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Special Section Articles

Computation of Flow Through a Three-Dimensional Periodic Array of Porous Structures by a Parallel Immersed-Boundary Method

[+] Author and Article Information
Zhenglun Alan Wei

Department of Aerospace Engineering,
University of Kansas,
Lawrence, KS 66045
e-mail: alanwei@ku.edu

Zhongquan Charlie Zheng

Professor
Department of Aerospace Engineering,
University of Kansas,
Lawrence, KS 66045
e-mail: zzheng@ku.edu

Xiaofan Yang

Research Associate
Pacific Northwest National Laboratory,
Richland, WA 99352
e-mail: Xiaofan.Yang@pnnl.gov

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received July 18, 2013; final manuscript received December 18, 2013; published online February 28, 2014. Assoc. Editor: Elias Balaras.

J. Fluids Eng 136(4), 040905 (Feb 28, 2014) (10 pages) Paper No: FE-13-1434; doi: 10.1115/1.4026357 History: Received July 18, 2013; Revised December 18, 2013

A parallel implementation of an immersed-boundary (IB) method is presented for low Reynolds number flow simulations in a representative elementary volume (REV) of porous media that are composed of a periodic array of regularly arranged structures. The material of the structure in the REV can be solid (impermeable) or microporous (permeable). Flows both outside and inside the microporous media are computed simultaneously by using an IB method to solve a combination of the Navier–Stokes equation (outside the microporous medium) and the Zwikker–Kosten equation (inside the microporous medium). The numerical simulation is firstly validated using flow through the REVs of impermeable structures, including square rods, circular rods, cubes, and spheres. The resultant pressure gradient over the REVs is compared with analytical solutions of the Ergun equation or Darcy–Forchheimer law. The good agreements demonstrate the validity of the numerical method to simulate the macroscopic flow behavior in porous media. In addition, with the assistance of a scientific parallel computational library, PETSc, good parallel performances are achieved. Finally, the IB method is extended to simulate species transport by coupling with the REV flow simulation. The species sorption behaviors in an REV with impermeable/solid and permeable/microporous materials are then studied.

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References

Figures

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Fig. 1

Porous medium REVs represented by fluid/solid-cylinder and fluid/porous-cylinder interactions

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Fig. 2

Computational domain of a representative unit structure; the depth is H

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Fig. 3

Velocity profiles at the outlet for grid independence check for flow through an REV with impermeable square rods with (a) FLUENT and (b) IB method

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Fig. 4

A comparison of streamwise velocity contours between (a) FLUENT and (b) the IB method. The contour level is 0∼3 for both pictures.

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Fig. 5

The parallel speedup with different number of processes

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Fig. 6

The correlation between the dimensionless pressure drop and ε3/(1 – ε)2 for 2D patterns of objects in REVs. The solid line is for the analytical values based on the permeability equation expressed in the figure. The symbols indicate the results from simulations of the IB method. (a) Square rods and (b) circular rods.

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Fig. 7

The correlation between the dimensionless pressure drop and ε3/(1 – ε)2 for 3D patterns of objects in REVs. The solid line implies the analytical values based on the permeability equation attached on the figure. The symbols indicate the results from simulations of the IB method. (a) Cubes and (b) spheres.

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Fig. 8

Species percentage sorption with different patterns of REV with impermeable materials

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Fig. 9

Species percentage sorption with solid or microporous circular rods in REV

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Fig. 10

Species percentage sorption with solid or microporous circular rods in REV in comparison with that of the analytical solution in a uniform porous medium

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