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Flow-Induced Deformations Within Random Packed Beds of Spheres

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Abstract

Low Reynolds number flow-induced alterations of permeability of random packing of mono-sized spheres is studied. The number of spheres is several thousands and the porosities ranges between 0.4 and 0.6. The change of permeability is obtained for elastic deformations of the positions of the spheres using either of two methods. Each sphere is elastically attached to single points or the spheres that are connected via an elastic porous network. The system of spheres is divided into smaller volumes with Voronoi diagrams and the flow is derived by usage of a dual stream function. The local saturated flow fields are approximated as for close packed spheres and the overall flow pattern is obtained by minimising the dissipation rate of energy. The results show that the permeability for large random systems increases as a function of velocity and thus the deformation. The alteration is, however, much less than for two-dimensional cases like parallel cylinders. The relative increase in permeability becomes larger as the porosity increases from 0.4 to 0.6.

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References

  • Akbari, M., Sinton, D., Bahrami, M.: Viscous flow in variable cross-section microchannels of arbitrary shapes. Int. J. Heat Mass Transf. 54, 3970–3978 (2011)

    Article  Google Scholar 

  • Andersson, H.M., Lundstrom, T.S., Gebart, B.R.: Numerical model for vacuum infusion manufacturing of polymer composites. Int J Numer Methods Heat Fluid Flow 13(2–3), 383–394 (2003)

    Article  Google Scholar 

  • Anikeenko, A.V., Gavrilova, M.L., Medvedev, N.: Shapes of delaunay simplexes and structural analysis of hard sphere packings. In: Gavrilova, M.L. (ed.) Generalized Voronoi Diagram A Geometry-Based Approach to Computational Intelligence, pp. 13–45. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  • Barry, S.I., Aldis, G.K., Mercer, G.: Injection of fluid into a layer of deformable porous medium. Appl. Mech. Rev. 48(10), 722–726 (1995)

    Article  Google Scholar 

  • Batchelor, G.K.: An introduction to fluid mechanics. Cambridge University Press, Cambridge (1967)

  • Bear, J.: Hydraulics of groundwater. Mc-Graw-Hill, New York (1979)

  • Berlyand, L., Panchenko, A.: Strong and weak blow-up of the viscous dissipation rates for concentrated suspensions. J. Fluid Mech. 578, 1–34 (2007)

    Article  Google Scholar 

  • Boek, E.S., Hall, C., Tardy, P.M.J.: Deep bed filtration modelling of formation damage due to particulate invasion from drilling fluids. Transp. Porous Media 91(2), 479–508 (2012)

    Article  Google Scholar 

  • Chen, X., Papathanasiou, T.D.: The transverse permeability of disordered fiber arrays: a statistical correlation in terms of the mean nearest interfiber spacing. Transp. Porous Media 71(2), 233–251 (2008)

    Article  Google Scholar 

  • Deleglise, M., Binetruy, C., Krawczak, P.: Simulation of LCM processes involving induced or forced deformations. Compos. Part A 37(6), 874–880 (2006)

    Article  Google Scholar 

  • Drummond, J., Tahir, M.: Laminar viscous flow through regular arrays of parallel solid cylinders. Int. J. Multiph. Flow 10(5), 515–540 (1984)

    Article  Google Scholar 

  • Endruweit, A., Gehrig, S., Ermanni, P.: Mechanisms of hydrodynamically induced in-plane deformation of reinforcement textiles in resin injection processes. J. Compos. Mater. 37(18), 1675–1692 (2003)

    Article  Google Scholar 

  • Freund, H., Bauer, J., Zeiser, T., Emig, G.: Detailed simulation of transport processes in fixed-beds. Ind. Eng. Chem. Res. 44(16), 6423–6434 (2005)

    Article  Google Scholar 

  • Frishfelds, V., Hellström, J.G.I., Lundström, T.S., Mattsson, H.: Fluid flow induced internal erosion within porous media: modelling of the no erosion filter test experiment. Transp. Porous Media. 89(3), 441–457 (2011)

