevin Barraclough,et al.  I and i , 2001, BMJ : British Medical Journal.

[25]  Y. Takatsu,et al.  Turbulence model for flow through porous media , 1996 .

[26]  P. Cheng,et al.  Thermal dispersion in a porous medium , 1990 .

[27]  B. Launder,et al.  THE NUMERICAL COMPUTATION OF TURBULENT FLOW , 1974 .

[28]  R. Mahajan,et al.  Thermophysical properties of high porosity metal foams , 2002 .

[29]  Stanley Middleman,et al.  Flow of Viscoelastic Fluids through Porous Media , 1967 .

[30]  M. D. de Lemos,et al.  Heat Transfer in Suddenly Expanded Flow in a Channel With Porous Inserts , 2000, Heat Transfer: Volume 5.

[31]  J. Bear.  Dynamics of Fluids in Porous Media , 1975 .

[32]  Stephen Whitaker,et al.  ADVANCES IN THEORY OF FLUID MOTION IN POROUS MEDIA , 1969 .