A New Mathematical Model for Permeability of Composites

Study of permeability of Fibrous Composites is important in several natural and industrial processes in mechanical engineering. In this study, a comprehensive mathematical model is presented for calculation of normal permeability of ordered elliptical fibrous media. An innovative scale-analysis technique is employed for determining the normal permeability of elliptical fibrous media. In this technique, the permeability is related to the porosity, elliptical fiber diameters, and tortuosity of the medium. In other word, the normal permeability of the circular fibrous structures, which presented in the literature, is extended to the general case of elliptical fibrous media. The composite material is represented by a “unit cell” which is assumed to be repeated throughout the media. A closed-form relation is obtained for non-dimensional permeability using scale analysis approach. Due to lack of experimental data for permeability of fibrous porous media (composite media), with elliptical cross section, a numerical analysis is also employed. The governing equations are solved numerically in the unit cells using finite volume method. The results obtained by numerical solution are compared with those presented by scale analysis method. The presented relation for normal permeability can suitably cover the case of fibrous media with circular cross section. The results are also compared with those presented in the literature for the case of cylindrical fibers. The developed compact relationships are successfully verified through comparison with the present experimental results and the data reported by others.