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Research Papers: Fundamental Issues and Canonical Flows

A General Macroscopic Model for Turbulent Flow in Porous Media

[+] Author and Article Information
Nima F. Jouybari

Department of Mechanical Engineering,
Tarbiat Modares University,
P.O. Box 14115-143,
Tehran 1411713116, Iran
e-mail: nima.jouybari@gmail.com

Mehdi Maerefat

Department of Mechanical Engineering,
Tarbiat Modares University,
P.O. Box 14115-143,
Tehran 1411713116, Iran
e-mail: maerefat@modares.ac.ir

T. Staffan Lundström

Division of Fluid Mechanics,
Luleå University of Technology,
Luleå 971 87, Sweden
e-mail: staffan.lundstrom@ltu.se

Majid E. Nimvari

Faculty of Engineering Technologies,
Amol University of Special
Modern Technologies,
Amol 4614849767, Iran
e-mail: m.eshagh@ausmt.ac.ir

Zahra Gholami

Department of Food and Agriculture,
Standard Research Institute,
Karaj 3174734563, Iran
e-mail: gholamizahram83@gmail.com

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received April 9, 2016; final manuscript received August 6, 2017; published online September 20, 2017. Assoc. Editor: Elias Balaras.

J. Fluids Eng 140(1), 011201 (Sep 20, 2017) (9 pages) Paper No: FE-16-1224; doi: 10.1115/1.4037677 History: Received April 09, 2016; Revised August 06, 2017

The present study deals with the generalization of a macroscopic turbulence model in porous media using a capillary model. The additional source terms associated with the production and dissipation of turbulent kinetic energy due to the presence of solid matrix are calculated using the capillary model. The present model does not require any prior pore scale simulation of turbulent flow in a specific porous geometry in order to close the macroscopic turbulence equations. Validation of the results in packed beds, periodic arrangement of square cylinders, synthetic foams, and longitudinal flows such as pipes, channels, and rod bundles against available data in the literature reveals the ability of the present model in predicting turbulent flow characteristics in different types of porous media. Transition to the fully turbulent regime in porous media and different approaches to treat this phenomenon are also discussed in the present study. Finally, the general model is modified so that it can be applied to lower Reynolds numbers below the range of fully turbulent regime in porous media.

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References

Figures

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Fig. 1

Limits of flow regimes in different porous media

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Fig. 2

(a) Schematic representation of the capillary model and (b) macroscopic pressure gradient calculated from the capillary model and Ergun's [38] correlation

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Fig. 3

Normalized effective viscosity in the packed bed of spheres

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Fig. 4

Normalized effective viscosity in the packed bed of cylinders

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Fig. 5

Comparison of turbulent intensity calculated from Eq.(21) in synthetic foam with the x and y components of turbulent intensity in the experimental study of Hall and Hiatt [26]

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Fig. 6

Staggered arrangement of square cylinders

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Fig. 7

Normalized macroscopic turbulent kinetic energy in the staggered arrangement of square cylinders

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Fig. 8

Turbulent kinetic energy as a function of Redh

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Fig. 9

Normalized effective viscosity in the packed bed of spheres modified for transition effects

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Fig. 10

Normalized effective viscosity in the packed bed of cylinders modified for transition effects

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Fig. 11

Normalized turbulent kinetic energy as a function of Reynolds number in the staggered arrangement of square cylinders modified for transition effects

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Fig. 12

Normalized effective viscosity as a function of Reynolds number in the staggered arrangement of square cylinders modified for transition effects

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