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.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Philip, J. R., 1970, “Flow in Porous Media,” Annu. Rev. Fluid Mech., 2(1), pp. 177–204. [CrossRef]
Zick, A. A., and Homsy, G. M., 1982, “Stokes Flow Through Periodic Arrays of Spheres,” J. Fluid Mech., 115, pp. 13–26. [CrossRef]
Rahimian, M. H., and Pourshaghaghy, A., 2002, “Direct Simulation of Forced Convection Flow in a Parallel Plate Channel Filled With Porous Media,” Int. Commun. Heat Mass Transfer, 29(6), pp. 867–878. [CrossRef]
Morais, A. F., Seybold, H., Herrmann, H. J., and Andrade, J. S., Jr., 2009, “Non-Newtonian Fluid Flow Through Three-Dimensional Disordered Porous Media,” Phys. Rev. Lett., 103(19), p. 194502. [CrossRef] [PubMed]
Hill, R. J., Koch, D. L., and Ladd, A. J. C., 2001, “The First Effects of Fluid Inertia on Flows in Ordered and Random Arrays of Spheres,” J. Fluid Mech., 448(2), pp. 213–241.
Smolarkiewicz, P. K., and Winter, C. L., 2010, “Pores Resolving Simulation of Darcy Flows,” J. Comput. Phys., 229(9), pp. 3121–3133. [CrossRef]
Ovaysi, S., and Piri, M., 2010, “Direct Pore-Level Modeling of Incompressible Fluid Flow in Porous Media,” J. Comput. Physics, 229(19), pp. 7456–7476. [CrossRef]
Andrade, J. S., Jr., Costa, U. M. S., Almeida, M. P., Makse, H. A., and Stanley, H. E., 1999, “Inertial Effects on Fluid Flow Through Disordered Porous Media,” Phys. Rev. Lett., 82(26), pp. 5249–5252. [CrossRef]
Jaganathan, S., Vahedi Tafreshi, H., and Pourdeyhimi, B., 2008, “A Realistic Approach for Modeling Permeability of Fibrous Media: 3-D Imaging Coupled With CFD Simulation,” Chem. Eng. Sci., 63(1), pp. 244–252. [CrossRef]
Li, H., Pan, C., and Miller, C. T., 2005, “Pore-Scale Investigation of Viscous Coupling Effects for Two-Phase Flow in Porous Media,” Phys. Rev. E, 72(2), p. 026705. [CrossRef]
Zhao, C.-Y., Dai, L., Tang, G., Qu, Z., and Li, Z., 2010, “Numerical Study of Natural Convection in Porous Media (Metals) Using Lattice Boltzmann Method (LBM),” Int. J. Heat Fluid Flow, 31(5), pp. 925–934. [CrossRef]
Ovaysi, S., and Piri, M., 2011, “Pore-Scale Modeling of Dispersion in Disordered Porous Media,” J. Contam. Hydrol., 124(1), pp. 68–81. [CrossRef] [PubMed]
Malico, I., and de Sousa, P. J. F., 2012, “Modeling the Pore Level Fluid Flow in Porous Media Using the Immersed Boundary Method,” Numerical Analysis of Heat and Mass Transfer in Porous Media, J. M. P. Q.Delgado, A. G.Barbosa de Lima, and M.Vázquez da Silva, eds., Springer, New York, pp. 229–251.
Zaretskiy, Y., Geiger, S., Sorbie, K., and Förster, M., 2010, “Efficient Flow and Transport Simulations in Reconstructed 3D Pore Geometries,” Adv. Water Resour., 33(12), pp. 1508–1516. [CrossRef]
Adler, P. M., Jacquin, C. G., and Quiblier, J. A., 1990, “Flow in Simulated Porous Media,” Int. J. Multiphase Flow, 16(4), pp. 691–712. [CrossRef]
Yeong, C. L. Y., and Torquato, S., 1998, “Reconstructing Random Media,” Phys. Rev. E, 57(1), pp. 495–506. [CrossRef]
Yeong, C. L. Y., and Torquato, S., 1998, “Reconstructing Random Media. II. Three-Dimensional Media From Two-Dimensional Cuts,” Phys. Rev. E, 58(1), pp. 224–233. [CrossRef]
Politis, M. G., Kikkinides, E. S., Kainourgiakis, M. E., and Stubos, A. K., 2008, “A Hybrid Process-Based and Stochastic Reconstruction Method of Porous Media,” Microporous Mesoporous Mater., 110(1), pp. 92–99. [CrossRef]
Peskin, C. S., 1972, “Flow Patterns Around Heart Valves: A Numerical Method,” J. Comput. Phys., 10(2), pp. 252–271. [CrossRef]
Peskin, C. S., 1977, “Numerical Analysis of Blood Flow in the Heart,” J. Comput. Phys., 25(3), pp. 220–252. [CrossRef]
Mittal, R., and Iaccarino, G., 2005, “Immersed Boundary Methods,” Annu. Rev. Fluid Mech., 37, pp. 239–261. [CrossRef]
Fadlun, E. A., Verzicco, R., Orlandi, P., and Mohd-Yusof, J., 2000, “Combined Immersed-Boundary Finite-Difference Methods for Three-Dimensional Complex Flow Simulations,” J. Comput. Phys., 161(1), pp. 35–60. [CrossRef]
