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Velocity Distribution of Non-Darcy Flow in a Porous Medium

Published online by Cambridge University Press:  05 May 2011

J. M. Leu ,
H. C. Chan ,
Lih-Fu Tu ,
Yafei Jia  and
S. Y. Wang
J. M. Leu*
Affiliation:
Department of Hydraulic and Ocean Engineering, Cheng-Kung University, Tainan, Taiwan 70101, R.O.C.
H. C. Chan*
Affiliation:
Department of Hydraulic and Ocean Engineering, Cheng-Kung University, Tainan, Taiwan 70101, R.O.C.
Lih-Fu Tu*
Affiliation:
Department of Hydraulic and Ocean Engineering, Cheng-Kung University, Tainan, Taiwan 70101, R.O.C.
Yafei Jia*
Affiliation:
National Center for Computational Hydroscience and Engineering, The University of Mississippi, Carrier Hall 102, University, MS 38677, USA.
S. Y. Wang*
Affiliation:
National Center for Computational Hydroscience and Engineering, The University of Mississippi, Carrier Hall 102, University, MS 38677, USA.
*
* Associate Professor
** Post-Doctoral Researcher
*** Ph.D. candidate
**** Professor
**** Professor
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Abstract

This study theoretically and experimentally investigates the velocity distributions of the interface boundary layer region in a porous medium. By combining a quadratic non-Darcy law and a practical eddy viscosity model, an analytical solution is derived and presented. Three additional parameters, i.e., the depth of the interface boundary layer region, the slip velocity, and proportionality constant, are contained in the analytical solution. The measured experimental data show the depth of the interface boundary layer region only depends on the characteristics of the porous medium rather than the relative flow depth, bed slop, or Reynolds number. The values of the slip velocity are found to increase with increasing relative mean clear fluid velocities. The proportionality constant plays an important role in modeling the penetration of turbulence and the associated momentum transfer. The measured experimental velocity distribution is used to evaluate the accuracy of the analytical predicted profile. The analytical results obtained in this study are in agreement with the measured experimental results.

Keywords

Porous mediumNon-Darcy flowInterface regionForchheimer equation.
Type
Articles
Information
Journal of Mechanics , Volume 25 , Issue 1 , March 2009 , pp. 49 - 58
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2009

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