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Mechanisms of flow-induced deformation of porous media

Published online by Cambridge University Press:  12 October 2010

J. G. I. HELLSTRÖM
Affiliation:
Division of Fluid Mechanics, Luleå University of Technology, SE-971 87 Luleå, Sweden
V. FRISHFELDS*
Affiliation:
Division of Fluid Mechanics, Luleå University of Technology, SE-971 87 Luleå, Sweden Faculty of Physics and Mathematics, University of Latvia, Zellu 8, LV-1002 Riga, Latvia
T. S. LUNDSTRÖM
Affiliation:
Division of Fluid Mechanics, Luleå University of Technology, SE-971 87 Luleå, Sweden
*
Email address for correspondence: [email protected]

Abstract

The study investigates creeping flow-induced alteration in the permeability of deformable particle systems. Low-Reynolds-number transversal flow through random arrays of aligned cylinders is considered by means of a combined methodology of directly solving the two-dimensional (2D) Stokes equations for the flow in the vicinity of two particles and minimising the dissipation rate in a system comprising thousands of particles. The results demonstrate that the more compact the system, the greater the possible relative change of permeability when a high flow rate is applied. The permeability of large random arrays always increases when increasing the flow rate, which is most apparent in compact systems with equal-sized particles. The permeability can sometimes decrease but only in structured or small systems.

Type
Papers
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Bampalas, N. & Graham, J. M. R. 2008 Flow-induced forces arising during the impact of two circular cylinders. J. Fluid Mech. 616, 205234.CrossRefGoogle Scholar
Barry, S. I. & Aldis, G. K. 1993 Radial flow through deformable porous shells. J. Austral. Math. Soc. B 34, 333354.CrossRefGoogle Scholar
Barry, S. I., Aldis, G. K. & Mercer, G. 1995 Injection of fluid into a layer of deformable porous medium. Appl. Mech. Rev. 48 10, 722726.CrossRefGoogle Scholar
Berg, M., Kreveld, M., Overmars, M. & Schwarzkopf, O. 2000 Computational Geometry. Springer.CrossRefGoogle Scholar
Berlyand, L., Borcea, L. & Panchenko, A. 2005 Network approximation for effective viscosity of concentrated suspension with complex geometry. Siam. J. Math. Anal. 36 5, 15801628.CrossRefGoogle Scholar
Berlyand, L. & Panchenko, A. 2007 Strong and weak blow-up of the viscous dissipation rates for concentrated suspensions. J. Fluid Mech. 578, 134.CrossRefGoogle Scholar
Brosa, U. & Stauffer, D. 1991 Simulation of flow through a two-dimensional random porous medium. J. Stat. Phys. 63 (1–2), 405409.CrossRefGoogle Scholar
Chefranov, A. S. & Chefranov, S. G. 2003 Extrema of the kinetic energy and its dissipation rate in vortex flows. Dokl. Phys. 48 12, 696700.CrossRefGoogle Scholar
Chen, X. & Papathanasiou, D. 2008 The transverse permeability of disordered fiber arrays: a statistical correlation in terms of the mean nearest interfiber spacing. Transp. Porous Med. 71 2, 233251.CrossRefGoogle Scholar
Derksen, J. J. 2008 Flow-induced forces in sphere doublets. J. Fluid Mech. 608, 337356.Google Scholar
ERCOFTAC 2000 Special Interest Group on Quality and Trust in Industrial CFD: Best Practice Guidelines, 1st edn. European Research Community On Flow, Turbulence And Combustion.Google Scholar
Frishfelds, V., Lundström, T. S. & Jakovics, A. 2008 Bubble motion through non-crimp fabrics during composites manufacturing. Composites A 39 2, 243251.CrossRefGoogle Scholar
Gebart, B. R. 1992 Permeability of unidirectional reinforcements for RTM. J. Compos. Mater. 26, 11001133.CrossRefGoogle Scholar
Ghaddar, C. K. 1995 On the permeability of unidirectional fibrous media: a parallel computational approach. Phys. Fluids 7 11, 25632586.CrossRefGoogle Scholar
Hoef, M. A. Van Der, Beetstra, R. & Kuipers, J. A. M. 2005 Lattice-Boltzmann simulations of low-Reynolds-number flow past mono- and bidisperse arrays of spheres: results for the permeability and drag force. J. Fluid Mech. 528, 233254.Google Scholar
Khuzhaerov, B. 1990 Effects of blockage and erosion on the filtration of suspensions. J. Engng Phys. Thermophys. 58 2, 185190.CrossRefGoogle Scholar
Kim, S. & Karilla, S. J. 1991 Microhydrodynamics: Principles and Selected Applications. Butterworth-Heinemann.Google Scholar
Koch, D. L. & Ladd, A. J. C. 1997 Moderate Reynolds number flows through periodic and random arrays of aligned cylinders. J. Fluid Mech. 349, 3166.CrossRefGoogle Scholar
Lomov, S. V., Huysmans, G., Luo, Y., Parnas, R. S., Proromou, A., Verpoest, I. & Phelan, F. R. 2001 Textile composites: modelling strategies. Composites A 32 10, 13791394.Google Scholar
Lundström, T. S., Frishfelds, V. & Jakovics, A. 2004 A statistical approach to permeability of clustered fibre reinforcements. J. Compos. Mater. 38 13, 11371149.CrossRefGoogle Scholar
Lundström, T. S. & Gebart, B. R. 1995 Effect of perturbation of fibre architecture on permeability inside fibre tows. J. Compos. Mater. 29, 424443.CrossRefGoogle Scholar
Lundström, T. S., Holmberg, J. A. & Sundlöf, H. 2006 Modelling of power-law fluid flow through fibre beds. J. Compos. Mater. 40 3, 283296.CrossRefGoogle Scholar
Milne-Thomson, L. M. 1996 Theoretical Hydrodynamics. Dover.Google Scholar
Nordlund, M., Lundström, T. S., Frishfelds, V. & Jacovics, A. 2006 Permeability network model for non-crimp fabrics. Composites A 37 6, 826835.CrossRefGoogle Scholar
Preziosi, L., Joseph, D. D. & Beavers, G. S. 1996 Infiltration of initially dry, deformable porous media. Intl J. Multiphase Flow 22 6, 12051222.CrossRefGoogle Scholar
Sangani, A. S. & Mo, G. 1994 Inclusion of lubrication forces in dynamic simulations. Phys. Fluids 6 5, 16531662.CrossRefGoogle Scholar
Sangani, A. S. & Yao, C. 1988 Transport processes in random arrays of cylinders. II. Viscous flow. Phys. Fluids 31 9, 24352444.CrossRefGoogle Scholar
Sommer, J. L. & Mortensen, A. 1996 Forced unidirectional infiltration of deformable porous media. J. Fluid Mech. 311, 193217.CrossRefGoogle Scholar
Tomadakis, M. M. & Robertson, T. J. 2005 Viscous permeability of random fiber structures: Comparison of electrical and diffusional estimates with experimental and analytical results. J. Compos. Mater. 71 2, 163188.CrossRefGoogle Scholar
Westhuizen, J. Van Der & Plessis, J. P. D. 1996 An attempt to quantify fibre bed permeability utilizing the phase average Navier–Stokes equation. Composites A 27 4, 263269.Google Scholar
White, B. L. & Nepf, H. M. 2003 Scalar transport in random cylinder arrays at moderate Reynolds number. J. Fluid Mech. 487, 4379.CrossRefGoogle Scholar
Ziman, J. M. 1979 Models of Disorder: The Theoretical Physics of Homogeneously Disordered Systems. Cambridge University Press.Google Scholar