Abstract
An isotropic elastic porous structure whose initial geometry is regular (periodically uniform) will experience non-uniform deformation when a viscous fluid flows through the matrix under the influence of an externally applied pressure difference. In such a case, the flow field will experience a non uniform pressure gradient whose magnitude increases in the direction of bulk flow. The closed solution to the problem of low Re flow through deformable porous media requires the simultaneous solution of the flow field in the void space and of the stress distribution in the solid matrix. The focus of the current study is to attempt to predict the pressure distribution of the flow field based only on the geometry of the media. The intention is to eventually simplify the coupled fluid-solid problem by replacing explicitly solution of the flow field with a pressure boundary condition in the stress distribution of the solid matrix.
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References
Mathieu-Potvin, F., Gosselin, L.: Impact of non-uniform properties on governing equations for fluid flows in porous media. Transp. Porous Media 105(2), 277–314 (2014)
Vafai, K.: Convective flow and heat transfer in variable-porosity media. J. Fluid Mech. 147(1), 233–259 (1984)
Goyeau, B., et al.: Numerical calculation of the permeability in a dendritic mushy zone. Metall. Mater. Trans. B 30(4), 613–622 (1999)
Goyeau, B., et al.: Averaged momentum equation for flow through a nonhomogenenous porous structure. Transp. Porous Media 28(1), 19–50 (1997)
Azzam, M.I.S., Dullien, F.A.L.: Flow in tubes with periodic step changes in diameter: a numerical solution. Chem. Eng. Sci. 32(12), 1445–1455 (1977)
Dullien, F.A.L., Azzam, M.I.S.: Effect of geometric parameters on the friction factor in periodically constricted tubes. AIChE J. 19(5), 1035–1036 (1973)
Dullien, F.A.L., Azzam, M.I.S.: Comparison of pore size as determined by mercury porosimetry and by miscible displacement experiment. Ind. Eng. Chem. Fundam. 15(2), 147–147 (1976)
Dullien, F.A.L., Elsayed, M.S., Batra, V.K.: Rate of capillary rise in porous-media with nonuniform pores. J. Colloid Interface Sci. 60(3), 497–506 (1977)
Becker, S.M.: Prediction of local losses of low Re flows in non-uniform media composed of parrallelpiped structures. Transp. Porous Media 122(1), 185–201 (2018)
Becker, S.M., Gasow, S.: Prediction of local losses of low Re flows in elastic porous media 2017(58066), V01CT23A009 (2017)
Beavers, G.S., Wittenberg, K., Sparrow, E.M.: Fluid-flow through a class of highly-deformable porous-media. 2. Experiments with water. J. Fluids Eng. Trans. ASME. 103(3), 440–444 (1981)
Siddique, J.I., Anderson, D.M., Bondarev, A.: Capillary rise of a liquid into a deformable porous material. Phys. Fluids 21(1) (2009)
Munro, B., et al.: Fabrication and characterization of deformable porous matrices with controlled pore characteristics. Transp. Porous Media 107(1), 79–94 (2015)
Chen, H., et al.: A numerical algorithm for single phase fluid flow in elastic porous media. In: Chen, Z., Ewing, R.E., Shi, Z.-C. (eds.) Numerical Treatment of Multiphase Flows in Porous Media: Proceedings of the International Workshop Held a Beijing, China, 2–6 August 1999, pp. 80–92. Springer, Berlin (2000)
Spiegelman, M.: Flow in deformable porous media. Part 1 simple analysis. J. Fluid Mech. 247(1), 17–38 (1993)
Cao, Y., Chen, S., Meir, A.J.: Steady flow in a deformable porous medium. Math. Methods Appl. Sci. 37(7), 1029–1041 (2014)
Bociu, L., et al.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Arch. Rat. Mech. Anal. 222(3), 1445–1519 (2016)
Hou, G., Wang, J., Layton, A.: Numerical methods for fluid-structure interaction—a review. Commun. Comput. Phys. 12(2), 337–377 (2012)
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Becker, S. (2019). Toward the Problem of Low Re Flows Through Linearly Elastic Porous Media. In: Gutschmidt, S., Hewett, J., Sellier, M. (eds) IUTAM Symposium on Recent Advances in Moving Boundary Problems in Mechanics. IUTAM Bookseries, vol 34. Springer, Cham. https://doi.org/10.1007/978-3-030-13720-5_15
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DOI: https://doi.org/10.1007/978-3-030-13720-5_15
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