Hostname: page-component-848d4c4894-r5zm4 Total loading time: 0 Render date: 2024-07-03T11:01:50.321Z Has data issue: false hasContentIssue false
  • English
  • Français

PIV measurements of flow through a model porous medium with varying boundary conditions

Published online by Cambridge University Press:  15 June 2009

JAMES K. ARTHUR ,
DOUGLAS W. RUTH  and
MARK F. TACHIE
JAMES K. ARTHUR
Affiliation:
Department of Mechanical and Manufacturing Engineering, University of Manitoba, Winnipeg, Manitoba R3T 5V6, Canada
DOUGLAS W. RUTH*
Affiliation:
Department of Mechanical and Manufacturing Engineering, University of Manitoba, Winnipeg, Manitoba R3T 5V6, Canada
MARK F. TACHIE
Affiliation:
Department of Mechanical and Manufacturing Engineering, University of Manitoba, Winnipeg, Manitoba R3T 5V6, Canada
*
†Email address for correspondence: druth@cc.umanitoba.ca
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper reports an experimental investigation of pressure-driven flow through models of porous media. Each model porous medium is a square array of circular acrylic rods oriented across the flow in a rectangular channel. The solid volume fraction φ of the arrays ranged from 0.01 to 0.49. Three boundary conditions were studied. In the first boundary condition, the model porous medium was installed on the lower wall of the channel only and was bounded by a free zone. In the second and third boundary conditions, porous media of equal and unequal φ were arranged on the lower and upper channel walls so that the two media touched (second boundary condition), and did not touch (third boundary condition). Using water as the working fluid, the Reynolds number was kept low so that inertia was not a factor. Particle image velocimetry was used to obtain detailed velocity measurements in the streamwise-transverse plane of the test section. The velocity data were used to study the effects of φ and the different boundary conditions on the flow through and over the porous medium, and at the interface. For the first boundary condition, it was observed that at φ = 0.22, flow inside the porous medium was essentially zero, and the slip velocity at the porous medium and free zone interface decayed with permeability. In the second and third boundary conditions, flow communication between the porous media was observed to be dependent on the combinations of φ used, and the trends of the slip velocities at the interface between the two porous media obtained for that boundary condition were indicative of complicated interfacial flow.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 629 , 25 June 2009 , pp. 343 - 374
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Agelinchaab, M., Tachie, M. F. & Ruth, D. W. 2006 Velocity measurement of flow through a model three-dimensional porous medium. Phys. Fluids 18, 017105-1–11.CrossRefGoogle Scholar
Alazmi, B. & Vafai, K. 2001 Analysis of fluid flow and heat transfer interfacial conditions between a porous medium and a fluid layer. Intl J. Heat Mass Transfer 44, 1735–1749.CrossRefGoogle Scholar
Allan, F. M. & Hamdan, M. H. 2002 Fluid mechanics of the interface region between two porous layers. Appl. Math. Comput. 128, 37–43.Google Scholar
Arthur, J. K. 2008 Velocity measurements of flow through a model three-dimensional porous medium with varying boundary conditions. Master of Science Thesis, University of Manitoba, Winnipeg, Manitoba.Google Scholar
Bear, J. 1972 Dynamics of Fluids in Porous Media. Elsevier.Google Scholar
Beavers, G. S. & Joseph, D. D. 1967 Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30, 197–207.CrossRefGoogle Scholar
Beavers, G. S., Sparrow, E. M. & Magnuson, R. A. 1970 Experiments on coupled-parallel flows in a channel and a bounding porous medium, J. Basic Engng Trans. A.S.M.E. 92D, 843–848.CrossRefGoogle Scholar
Breugem, W. P., Boersma, B. J. & Uittenbogaard, R. E. 2005 The laminar boundary layer over a permeable wall. Transp. Porous Med. 59, 267–300.CrossRefGoogle Scholar
