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Flow Through a Two-Scale Porosity, Oriented Fibre Porous Medium

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Abstract

A model is described for the meso- and micro-flow through an array of oriented fibre tows with meso-channels between the tows. Axial Stokes's flow was considered in the meso-channels and Darcy's law was applied within the porous fibre tows, taking into account injection pressure and capillary pressures in both types of flow. Transverse flow transfer was modelled from the leading flow front to the lagging flow and a partial-slip boundary condition was applied at the permeable boundaries of meso-channels. Flow visualisation experiments and microstructural characterisation of laminates provided appropriate experimental data for model validation. In this, the predictions for the progress of the leading meso-flow were in excellent agreement with the experimental data. Parametric studies followed including the effects of injection pressure and meso-channel size.

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References

  • Ahn, K. J., Seferis, J. C. and Berg, J. C.: 1991, Simultaneous measurements of permeability and capillary pressure of thermosetting matrices in woven fabric reinforcements, Polym. Compos. 12(3), 146-152.

    Google Scholar 

  • Amico, S. C.: 2000, Permeability and capillary pressure in the infiltration of fibrous porous media in resin transfer moulding, PhD Thesis, Department of Materials Science and Engineering, University of Surrey, UK.

    Google Scholar 

  • Amico, S. C. and Lekakou, C.: 2000, Mathematical modelling of capillary micro-flow through woven fabrics, Compos. Part A - Appl. Sci. 31(12), 1331-1344.

    Google Scholar 

  • Amico, S. C. and Lekakou, C.: 2002a, Axial impregnation of a fiber bundle. Part 1. Capillary experiments, Polym. Compos. 23(2), 249-263.

    Google Scholar 

  • Amico, S. C. and Lekakou, C.: 2002b, Axial impregnation of a fiber bundle. Part 2. Theoretical analysis, Polym. Compos. 23(2), 264-273.

    Google Scholar 

  • Baish, J.W., Netti, P. A. and Jain, R. K.: 1997, Transmural coupling of fluid flow in microcirculatory network and interstitium in tumors, Microvasc. Res. 53(2), 128-141.

    Google Scholar 

  • Batch, G. L., Chen, Y.-T. and Macosko, C.W.: 1996, Capillary impregnation of aligned fibrous beds: experiments and model, J. Reinf. Plast. Comp. 15, 1027-1051.

    Google Scholar 

  • Beavers, G. S. and Joseph, D. D.: 1967, Boundary conditions at a naturally permeable wall, J. Fluid Mech. 30(1), 197-207.

    Google Scholar 

  • Bruschke, M. V. and Advani, S. G.: 1993, Flow of generalised Newtonian fluids across a periodic array of cylinders, J. Rheol. 37(3), 479-498.

    Google Scholar 

  • Calhoun, D. R., Yalvac, S., Wetters, D. G., Wu, C.-H., Wang, T. J., Tsai, J. S. and Lee, L. J.: 1996, Mold filling analysis in resin transfer molding, Polym. Compos. 17(2), 251-264.

    Google Scholar 

  • Carleton, P. S. and Nelson, G. L.: 1994, Wetout of glass fiber tows in structural reaction moulding. 1. Capillary action and fiber mobility, J. Reinf. Plast. Comp. 13, 20-37.

    Google Scholar 

  • Chan, A. W. and Morgan, R. J.: 1993, Tow impregnation during resin transfer molding of bi-directional nonwoven fabrics, Polym. Compos. 14(4), 335-340.

    Google Scholar 

  • Chen, Y. T., Davis, H. T. and Macosko, C. W.: 1995, Wetting of fibre mats for composites manufacturing: I. Visualisation experiments, AIChE J. 41(10), 2261-2273.

    Google Scholar 

  • Choi, C. Y. and Waller, P. M.: 1997, Momentum transport mechanism for water flow over porous media, J. Environ. Eng. - ASCE 123(8), 792-799.

    Google Scholar 

  • Davé, R.: 1990, A unified approach to modelling resin flow during composite processing, J. Compos. Mater. 24(1), 22-41.

    Google Scholar 

  • Gauvin, R., Trochu, F., Lemenn, Y. and Diallo, L.: 1996, Permeability measurement and flow simulation through fiber reinforcement, Polym. Compos. 17(1), 34-42.

    Google Scholar 

  • Gebart, B. R.: 1992, Permeability of unidirectional reinforcements for RTM, J. Compos. Mater. 26(8), 1100-1133.

    Google Scholar 

  • Guha, H. S. and Chaudhury, T. K.: 1993, Flow over a highly porous inclined bed under surface traction: boundary layer in the porous region, Int. J. Eng. Sci. 31(8), 1191-1196.

    Google Scholar 

  • Gupte, S. K. and Advani, S. G.: 1997, Flow near the permeable boundary of an aligned fiber preform: an experimental investigation using laser doppler anemometry, Polym. Compos. 18(1), 114-124.

    Google Scholar 

  • Gutowski, T., Cai, Z., Bauer, S., Boucher, D., Kingery, J. and Wineman, S.: 1987, Consolidation experiments for laminate composites, J. Compos. Mater. 21(7), 650-669.