Mohd-Yusof, J., 1998, “Development of Immersed Boundary Methods for Complex Geometries,” Center for Turbulence Research, Annual Research Briefs.
Gilmanov, A., and Sotiropoulos, F., 2005, “A Hybrid Cartesian/Immersed Boundary Method for Simulating Flows With 3D, Geometrically Complex, Moving Bodies,” J. Comput. Phys., 207(2), pp. 457–492. [CrossRef]
Tafti, D. K., 2001, “GenIDLEST—A Scalable Parallel Computational Tool for Simulating Complex Turbulent Flows,” Proceedings of the ASME Fluids Engineering Division, ASME-FED, New York, pp. 347–356.
Tafti, D. K., 2009, “Time-Accurate Techniques for Turbulent Heat Transfer Analysis in Complex Geometries,” Computational Fluid Dynamics and Heat Transfer: Emerging topics, R. S.Amano, and B.Sunden, eds., WIT, Southampton, UK.
Kang, S., Iaccarino, G., Ham, F., and Moin, P., 2009, “Prediction of Wall-Pressure Fluctuation in Turbulent Flows With an Immersed Boundary Method,” J. Comput. Phys., 228(18), pp. 6753–6772. [CrossRef]
Torquato, S., 2002, “Statistical Description of Microstructures,” Annu. Rev. Mater. Res., 32(1), pp. 77–111. [CrossRef]
Čapek, P., Hejtmánek, V., Brabec, L., Zikánová, A., and Kočiřík, M., 2009, “Stochastic Reconstruction of Particulate Media Using Simulated Annealing: Improving Pore Connectivity,” Transp. Porous Media, 76(2), pp. 179–198. [CrossRef]
Park, J., Kwon, K., and Choi, H., 1998, “Numerical Solutions of Flow Past a Circular Cylinder at Reynolds Numbers up to 160,” J. Mech. Sci. Technol., 12(6), pp. 1200–1205.
Norberg, C., 1994, “An Experimental Investigation of the Flow Around a Circular Cylinder: Influence of Aspect Ratio,” J. Fluid Mech., 258, pp. 287–316. [CrossRef]
Zhang, H.-Q., Fey, U., Noack, B. R., Konig, M., and Eckelmann, H., 1995, “On the Transition of the Cylinder Wake,” Phys. Fluids, 7(4), pp. 779–794. [CrossRef]
Barkley, D., and Henderson, R. D., 1996, “Three-Dimensional Floquet Stability Analysis of the Wake of a Circular Cylinder,” J. Fluid Mech., 322, pp. 215–241. [CrossRef]
Poulikakos, D., and Renken, K., 1987, “Forced Convection in a Channel Filled With Porous Medium, Including the Effects of Flow Inertia, Variable Porosity, and Brinkman Friction,” ASME J. Heat Transfer, 109(4), pp. 880–888. [CrossRef]
Thies-Weesie, D. M. E., and Philipse, A. P., 1994, “Liquid Permeation of Bidisperse Colloidal Hard-Sphere Packings and the Kozeny-Carman Scaling Relation,” J. Colloid Interface Sci., 162(2), pp. 470–480. [CrossRef]
Adler, P. M., 1988, “Fractal Porous Media III: Transversal Stokes Flow Through Random and Sierpinski Carpets,” Transp. Porous Media, 3(2), pp. 185–198. [CrossRef]
Zeng, Z., and Grigg, R., 2006, “A Criterion for Non-Darcy Flow in Porous Media,” Transp. Porous Media, 63(1), pp. 57–69. [CrossRef]
Larson, R., and Higdon, J., 1987, “Microscopic Flow Near the Surface of Two-Dimensional Porous Media. Part 2. Transverse Flow,” J. Fluid Mech., 178(1), pp. 119–136. [CrossRef]
Koch, D. L., and Ladd, A. J. C., 1997, “Moderate Reynolds Number Flows Through Periodic and Random Arrays of Aligned Cylinders,” J. Fluid Mech., 349, pp. 31–66. [CrossRef]


Grahic Jump Location
Fig. 1

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

Grahic Jump Location
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)

Grahic Jump Location
Fig. 3

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

Grahic Jump Location
Fig. 4

Schematic representation of the porous channel geometry

Grahic Jump Location
Fig. 5

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

Grahic Jump Location
Fig. 11

Computed diffusion times for porous spherical particles of varying porosities

Grahic Jump Location
Fig. 6

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

Grahic Jump Location
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.

Grahic Jump Location
Fig. 8

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

Grahic Jump Location
Fig. 9

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

Grahic Jump Location
Fig. 10

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




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In