Brinkman, H. C. 1947 A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particle. Appl. Sci. Res. A 1, 27–34.CrossRefGoogle Scholar
Budwig, R. 1994 Refractive index matching methods for liquid flow investigations. Exp. Fluids 17, 350–355.CrossRefGoogle Scholar
Chandesris, M. & Jamet, D. 2006 Boundary conditions at a planar fluid–porous interface for a Poiseuille flow. Intl J. Heat Mass Transfer 49, 2137–2150.CrossRefGoogle Scholar
Coleman, H. W. & Steele, W. G. 1995 Engineering application of experimental uncertainty analysis. AIAA J. 33, 1888–1896.CrossRefGoogle Scholar
Cui, M. M. & Adrian, R. J. 1997 Refractive index matching and marking methods for highly concentrated solid–liquid flows. Exp. Fluids. 22, 261–264.CrossRefGoogle Scholar
Davis, A. M. J. & James, D. F. 2003 The slip velocity at the edge of a porous medium: effects of interior resistance and interface. Transp. Porous Med. 53, 175–196.CrossRefGoogle Scholar
Davis, A. M. J. & James, D. F. 2004 Penetration of shear flow into an array of rods aligned with the flow. Can. J. Chem. Engng 82, 1169–1174.CrossRefGoogle Scholar
Deng, C. & Martinez, D. M. 2005 Viscous flow in a channel partially filled with a porous medium and with wall suction. Chem. Engng Sci. 60, 329–336.CrossRefGoogle Scholar
Greenkorn, R. A. 1983 Flow Phenomena in Porous Media. Marcel Dekker.Google Scholar
Gupte, S. K. & Advani, S. G. 1997 Flow near the permeable boundary of a porous medium: an experimental investigation using LDA. Exp. Fluids 22, 408–422.CrossRefGoogle Scholar
Huang, H. & Ayoub, J. 2008 Applicability of the Forcheimer equation for non-Darcy flow in porous media. Applicability of the Forcheimer equation for non-Darcy flow in porous media 13 (1), 112–122.Google Scholar
Huang, A. Y. L., Huang, M. Y. F., Capart, H. & Chen, R.-H. 2008 Optical measurements of pore geometry and fluid velocity in a bed of irregularly packed spheres. Exp. Fluids 45, 309–321.CrossRefGoogle Scholar
Jackson, G. W. & James, D. F. 1986 The permeability of fibrous porous media. Can. J. Chem. Engng 64, 364–374.CrossRefGoogle Scholar
James, D. F. & Davis, A. M. J. 2001 Flow at the interface of a model fibrous medium. J. Fluid Mech. 426, 47–72.CrossRefGoogle Scholar
Khalili, A., Basu, A. J., Pietrzyk, U. & Raffel, M. 1999 An experimental study of recirculating flow through fluid-sediment interfaces. J. Fluid Mech. 383, 229–247.CrossRefGoogle Scholar
Kim, S. & Kussel, W. B. 1985 Modelling of porous media renormalization of the Stokes equations. J. Fluid Mech. 154, 269–286.CrossRefGoogle Scholar
Larson, R. E. & Higdon, J. J. L. 1986 Microscopic flow near the surface of two dimensional porous media. Part 1. Axial flow. J. Fluid Mech. 166, 449–472.CrossRefGoogle Scholar
Larson, R. E. & Higdon, J. J. L. 1987 Microscopic flow near the surface of two-dimensional porous media. Part 2. Transverse flow. J. Fluid Mech. 178, 119–136.CrossRefGoogle Scholar
Moroni, M. & Cushman, J. H. 2001 Statistical mechanics with three-dimensional particle tracking velocimetry experiments in the study of anomalous dispersion. II. Experiments. Phys. Fluids 13, 81–91.CrossRefGoogle Scholar
Moroni, M., Kleinfelter, N. & Cushman, J. H. 2007 Analysis of dispersion in porous media via matched-index particle tracking velocimetry experiments. Adv. Water Res. 30, 1–15.CrossRefGoogle Scholar
Nield, D. A. & Bejan, A. 1992 Convection in Porous Media. Springer.CrossRefGoogle Scholar
Northrup, M. A., Kulp, T. J., Angel, S. M. & Pinder, G. F. 1993 Direct measurement of interstitial velocity field variations in a porous medium using fluorescent-particle image velocimetry. Chem. Engng Sci. 48, 13–21.CrossRefGoogle Scholar
Ochoa-Tapia, J. A. & Whitaker, S. 1995 Momentum transfer at the boundary between a porous medium and a homogenous fluid. 1. Theoretical development. Intl J. Heat Mass Transfer 38, 2635–2646.CrossRefGoogle Scholar
