A finite element-based approach was created to generate fiber scale permeability and thermal conductivity tensors for unidirectional fiber-reinforced composites. This model used fiber radius, volume fraction, and symmetry angle in addition to an assigned temperature and pressure gradient as inputs. Results and comparisons are presented for both Newtonian and non-Newtonian fluids. Permeability and conductivity values generated by the model agreed strongly with experimental and numerical data obtained by other research. The model was also able to capture the dependence of these tensors on fiber structure and fluid properties. This was accomplished within the confines of a small computational domain.
Åström, B.T. and Pipes, R.B. (1993). A Modeling Approach to Thermoplastic Pultrusion. I: Formulation of Models, Polymer Composites, 14(3): 173-183.
2.
Haffner, S.M. , Friedrich, K., Hogg , P.J. and Busfield, J.J.C. (1998). Finite-Element-Assisted Modeling of a Thermoplastic Pultrusion Process for Powder-Impregnated Yarn , Composites Science and Technology , 58(8): 1371-1380.
3.
Liang, E.W. and Tucker III, C.L. ( 1995). A Finite Element Method for Flow in Compression Molding of Thin and Thick Parts, Polymer Composites, 16(1): 70-82.
4.
Gutowski, T.G. , Cai, Z., Bauer , S., Boucher, D., Kingery, J. and Wineman, S. (1987). Consolidation Experiments for Laminate Composites, Journal of Composite Materials, 21(7): 650-669.
5.
Larson, R.E. and Higdon, J.J.L. (1986). Microscopic Flow Near the Surface of Two-dimensional Porous Media. Part 1. Axial Flow , Journal of Fluid Mechanics, 166: 449-472.
6.
Larson, R.E. and Higdon, J.J.L. ( 1987). Microscopic Flow Near the Surface of Two-dimensional Porous Media. Part 2. Transverse Flow , Journal of Fluid Mechanics , 178: 119-136.
7.
Islam, M.R. and Pramila, A. ( 1999). Thermal Conductivity of Fiber Reinforced Composites by the FEM, Journal of Composite Materials, 33(18): 1699-1715.
8.
Rolfes, R. and Hammerschmidt, U. ( 1995). Transverse Thermal Conductivity of CFRP Laminates: A Numerical and Experimental Validation of Approximation Formulae, Composites Science and Technology, 54(1): 45-54.
9.
Gebart, B.R. ( 1992). Permeability of Unidirectional Reinforcements for RTM , Journal of Composite Materials, 26(8): 1100-1133.
10.
Van der Westhuizen, J. and Du Plessis, J.P. (1996). An Attempt to Quantify Fiber Bed Permeability Utilizing the Phase Average Navier-Stokes Equation , Composites: Part A, 27(4): 263-269.
11.
Lundström, T.S., Sundlöf , H. and Holmberg, J.A. (2006). Modeling of Power-Law Fluid Flow Through Fiber Beds, Journal of Composite Materials, 40(3): 283-296.
12.
Orgéas, L., Idris, Z., Geindreau , C., Bloch, J.-F. and Auriault , J.-L. (2006). Modelling the Flow of Power-Law Fluids Through Anisotropic Porous Media at Low-Pore Reynolds Number, Chemical Engineering Science , 61(14): 4490-4502.
13.
Bruschke, M.V. and Advani, S.G. (1993). Flow of Generalized Newtonian Fluids Across a Periodic Array of Cylinders, Journal of Rheology, 37(3): 479-498.
14.
Vijaysri, M. , Chhabra, R.P. and Eswaran, V. (1999). Power-Law Fluid Flow Across An Array of Infinite Circular Cylinders: A Numerical Study, Journal of Non-Newtonian Fluid Mechanics, 87(2-3): 263-282.
15.
Brennan, K.P. (2008). Numerical Multi-scale Resin Infiltration Modeling of Unidirectional Fiber Reinforcements, PhD Dissertation , University of Wyoming, Laramie, WY.
16.
Brennan, K.P. and Walrath, D.E. (2008). Analysis of Underlying Organization in Randomized Fiber Arrays, accepted for publication in the Journal of Composite Materials.
17.
Bafna, S.S. and Baird, D.G. (1992). Impregnation Model for the Preparation of Thermoplastic Prepregs, Journal of Composite Materials, 26(5): 683-707.
18.
Wetherhold, R.C. and Wang, J. (1994). Difficulties in the Theories for Predicting Transverse Thermal Conductivity of Continuous Fiber Composites , Journal of Composite Materials, 28(15): 1491-1498.
19.
Adams, D.F. and Tsai, S.W. (1969). The Influence of Random Filament Packing on the Transverse Stiffness of Unidirectional Composites , Journal of Composite Materials, 3(3): 368-381.
20.
Faires, J.D. and Burden, R. ( 1998). Numerical Methods, 2nd edn, pp. 268-273, Brooks/ Cole Publishing Co., Pacific Grove, CA.
21.
Pearson, J.R.A. and Tardy, P.M.J. (2002). Models for Flow of Non-Newtonian and Complex Fluids Through Porous Media, Journal of Non-Newtonian Fluid Mechanics, 102(2): 447-473.
22.
Malvern, L.E. (1969). Introduction to the Mechanics of a Continuous Medium, p. 103, Prentice-Hall, Inc., Upper Saddle River, NJ.
23.
Brennan, K.P. , Straka, B.D. and Walrath, D.E. (2008). Investigation of a Simple Tensorial Permeameter, accepted for publication in Polymer Composites.
24.
Belov, E.B. , Lomov, S.V., Verpoest, I., Peters, T., Roose, D., Parnas, R.S., Hoes, K. and Sol , H. (2004). Modeling of Permeability of Textile Reinforcements: Lattice Boltzmann Method , Composites Science and Technology, 64(7-8): 1069-1080.
25.
Ranganathan, S., Phelan Jr, F.R. and Advani, S.G. (1996). Generalized Model for the Transverse Fluid Permeability in Unidirectional Fibrous Media, Polymer Composites, 17(2): 222-230.
26.
Skartsis, L. , Khomami, B. and Kardos, J.L. ( 1992). Polymeric Flow Through Fibrous Media, Journal of Rheology, 36(4): 589-620.
27.
Lord Rayleigh (1892). On the Influence of Obstacles Arranged in Rectangular Order Upon the Properties of a Medium, Philosophical Magazine, 34: 481-502.
