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Special Section Articles

Flows Through Reconstructed Porous Media Using Immersed Boundary Methods

[+] Author and Article Information
Krishnamurthy Nagendra

National Energy Technology Laboratory,
Pittsburgh, PA 15236;
Virginia Tech.,
Blacksburg, VA 24061

Danesh K. Tafti

National Energy Technology Laboratory,
Pittsburgh, PA 15236;
Virginia Tech.,
Blacksburg, VA 24061
e-mail: dtafti@vt.edu

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received February 11, 2013; final manuscript received November 8, 2013; published online February 28, 2014. Assoc. Editor: Zhongquan Charlie Zheng.

J. Fluids Eng 136(4), 040908 (Feb 28, 2014) (9 pages) Paper No: FE-13-1081; doi: 10.1115/1.4026102 History: Received February 11, 2013; Revised November 08, 2013

Understanding flow through real porous media is of considerable importance given their significance in a wide range of applications. Direct numerical simulations of such flows are very useful in their fundamental understanding. Past works have focused mainly on ordered and disordered arrays of regular shaped structures such as cylinders or spheres to emulate porous media. More recently, extension of these studies to more realistic pore spaces are available in the literature highlighting the enormous potential of such studies in helping the fundamental understanding of pore-level flow physics. In an effort to advance the simulation of realistic porous media flows further, an immersed boundary method (IBM) framework capable of simulating flows through arbitrary surface contours is used in conjunction with a stochastic reconstruction procedure based on simulated annealing. The developed framework is tested in a two-dimensional channel with two types of porous sections—one created using a random assembly of square blocks and another using the stochastic reconstruction procedure. Numerous simulations are performed to demonstrate the capability of the developed framework. The computed pressure drops across the porous section are compared with predictions from the Darcy–Forchheimer equation for media composed of different structure sizes. Finally, the developed methodology is applied to study CO2 diffusion in porous spherical particles of varying porosities.

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Figures

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Fig. 1

A schematic representation of the solid node, IB node, and its probe for a circular IB surface

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Fig. 2

A 2D reconstruction with porosity of 0.75 and average structure size of 0.25 generated on a 200 × 200 grid (black represents solid region)

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Fig. 3

Distribution of pressure coefficients obtained around the cylinder surface at various Reynolds numbers for the stationary cylinder

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Fig. 4

Schematic representation of the porous channel geometry

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Fig. 5

Porous channel geometry used for the grid sensitivity study showing the stream-wise velocity contour

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Fig. 11

Computed diffusion times for porous spherical particles of varying porosities

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Fig. 6

Comparison of u velocity profiles obtained at the three grid levels at (a) section 1 and (b) section 2

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Fig. 7

Enlarged views of realizations obtained using stochastic reconstruction procedure for dp values of (a) 0.25, (b) 0.50, and (c) 1.00. The porosity for each of these cases is fixed at ε = 0.85.

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Fig. 8

Comparison of pressure drops from simulations and Darcy–Forchheimer equation for porous channel constructed using square blocks

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Fig. 9

Comparison of pressure drops from simulations and Darcy–Forchheimer equation for porous channel constructed using stochastic reconstruction

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Fig. 10

A 3D porous spherical particle of diameter 100 μm and porosity of 0.45

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