Two Types of Nonlinear Pressure-Drop Versus Flow-Rate Relation Observed for Saturated Porous Media

[+] Author and Article Information
J. L. Lage

Mechanical Engineering Department, Southern Methodist University, Dallas, TX 75275-0337

B. V. Antohe

MicroFab Technologies Inc., Plano, TX 75074

D. A. Nield

Department of Engineering Science, University of Auckland, Private Bag 92019, Auckland, NZ

J. Fluids Eng 119(3), 700-706 (Sep 01, 1997) (7 pages) doi:10.1115/1.2819301 History: Received April 17, 1996; Revised March 31, 1997; Online December 04, 2007


Previous reports of experiments performed with water (Fund et at., 1987 and Kececioglu and Jiang, 1994) indicated that beyond the Forchheimer regime the rate of change of the hydrostatic pressure gradient along a porous medium suddenly decreases. This abnormal behavior has been termed “transition to turbulence in a porous medium.” We investigate the relationship between the hydrostatic pressure gradient of a fluid (air) through a porous medium and the average seepage fluid velocity. Our experimental results, reported here, indicate an increase in the hydrostatic pressure rate beyond a certain transition speed, not a decrease. Physical arguments based on a consideration of internal versus external incompressible viscous flow are used to justify this distinct behavior, a consequence of the competition between a form dominated transition and a viscous dominated transition. We establish a criterion for the viscous dominated transition from consideration of the results of three porous media with distinct hydraulic characteristics. A theoretical analysis based on the semivariance model validation principle indicates that the pressure gradient versus fluid speed relation indeed departs from the quadratic Forchheimer-extended Darcy flow model, and can be correlated by a cubic function of fluid speed for the velocity range of our experiments.

Copyright © 1997 by The American Society of Mechanical Engineers
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