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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*
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.

Type
Articles
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2009

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References

1.Zippe, H. J. and Graf, W. H., “Turbulent Boundary-Layer Flow Over Permeable and Nonpermeable Rough Surfaces,” J. Hydraul. Res., 21, pp. 5165 (1983).CrossRefGoogle Scholar
2.Mendoza, C. and Zhou, D., “Effect of Porous Bed on Turbulent Stream Flow Above Bed,” J. Hydraul. Engrg., 118, pp. 12221240 (1992).CrossRefGoogle Scholar
3.Cheng, X. and Chiew, Y. M., “Modified Logarithmic Law for Velocity Distribution Subjected to Upward Seepage,” J. Env. Engrg., 124, pp. 12351241 (1998).Google Scholar
4.Cheng, X. and Chiew, Y. M., “Velocity Distribution of Turbulent Open-Channel Flow with Bed Suction,” J. Env. Engrg., 130, pp. 140148 (2004).Google Scholar
5.Prinos, P., Sofialidis, D. and Keramaris, E., “Turbulent Flow Over and Within a Porous Bed,” J. of Hydraul. Engrg., 129, pp. 720733 (2003).CrossRefGoogle Scholar
6.Chan, H. C., Leu, J. M., Lai, C. J. and Jia, Yafei, “Turbulent Flow Over a Channel with Fluid-Saturated Porous Bed,” J. Hydraul. Engrg., 133, pp. 610617 (2007).CrossRefGoogle Scholar
7.Shimizu, Y., Tsujimoto, T. and Nakagawa, H., “Experimental and Macroscopic Modeling of Flow in Highly Porous Medium Under Free-Surface Flow,” J. of Hydroscience and Hydraulic. Engrg., 8, pp. 6978 (1990).Google Scholar
8.Zhou, D. and Mendoza, C., “Flow Through Porous Bed of Turbulent Stream,” J. Engrg. Mech., 119, pp. 365383 (1993).CrossRefGoogle Scholar
9.Li, B. and Garga, V. K., “Theoretical Solution for Seepage Flow in Overtopped Rockfill,” J. Hydraul. Engrg., 124, pp. 213217 (1998).CrossRefGoogle Scholar
10.Nezu, I., “Turbulent Structure in Open-Channel Flows,” Ph.D. Dissertation, Dept. of Civil Engineering, Kyoto Univ., Japan (1977).Google Scholar
11.Liu, I. C., “Exact Solutions for a Fluid-Saturated Porous Medium with Heat and Mass Transfer,” Journal of Mechanics, 21, pp. 5762 (2005).CrossRefGoogle Scholar
12.Venkataraman, P. and Rama Mohan Rao, P., “Darcian, Transitional, and Turbulent Flow Through Porous Media,” J. Hydraul. Engrg., 124, pp. 840846 (1998).CrossRefGoogle Scholar
13.Li, B., Garga, V. K. and Davies, M. H., “Relationships for Non-Darcy Flow in Rockfill,” J. Hydraul. Engrg., 124, pp. 206212 (1998).CrossRefGoogle Scholar
14.Scheidegger, A. E., The Physics of Flow Through Porous Media, 3rd Ed., Univ. of Toronto Press, Toronto (1974).Google Scholar
15.Ergun, S., “Fluid Flow Through Packed Columns,” Chemical Engrg. Progress, 48, p. 89 (1952).Google Scholar
16.Ward, J. C., “Turbulent Flows in Porous Media,” J. Hydraul. Div., ASCE, 90, pp. 112 (1964).CrossRefGoogle Scholar
17.Ahmed, N. and Sunada, D. K., “Nonlinear Flow in Porous Media,” J. Hydraul. Div., ASCE, 95, pp. 18471857 (1969).CrossRefGoogle Scholar
18.Arbhabhirama, A. and Dinoy, A. A., “Friction Factor and Reynold's Number in Porous Media Flow,” J. Hydraul. Div., ASCE, 99, pp. 901911 (1973).CrossRefGoogle Scholar
19.McCorquodale, J. A., Hannoura, A. A. and Nasser, M. S., “Hydraulic Conductivity of Rockfill,” J. Hydraul. Res., Delft, The Netherlands, 16, pp. 123137 (1978).CrossRefGoogle Scholar
20.Stephenson, D., Rockfill in Hydraulic Engineering, Elsevier Scientific, Amsterdam, The Netherlands (1979).Google Scholar
21.Martins, R., “Turbulent Seepage Flow Through Rockfill Structures,” Water Power and Dam Construction, 40, pp. 4145 (1990).Google Scholar
22.Sidiropoulou, M. G., Moutsopoulos, K. N. and Tsihrintzis, V. A., “Determination of Forchheimer Equation Coefficients A and B,” Hydrol. Process., 21, pp. 534554 (2007).CrossRefGoogle Scholar
23.Vafai, K. and Tien, C. L., “Boundary and Inertial Effects on Flow and Heat Transfer in Porous Media,” Int. J. Heat Mass Transfer, 24, pp. 195203 (1981).CrossRefGoogle Scholar
24.Choi, C. Y. and Waller, P. M., “Momentum Transport Mechanism for Water Flow Over Porous Media,” J. Env. Engrg., 123, pp. 792799 (1997).CrossRefGoogle Scholar
25.Fu, W. S. and Chen, S. F., “A Numerical Study of Heat Transfer of a Porous Block with the Random Porosity Model in a Channel Flow,” Heat and Mass Transfer, 38, pp. 695704 (2002).CrossRefGoogle Scholar
26.Cheng, N. S., “Application of Ergun Equation to Computation of Critical Shear Velocity Subject to Seepage,” J. Irrig. Drain. Engrg., 129, pp. 278283 (2003).CrossRefGoogle Scholar
27.Michioku, K., Maeno, S., Furusawa, T. and Haneda, M., “Discharge Through a Permeable Rubble Mound Weir,” J. Hydraul. Engrg., 131, pp. 110 (2005).CrossRefGoogle Scholar
28.Whitaker, S., “Advances in Theory of Fluid Motion in Porous Media,” Ind. Eng. Chem., 61, p. 14 (1969).CrossRefGoogle Scholar