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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,
Chennai 600 036, India
e-mail: arunn@iitm.ac.in

K. S. Raju

Department of Mechanical Engineering,
Chennai 600 036, India

S. R. Chakravarthy

Professor
Department of Aerospace Engineering,
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

## Abstract

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 $0.2≤φ≤0.95$ and flow direction permeability $10-6. 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.

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## Figures

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

Fig. 2

Schematic of the experimental setup

Fig. 6

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

Fig. 4

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

Fig. 3

Comparison of present experimental data with theory [24]

Fig. 5

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

Fig. 7

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

Fig. 8

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

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

Fig. 10

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

Fig. 11

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

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