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Stress-jump and Continuity Interface Conditions for a Cylinder Embedded in a Porous Medium

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Abstract

The selection of interface boundary conditions between porous-medium and clear-fluid regions is very important for the wide range of engineering applications. In this paper, the difference between two common types of fluid flow interfacial conditions between clear fluid and porous medium is analyzed in detail. These two types of fluid flow interfacial condition are stress-jump and stress-continuity conditions. The effects of porosity on these types of interface condition are studied. The results are presented for different Reynolds numbers in the range 1–40, porosity equal to 0.4 and 0.8 and Darcy number \(Da=5\times 10^{- 4}\). In this study, the Darcy–Brinkmann–Forchheimer model is used to model the momentum transfer in the porous medium. The dimensionless governing equations consisting of continuity and momentum equations are discretized using control volume technique. The set of algebraic discretized coupled equations is solved using SIMPLE algorithm. It was found that for high porosity (i.e., \(\varepsilon =0.8)\), there is a large difference between two boundary conditions for the velocity profile along the horizontal and vertical directions in the porous layer.

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Abbreviations

\(C\) :

Dimensionless coefficient

\(d\) :

Thickness of porous layer (m)

\(D\) :

Diameter (m)

\(Da\) :

Darcy number, \(Da=K/D^{2}\)

\(F\) :

Force (N)

\(K \) :

Permeability \((\hbox {m}^{2})\)

\(p \) :

Pressure (Pa)

\(r \) :

Radial coordinate (m)

\(R\) :

Cylinder radius (m)

\(Re\) :

Reynolds number, \(Re=U_\infty D/\nu \)

t:

Time (s)

\(u, v \) :

Velocity components in the \(r \) and \(\theta \) directions, respectively \((\hbox {m\,s}^{-1})\)

\(\beta \) :

Stress-jump parameter

\(\beta _1 \) :

Stress-jump parameter related to inertia

\(\delta \) :

Dimensionless porous layer thickness, \(\delta =d/D\)

\(\varepsilon \) :

Porosity

\(\mu \) :

Dynamic viscosity of the fluid \(\left( {\hbox {kg}\,\hbox {m}^{- 1}\, \hbox {s}^{- 1}} \right) \)

\(\nu \) :

Kinematic viscosity of the fluid \((\hbox {m}^{2}\,\hbox {s}^{-1})\)

\(\theta \) :

Cross-radial coordinate

\(\rho \) :

Fluid density \((\hbox {kg\,m}^{-3})\)

eff:

Effective

f:

Fluid

F:

Forchheimer

p:

Pressure

s:

Solid

v:

Viscous

\(\infty \) :

Free stream

1:

Clear-fluid domain

2:

Porous domain

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, Semnan University, P.O. Box: 35131-19111, Semnan, Iran

    S. Rashidi & M. S. Valipour

  2. School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran

    A. Nouri-Borujerdi

  3. Department of Mathematics & Statistics, FBAS, IIUI, H-10 Sector, Islamabad, Pakistan

    R. Ellahi

  4. Department of Mechanical Engineering, Bourns Hall, University of California, Riverside, USA

    R. Ellahi

  5. Department of Mathematics, Babeş-Bolyai University, 400084, Cluj-Napoca, Romania

    I. Pop

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  1. S. Rashidi
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  2. A. Nouri-Borujerdi
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  3. M. S. Valipour
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  4. R. Ellahi
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  5. I. Pop
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Correspondence to I. Pop.

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Rashidi, S., Nouri-Borujerdi, A., Valipour, M.S. et al. Stress-jump and Continuity Interface Conditions for a Cylinder Embedded in a Porous Medium. Transp Porous Med 107, 171–186 (2015). https://doi.org/10.1007/s11242-014-0431-3

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