    Article  Google Scholar 

  • Frishfelds, V., Lundström, T.S., Jakovics, A.: Permeability of clustered fiber networks: modeling of the unit cell. Mech. Compos. Mater. 39(3), 265–272 (2003)

    Article  Google Scholar 

  • Han, K., Lee, L.J., Liou, M.: Fiber mat deformation in liquid composite molding. 2. Modeling. Polym. Compos. 14(2), 151–160 (1993)

    Article  Google Scholar 

  • Hellström, J.G.I., Frishfelds, V., Lundström, T.S.: Mechanisms of flow-induced deformation of porous media. J. Fluid Mech. 664, 220–237 (2010)

    Article  Google Scholar 

  • Hwang, W.R., Advani, S.G.: Numerical simulations of Stokes-Brinkman equations for permeability prediction of dual scale fibrous porous media. Phys. Fluids. 22, 113101–1352 (2010)

    Article  Google Scholar 

  • Hwang, W.R., Advani, S.G., Walsh, S.: Direct simulations of particle deposition and filtration in dual-scale porous media. Compos. Part A. 42, 1344–1352 (2011)

    Article  Google Scholar 

  • Indraratna, B., Athukorala, R., Vinod, J.: Estimating the rate of erosion of a silty sand treated with lignosulfonate. J. Geotech. Geoenviron. Eng. 139(5), 701–714 (2013)

    Article  Google Scholar 

  • Jourak, A., Frishfelds, V., Hellström, J.G.I., Lundström, T.S.: Dependence of longitudinal dispersion coefficient on size distribution Inside three-dimensional randomly packed beds of spherical particles. Transp. Porous Media. 99, 1–16 (2013a)

    Article  Google Scholar 

  • Jourak, A., Frishfelds, V., Hellström, J.G.I., Lundström, T.S.: Numerical derivation of dispersion coefficients for flow through 3-D randomly packed beds of monodisperse spheres. AIChE J. 60(2), 749–761 (2014)

    Article  Google Scholar 

  • Jourak, A., Frishfelds, V., Lundström, T.S., Herrmann, I., Hedström, A.: The calculations of dispersion coefficients inside two-dimensional randomly packed beds of circular particles. AIChE J. 59(3), 1002–1011 (2013b)

    Article  Google Scholar 

  • Kacimov, A., Obnosov, Y.: Analytical solutions for seepage near material boundaries in dam cores: the Davison–Kalinin problems revisited. Appl. Math. Model. 36(3), 1286–1301 (2012)

    Article  Google Scholar 

  • Khayamyan, S., Lundström, T.S., Gustavsson, L.H.: Experimental investigation of transitional flow in porous media with usage of a pore doublet model. Transp. Porous Media. 101(2), 333–348 (2014)

    Article  Google Scholar 

  • Kress, J., Yun, T.S., Narsilio, G.A., Evans, T.M., Lee, D.S.: Evaluation of hydraulic conductivity in 3D random and heterogeneous particulate materials using network model. Comput. Geotechnol. 40, 45–52 (2012)

    Article  Google Scholar 

  • Lundström, T.S., Gebart, B.R.: Effect of perturbation of fibre architecture on permeability inside fibre tows. J. Compos. Mater. 29(4), 424–443 (1995)

    Article  Google Scholar 

  • Lundström, T.S., Hellström, J.G.I., Frishfelds, V.: Transversal flow-induced deformation of fibres during composites manufacturing and the effect on permeability. J. Reinf. Plast. Compos. 32, 1129–1135 (2013)

    Article  Google Scholar 

  • Maier, R.S., Kroll, D.M., Bernard, R.S., Howington, S.E., Peters, J.F., Davis, H.T.: Hydrodynamic dispersion in confined packed beds. Phys. Fluids. 15, 3795 (2003)

