Research Papers: Fundamental Issues and Canonical Flows

Experimental and Numerical Determination of Interface Slip Coefficient of Fluid Stream Exiting a Partially Filled Porous Medium Channel

[+] Author and Article Information
Arunn Narasimhan

Associate Professor
Department of Mechanical Engineering,
Indian Institute of Technology Madras,
Chennai 600 036, India
e-mail: arunn@iitm.ac.in

K. S. Raju

Department of Mechanical Engineering,
Indian Institute of Technology Madras,
Chennai 600 036, India

S. R. Chakravarthy

Department of Aerospace Engineering,
Indian Institute of Technology Madras,
Chennai 600 036, India

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received April 16, 2012; final manuscript received December 4, 2013; published online February 28, 2014. Assoc. Editor: Peter Vorobieff.

J. Fluids Eng 136(4), 041201 (Feb 28, 2014) (9 pages) Paper No: FE-12-1198; doi: 10.1115/1.4026194 History: Received April 16, 2012; Revised December 04, 2013

Stacks of parallel plates modeled as a standard fissure-type anisotropic porous medium are filled inside a rectangular channel up to half the cross section height. The interface slip coefficient α for the isothermal laminar incompressible flow exiting this partially filled porous-medium channel is then determined using particle image velocimetry (PIV) experiments and numerical simulations. Required measurements of the Darcy velocity uD on the porous-medium (PM) side, the local velocity uf, and its gradient uf/y on the clear-fluid (CF) side are performed across different length scales. The fissure-type porous-medium parameters are systematically varied in the porosity range 0.2φ0.95 and flow direction permeability 10-6<K,m2<10-9. From the exit-velocity profile, the empirical slip coefficient α is determined using a generalized relationship. When the measurements across the PM-CF interface are performed across a length scale equal to the representative elemental length (REL) of the porous media considered (i.e., equal to the sum of plate thickness (a) and gap (b)), the determined α value is found to remain invariant.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Whitaker, S., 1999, The Method of Volume Averaging, Kluwer Academic, The Netherlands.
Nield, D. A., and Bejan, A., 2006, Convection in Porous Media, Springer, New York.
Beavers, G. S., and Joseph, D. D., 1967, “Boundary Conditions at a Naturally Permeable Wall,” J. Fluid Mech., 30, pp. 197–207. [CrossRef]
Taylor, G. I., 1971, “A Model for the Boundary Condition of a Porous Material. Part 1,” J. Fluid Mech., 49, pp. 319–326. [CrossRef]
Richardson, S., 1971, “A Model for Boundary Condition of a Porous Material. Part 2,” J. Fluid Mech., 49, pp. 327–336. [CrossRef]
Goharzadeh, A., Khalili, A., and Jorgensen, B. B., 2005, “Transition Layer Thickness at a Fluid-Porous Interface,” Phys. Fluids, 17, p. 057102. [CrossRef]
Agelinchaab, M., Tachie, M. F., and Ruth, D. W., 2006, “Velocity Measurements of Flow Through a Model Three-Dimensional Porous Medium,” Phys. Fluids, 18, p. 017105. [CrossRef]
Vafai, K., and Thiyagaraja, R., 1987, “Analysis of the Flow and Heat Transfer at the Interface Region of a Porous Medium,” Int. J. Heat Mass Transfer, 30, p. 1391. [CrossRef]
Ochoa-Tapia, J. A., and Whitaker, S., 1995, “Momentum Transfer at the Boundary Between a Porous Medium and a Homogeneous Fluid-II Comparison With Experiments,” Int. J. Heat Mass Transfer, 38, pp. 2635–2646. [CrossRef]
Kuznestov, A. V., 1997, “Influence of the Stress Jump Condition at the Porous- Medium/Clear-Fluid Interface on a Flow at a Porous Wall,” Int. Commun. Heat Mass Transfer, 24, pp. 401–410. [CrossRef]
Kuznestov, A. V., 2000, “Analytical Studies of Forced Convection in Partly Porous Configuration,” Handbook of Porous Media, K.Vafai, ed., Marcel Dekker, New York, pp. 269–312.
Alazmi, B., and Vafai, K., 2001, “Analysis of Fluid Flow and Heat Transfer Interfacial Conditions Between a Porous Medium and a Fluid Layer,” Int. J. Heat Mass Transfer, 44, pp. 1735–1749. [CrossRef]
Gupte, S. K., and Advani, S. G., 1997, “Flow Near the Permeable Boundary of a Porous Medium: An Experimental Investigation Using LDA,” Exp. Fluids, 22, pp. 408–422. [CrossRef]
Sahraoui, M., and Kaviany, M., 1992, “Slip and No-Slip Velocity Boundary Conditions at Interface of Porous Plain Media,” Int. J. Heat Mass Transfer, 35, pp. 927–943. [CrossRef]
Shams, M., Currie, I. G., and James, D. F., 2003, “The Flow Near the Edge of a Model Porous Medium,” Exp. Fluids, 35, pp. 193–198. [CrossRef]
Tachie, M. F., James, D. F., and Currie, I. G., 2003, “Velocity Measurements of Shear Flow Penetrating a Porous Medium,” J. Fluid Mech., 493, pp. 319–343. [CrossRef]
Lage, J. L., Krueger, P. S., and Narasimhan, A., 2005, “Protocol for Measuring Permeability and Form Coefficient of Porous Media,” Phys. Fluids, 17(8), p. 088101. [CrossRef]
Bejan, A., 1997, Convection Heat Transfer, Wiley, New York.
Wilson, L., Narasimhan, A., and Venkateshan, S. P., 2006, “Permeability and Form Coefficient Measurement of Porous Inserts With Non-Darcy Model Using Non-plug Flow Experiments,” ASME J. Fluids Eng., 128, pp. 638–642. [CrossRef]
Papathanasioua, T. D., Markicevic, B., and Dendy, E. D., 2001, “A Computational Evaluation of the Ergun and Forchheimer Equations for Fibrous Porous Media,” Phys. Fluids, 13(10), pp. 2795–2804. [CrossRef]
Lage, J. L., and Antohe, B. V., 2000, “Darcy's Experiments and the Deviation to Nonlinear Flow Regime,” ASME J. Fluids Eng., 122, pp. 619–625. [CrossRef]
Raffel, M., Willert, C., and Kompenhans, J., 1998, Particle Image Velocimetry - A Practical Guide, 2nd ed., Springer, Berlin.
Patankar, S. V., 1980, Numerical Heat Transfer and Fluid Flow, Taylor and Francis, London.
White, F. M., 1991, Viscous Fluid Flow, McGraw-Hill, New York.
Narasimhan, A., 2012, Essentials of Heat and Fluid Flow in Porous Media, CRC, Boca Raton, FL.
Saffman, P. G., 1971, “On the Boundary Condition at the Surface of a Porous Medium,” Stud. Appl. Math., 1, pp. 93–101.


