A Macroscopic Turbulence Model for Flow in a Porous Medium

[+] Author and Article Information
A. Nakayama, F. Kuwahara

Department of Mechanical Engineering, Shizuoka University, 3-5-1 Johoku, Hamamatsu, 432 Japan

J. Fluids Eng 121(2), 427-433 (Jun 01, 1999) (7 pages) doi:10.1115/1.2822227 History: Received April 29, 1998; Revised March 12, 1999; Online January 22, 2008


A complete set of macroscopic two-equation turbulence model equations has been established for analyzing turbulent flow and heat transfer within porous media. The volume-averaged transport equations for the mass, momentum, energy, turbulence kinetic energy and its dissipation rate were derived by spatially averaging the Reynolds-averaged set of the governing equations. The additional terms representing production and dissipation of turbulence kinetic energy are modeled introducing two unknown model constants, which are determined from a numerical experiment using a spatially periodic array. In order to investigate the validity of the present macroscopic turbulence model, a macroscopically unidirectional turbulent flow through an infinite array of square rods is considered from both micro- and macroscopic-views. It has been found that the stream-wise variations of the turbulence kinetic energy and its dissipation rate predicted by the present macroscopic turbulence model agree well with those obtained from a large scale microscopic computation over an entire field of saturated porous medium.

Copyright © 1999 by The American Society of Mechanical Engineers
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