Flow through Porous Bed of Turbulent Stream
Publication: Journal of Engineering Mechanics
Volume 119, Issue 2
Abstract
An analysis of the flow through an inclined‐plane pervious substratum coupled to a turbulent, steady, uniform, and fully developed open channel flow above it is introduced. The porous material is taken to be homogeneous, isotropic, and formed by a square‐arrayed lattice made of circular cylinders with axes normal to the flow direction. Starting from the Navier‐Stokes equation for the flow through the pores, a combination of the ensemble average method and the method of multiple scales is used to derive the equations governing the macroscale flow through the bed. From them, the vertical variation of the velocity in the substratum, as well as the boundary at the pervious interface are obtained. Application of the derived boundary condition, which guarantees continuity of the total stress across the interface, to the frontier between a laminar flow and a porous material, recovers the condition proposed by Beavers and Joseph in 1967. Joint use of the obtained equation for the velocity distribution and available data, suggests that the parameter controlling its exponential decay, from the slip‐velocity at the interface to the Darcy velocity away from it, may be a function of the properties of the porous material. The analysis also indicated that the nonlinearity of the flow through the substratum originates from the curvature of the streamlines and the flow separation around the solid particles at the microscale level.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Beavers, G. S., and Joseph, D. D. (1967). “Boundary conditions at a naturally permeable wall.” J. Fluid Mech., 30(1), 197–207.
2.
Chu, Y. H., and Gelhar, L. W. (1972). “Turbulent pipe flow with granular permeable boundaries.” Report No. 148, Dept. of Civil Engineering, Massachusetts Inst. of Technology, Cambridge, Mass.
3.
Cvetkovic, V. D. (1986). “A continuum approach to high velocity flow in a porous medium.” Transport in Porous Media, 1, 63–97.
4.
Dagan, G. (1979). “The generalization of Darcy's law for nonuniform flows.” Water Resour. Res., 15(1), 1–7.
5.
Fand, R. M., Kim, B. Y. K., Lam, A. C. C., and Phan, R. T. (1987). “Resistance to the flow of fluids through simple and complex porous media whose matrix are composed of randomly packed spheres.” J. Fluids Engrg., 109, 268–374.
6.
Hassanizadeh, S. M., and Gray, W. G. (1987). “High velocity flow in porous media.” Transp. Porous Media, 2, 521–531.
7.
Irmay, S. (1958). “On the theoretical derivation of Darcy and Forchheimer formulas.” J. Geophys. Res., 39(4), 702–707.
8.
Mei, C. C., and Auriault, J.‐L. (1989). “Mechanics of heterogeneous porous media with several spatial scales.” Proc., Royal Society of London, Series A, 426, 391–423.
9.
Mei, C. C., and Auriault, J.‐L. (1991). “The effect of weak inertia on flow through a porous medium.” J. Fluid Mech., 222, 647–663.
10.
Mendoza, C., and Zhou, D. (1992). “Effects of porous bed on turbulent stream flow above bed.” J. Hydr. Engrg., ASCE, 118(9), 1222–1240.
11.
Miles, J. W. (1957). “On the generation of surface waves by shear flow.” J. Fluid Mech., 3, 185–204.
12.
Munoz‐Goma, R. J., and Gelhar, L. W. (1986). “Turbulent pipe flow with rough and porous walls.” Report No. 109, Dept. of Civil Engineering, Massachusetts Institute of Technology, Cambridge, Mass.
13.
Nezu, I. (1977). “Turbulent structure in open‐channel flows,” PhD thesis, Kyoto Univ., Kyoto, Japan.
14.
Phillips, O. M. (1967). “The maintenance of Reynolds stress in turbulent shear flows.” J. Fluid Mech., 13, 433–448.
15.
Ruff, J. F., and Gelhar, L. W. (1972). “Turbulent shear flow in porous boundary.” J. Eng. Mech. Div., ASCE, 98(4), 975–991.
16.
Shimizu, Y., Tsujimoto, T., and Nakagawa, H. (1990). “Experiment and macroscopic modelling of flow in highly permeable porous medium under free‐surface flow.” J. Hydrosc. and Hydr. Eng., 8(1), 69–78.
17.
Ward, J. C. (1964). “Turbulent flow in porous media.” J. Hydr. Div., ASCE, 90(5), 1–12.
18.
Zagni, A. F. E., and Smith, K. V. H. (1976). “Channel flow over permeable beds of graded spheres.” J. Hydr. Div., ASCE, 102(2), 207–222.
19.
Zippe, H. J., and Graf, W. H. (1983). “Turbulent boundary‐layer flow over permeable and non‐permeable rough surfaces.” J. Hydr. Res., 21(1), 51–65.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 119 • Issue 2 • February 1993
Pages: 365 - 383
Copyright
Copyright © 1993 American Society of Civil Engineers.
History
Received: Mar 27, 1992
Published online: Feb 1, 1993
Published in print: Feb 1993
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.