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.

References

References
1.
Whitaker
,
S.
,
1999
,
The Method of Volume Averaging
,
Kluwer Academic
,
The Netherlands
.
2.
Nield
,
D. A.
, and
Bejan
,
A.
,
2006
,
Convection in Porous Media
,
Springer
,
New York
.
3.
Beavers
,
G. S.
, and
Joseph
,
D. D.
,
1967
, “
Boundary Conditions at a Naturally Permeable Wall
,”
J. Fluid Mech.
,
30
, pp.
197
207
.10.1017/S0022112067001375
4.
Taylor
,
G. I.
,
1971
, “
A Model for the Boundary Condition of a Porous Material. Part 1
,”
J. Fluid Mech.
,
49
, pp.
319
326
.10.1017/S0022112071002088
5.
Richardson
,
S.
,
1971
, “
A Model for Boundary Condition of a Porous Material. Part 2
,”
J. Fluid Mech.
,
49
, pp.
327
336
.10.1017/S002211207100209X
6.
Goharzadeh
,
A.
,
Khalili
,
A.
, and
Jorgensen
,
B. B.
,
2005
, “
Transition Layer Thickness at a Fluid-Porous Interface
,”
Phys. Fluids
,
17
, p.
057102
.10.1063/1.1894796
7.
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
.10.1063/1.2164847
8.
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
.10.1016/0017-9310(87)90171-2
9.
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
.10.1016/0017-9310(94)00346-W
10.
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
.10.1016/S0735-1933(97)00025-0
11.
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
.
12.
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
.10.1016/S0017-9310(00)00217-9
13.
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
.10.1007/s003480050067
14.
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
.10.1016/0017-9310(92)90258-T
15.
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
.10.1007/s00348-003-0657-2
16.
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
.10.1017/S0022112003005986
17.
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
.10.1063/1.1979307
18.
Bejan
,
A.
,
1997
,
Convection Heat Transfer
,
Wiley
,
New York
.
19.
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
.10.1115/1.2175172
20.
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
.10.1063/1.1401811
21.
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
.10.1115/1.1287722
22.
Raffel
,
M.
,
Willert
,
C.
, and
Kompenhans
,
J.
,
1998
,
Particle Image Velocimetry - A Practical Guide
,
2nd ed.
,
Springer
,
Berlin
.
23.
Patankar
,
S. V.
,
1980
,
Numerical Heat Transfer and Fluid Flow
,
Taylor and Francis
,
London
.
24.
White
,
F. M.
,
1991
,
Viscous Fluid Flow
,
McGraw-Hill
,
New York
.
25.
Narasimhan
,
A.
,
2012
, Essentials of Heat and Fluid Flow in Porous Media, CRC, Boca Raton, FL.
26.
Saffman
,
P. G.
,
1971
, “
On the Boundary Condition at the Surface of a Porous Medium
,”
Stud. Appl. Math.
,
1
, pp.
93
101
.
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