    Article  Google Scholar 

  • Martys, N.S., Torquato, S., Bentz, D.P.: Universal scaling of fluid permeability for sphere packings. Phys. Rev. E 50, 403 (1994)

    Article  Google Scholar 

  • Minguez, R., Delgado, F., Escuder, I., Membrillera, M.G.: Reliability assessment of granular filters in embankment dams. Int. J. Numer. Anal. Methods Geomech. 30, 1019–1037 (2006)

    Article  Google Scholar 

  • Moutsopoulos, K.N., Papaspyros, J.N.E., Tsihrintzis, V.A.: Experimental investigation of inertial flow processes in porous media. J. Hydrol. 374, 242–254 (2009)

    Article  Google Scholar 

  • Mourzenko, V., Thovert, J.-F., Vizika, O., Adler, P.M.: Geometrical and transport properties of random packings of polydisperse spheres. Phys. Fluids. 77, 66306 (2008)

    Google Scholar 

  • Quinn, T.M.: Flow-induced deformation of poroelastic tissues and gels: a new perspective on equilibrium pressure-flow-thickness relations. J. Biomech. Eng. 135, 011009 (2013)

    Article  Google Scholar 

  • Reboul, N., Vincens, E., Cambou, B.: A computational procedure to assess the distribution of constriction sizes for an assembly of spheres. Comput. Geotechnol. 37, 195–206 (2010)

    Article  Google Scholar 

  • Richards, K.S., Reddy, K.R.: Critical appraisal of piping phenomena in earth dams. Bull. Eng. Geol. Environ. 66, 381–402 (2007)

    Article  Google Scholar 

  • Sedghi-Asl, M., Rahimi, H., Farhoudi, J., Hoorfar, A., Hartmann, S.: 1-D fully-developed turbulent flow through coarse porous medium. J. Hydrol. Eng. In Press, (2013)

  • Sedghi-Asl, M., Rahimi, H., Salehi, R.: Non-darcy flow of water through a packed column test. Trans. Porous Media (in Press) (2014)

  • Sherard, J.L., Dunnigan, L.P.: Critical filters for impervious soils. J. Geotechnol. Eng. 115, 927–947 (1989)

    Article  Google Scholar 

  • Thompson, K.E.: Fast and robust Delaunay tessellation in periodic domains. Int. J. Numer. Methods Eng. 55(11), 1345–1366 (2002)

    Article  Google Scholar 

  • Ye, X.G., Qiu, J.J., Zhang, C., Liang, R., Wang, B.: A finite element-based heuristic estimation of local preform permeability for resin transfer molding. Trans. Porous Media 76(2), 247–263 (2009)

    Article  Google Scholar 

  • Zaman, E., Jalali, P.: On hydraulic permeability of random packs of monodisperse spheres: direct flow simulations versus correlations. Phys. A 389, 205–214 (2010)

    Article  Google Scholar 

  • Zou, Y.-H., Chen, Q., Chen, X.-Q., Cui, P.: Discrete numerical modeling of particle transport in granular filters. Comput. Geotechnol. 47, 48–56 (2013)

    Article  Google Scholar 

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Authors and Affiliations

  1. Faculty of Natural Sciences, Liepaja University, Liela iela 14, 3401 , Liepaja, Latvia

    V. Frishfelds

  2. Division of Fluid and Experimental Mechanics, Luleå University of Technology, 971 87 , Luleå, Sweden

    J. G. I. Hellström & T. S. Lundström

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  1. V. Frishfelds
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  2. J. G. I. Hellström
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  3. T. S. Lundström
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Correspondence to V. Frishfelds.

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Frishfelds, V., Hellström, J.G.I. & Lundström, T.S. Flow-Induced Deformations Within Random Packed Beds of Spheres. Transp Porous Med 104, 43–56 (2014). https://doi.org/10.1007/s11242-014-0319-2

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  • DOI: https://doi.org/10.1007/s11242-014-0319-2

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