Grahic Jump Location
Fig. 2

Schematic of the experimental setup

Grahic Jump Location
Fig. 1

2D schematic of partially filled porous-medium channel: The stacks of parallel plates (plate thickness a separated by uniform gaps b) treated as porous media extend until δ in y direction

Grahic Jump Location
Fig. 3

Comparison of present experimental data with theory [24]

Grahic Jump Location
Fig. 4

Velocity vectors at the exit PM-CF slip-interface for various void fractions

Grahic Jump Location
Fig. 5

Comparison of PIV experimental exit-velocity profile data with corresponding numerical simulations for (a) Model-6 and (b) Model-8

Grahic Jump Location
Fig. 6

Exit velocities averaged over several channel heights in the porous-medium region

Grahic Jump Location
Fig. 7

α versus y/H for REL, Ω=0.166 models: (a) PIV experiments, (b) numerical simulation, and (c) combined results

Grahic Jump Location
Fig. 8

Velocity vectors for (a) Model-12 with REL = 7.5 mm and (b) Model-3 with REL = 2.5

Grahic Jump Location
Fig. 9

α versus y/H for all 15 models in Table 1 (comprising three REL values): (a) PIV experiments, (b) numerical simulation, and (c) combined results

Grahic Jump Location
Fig. 10

Interface slip coefficient α variation with solid volume fraction. Parameters determined at K distance across the interface.

Grahic Jump Location
Fig. 11

Interface slip coefficient α variation with solid volume fraction. Parameters determined at REL distance across the interface.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In