    Google Scholar 

  • Huang, L.-H., Chiang, I.-L. and Song, C.-H.: 1997, A reinvestigation of laminar channel flow passing over porous bed, J. Chin. Inst. Eng. 20(4), 435-441.

    Google Scholar 

  • Johari, M. A. K. B.: 1994, Resin transfer moulding (RTM): flow permeability of woven cloths and effects of flow on mechanical properties of RTM products, MSc Thesis, Department of Materials Science and Engineering, University of Surrey, UK.

    Google Scholar 

  • Labecki, M., Piret, J. M. and Bowen, B. D.: 1995, Two-dimensional analysis of fluid flow in hollow-fibre modules. Chem. Eng. Sci. 50(21), 3369-3384.

    Google Scholar 

  • Lam, R. C. and Kardos, J. L.: 1991, The permeability and compressibility of aligned and cross-plied carbon-fiber beds during processing of composites. Polym. Eng. Sci., 31(14), 1064-1070.

    Google Scholar 

  • Langlois, W. E.: 1964, Slow Viscous Flow, Macmillan, New York, USA.

    Google Scholar 

  • Lekakou, C. and Bader, M. G.: 1998, Mathematical modelling of macro-and micro-infiltration in resin transfer moulding (RTM), Compos. Part A - Appl. S. 29A, 29-37.

    Google Scholar 

  • Lekakou, C., Johari, M. A. K., Norman, D. and Bader, M. G.: 1996, Measurement techniques and effects on in-plane permeability of woven cloths in resin transfer moulding, Compos. Part A - Appl. S. 27A, 401-408.

    Google Scholar 

  • Lundstrom, T. S.: 2000, The permeability of non-crimp stitched fabrics, Compos. Part A - Appl. S. 31(12), 1345-1353.

    Google Scholar 

  • McCormack, P. D. and Crane, L.: 1973, Physical Fluid Dynamics, Academic Press, New York, USA.

    Google Scholar 

  • Mehta, K. N. and Narasimha Rao, K.: 1993, Plane flow impinging and flowing over a porous bed, J. Hydraul. Res. 31(4), 563-573.

    Google Scholar 

  • Nassehi, V.: 1998, Modelling of combined Navier-Stokes and Darcy flows in crossflow membrane filtration, Chem. Eng. Sci. 53(6), 1253-1265.

    Google Scholar 

  • Patel, N., Rohatgi, V. and Lee, L. J.: 1995, Microscale flow behavior and void formation mechanisms during impregnation through a unidirectional stitched fiberglass mat, Polym. Eng. Sci., 35(10), 837-851.

    Google Scholar 

  • Phelan Jr., F. R., Leung, Y. and Parnas, R. S.: 1994, Modeling of microscale flow in unidirectional fibrous porous media, J. Thermoplast. Compos. 7, 208-218.

    Google Scholar 

  • Poole, C. P.: 1998, The Physics Handbook: Fundamentals and Key Equations, Wiley, New York, USA.

    Google Scholar 

  • Rohatgi, V., Patel, N. and Lee, L. J.: 1996, Experimental investigation of flow-induced microvoids during impregnation of unidirectional stitched fiberglass mat, Pol. Comp. 17(2), 161-170.

    Google Scholar 

  • Ross, S. M.: 1983, Theoretical model of the boundary condition at a fluid-porous interface, AIChE J. 29(5), 840-846.

    Google Scholar 

  • Saunders, R. A.: 1997, Compression and microstructure of glass fibre fabrics in the processing of polymer composites, PhD Thesis, Department of Materials Science and Engineering, University of Surrey, UK.

    Google Scholar 

  • Simacek, P. and Advani, S. G.: 1996, Permeability model for a woven fabric, Polym. Compos. 17(6), 887-899.

    Google Scholar 

  • Skartsis, L., Kardos, J. L. and Khomani, B.: 1992, Resin flow through fiber beds during composite manufacturing processes, Polym. Eng. Sci., 32(4), 221-239.

    Google Scholar 

  • Stroud, K. A.: 1996, Further Engineering Mathematics: Programmes and Problems, 3rd edn., Macmillan, Basingstoke, UK.

    Google Scholar 

  • Vankan, W. J., Huyghe, J. M., Drost, M. R., Janssen, J. D. and Huson, A.: 1997, A finite element mixture model for hierarchical porous media, Int. J. Numer. Meth. Eng. 40, 193-210.

    Google Scholar 

  • White, F. M.: 1974, Viscous Fluid Flow, McGraw-Hill, New York, USA.

    Google Scholar 

  • Williams, J. G., Morris, C. E. M. and Ennis, B. C.: 1974, Liquid flow through aligned fiber beds, Polym. Eng. Sci. 14(6), 413-419.

    Google Scholar 

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Amico, S., Lekakou, C. Flow Through a Two-Scale Porosity, Oriented Fibre Porous Medium. Transport in Porous Media 54, 35–53 (2004). https://doi.org/10.1023/A:1025799404038

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