Ochoa-Tapia, J. A. & Whitaker, S. 1998 Momentum jump condition at the boundary between a porous medium and a homogenous fluid: inertial effects. J. Porous Media 1, 201–217.Google Scholar
Ogawa, K., Matsuka, T., Hirai, S. & Okazaki, K. 2001 Three-dimensional velocity measurement of complex interstitial flows through water-saturated porous media by the tagging method in the MRI technique. Meas. Sci. Technol. 12, 172–180.CrossRefGoogle Scholar
Peurrung, L. M., Rashidi, M. & Kulp, T. J. 1993 Measurement of porous medium velocity fields and their volumetric averaging characteristics using particle tracking velocimetry. Measurement of porous medium velocity fields and their volumetric averaging characteristics using particle tracking velocimetry 50 (14), 2243–2253.Google Scholar
Prasad, A. K. 2000 Particle image velocimetry. Particle image velocimetry 79 (1), 51–60.Google Scholar
Raffel, M., Willert, C., Wereley, S. & Kompenhans, J. 2007 Particle Image Velocimetry. A Practical Guide. Springer.CrossRefGoogle Scholar
Rashidi, M., Peurrung, L., Tompson, A. F. B. & Kulp, T. J. 1996 Experimental analysis of pore-scale flow and transport in porous media. Adv. Water Resour. 19, 163–180.CrossRefGoogle Scholar
Richardson, S. 1971 A model for the boundary condition of a porous material. Part 2. J. Fluid Mech. 49, 327–336.CrossRefGoogle Scholar
Rosenzweig, R. & Shavit, U. 2007 The laminar flow field at the interface of a Sierpinski carpet configuration. Water Resour. Res. 43, W10402. doi:10.1029/2006WR005801.CrossRefGoogle Scholar
Saffman, P. G. 1971 On the boundary condition at the surface of a porous medium. Stud. Appl. Math. 50, 93–101.CrossRefGoogle Scholar
Sahraoui, M. & Kaviany, M. 1992 Slip and no-slip velocity boundary at interface of porous, plain media. Slip and no-slip velocity boundary at interface of porous, plain media 35 (4), 927–943.Google Scholar
Saleh, S., Thovert, J. F. & Adler, P. M. 1992 Measurement of two-dimensional velocity fields in porous media by particle image displacement velocimetry. Exps. Fluids 12, 210–212.CrossRefGoogle Scholar
Sangani, A. S. & Acrivos, A. 1982 Slow flow past periodic arrays of cylinders with application to heat transfer. Int. J. Multiphase Flow 8, 193–206.CrossRefGoogle Scholar
Scheidegger, A. E. 1974 The Physics of Flow Through Porous Media. University of Toronto Press.Google Scholar
Shams, M., James, D. F. & Currie, I. G. 2003 The velocity field near the edge a model porous medium. Exp. Fluids 35, 193–198.CrossRefGoogle Scholar
Stephenson, J. L. & Stewart, W. E. 1986 Optical measurements of porosity and fluid motion in packed beds. Chem. Engng Sci. 41, 2161–2170.CrossRefGoogle Scholar
Stöhr, M., Roth, K. & Jähne, B. 2003 Measurement of 3D pore-scale flow in index-matched porous media. Exp. Fluids 35, 159–166.CrossRefGoogle Scholar
Tachie, M. F., James, D. F. & Currie, I. G. 2003 Velocity measurements of the shear flow penetrating a porous medium. J. Fluid Mech. 493, 319–343.CrossRefGoogle Scholar
Tachie, M. F., James, D. F. & Currie, I. G. 2004 Slow flow through a brush. Slow flow through a brush 16 (2), 445–451.Google Scholar
Taylor, G. I. 1971 A model for the boundary condition of a porous material. Part 1. J. Fluid Mech. 49, 319–326.CrossRefGoogle Scholar
Vafai, K. & Thyagaraja, R. 1987 Analysis of flow and heat transfer at the interface region of a porous medium. Intl J. Heat Mass Transfer 30, 1391–1405.CrossRefGoogle Scholar
Yarlagadda, A. P. & Yoganathan, A. P. 1989 Experimental studies of model porous media fluid dynamics. Exp. Fluids 8, 59–71.CrossRefGoogle Scholar
Zhong, W. H., Currie, I. G. & James, D. F. 2006 Creeping flow through a model fibrous porous medium. Exp. Fluids 40, 119–126.CrossRefGoogle Scholar
Zitoun, K. B., Sastry, S. K. & Guezennec, Y. 2001 Investigation of three-dimensional interstitial velocity, solids motion, and orientation in solid-liquid flow using particle tracking velocimetry. Int J. Multiphase Flow 27, 1397–1414.CrossRefGoogle Scholar