Abstract
Axial flow through gaps between aligned straight yarns with realistic cross-sectional shapes, described by power-ellipses, was analysed numerically. At a given fibre volume fraction, equivalent gap permeabilities have a maximum at minimum size of elongated tapering parts of the gap cross-section and a ratio of gap width to height near 1. When the yarn spacing is given in addition to the fibre volume fraction, calculated maximum and minimum values for the equivalent permeability of inter-yarn gaps, which occur at near-rectangular and lenticular cross-sections, differ by factors of up to 3.3. Novel approximations for the shape factor and the hydraulic diameter in Poiseuille flow were derived as a function of the fibre volume fraction, the yarn cross-sectional aspect ratio and the geometrical parameter describing the shape of the power-elliptical yarn cross-section. This allows the equivalent gap permeability to be predicted with good accuracy for any fibre volume fraction and yarn cross-section.
Highlights
In the manufacture of polymer composite components employing Liquid Composite Moulding (LCM) processes, dry fibrous reinforcements are impregnated with liquid resin systems
Since the fibre volume fraction, which significantly affects the mechanical properties of finished composite components, is a parameter commonly used for material specification, it is useful to describe the dependence of the permeability of fibrous reinforcements on the fibre volume fraction
At any fibre volume fraction and yarn spacing studied here, the maximum and minimum values for the equivalent permeability of inter-yarn gaps differ by factors of up to 3.3
Summary
In the manufacture of polymer composite components employing Liquid Composite Moulding (LCM) processes, dry fibrous reinforcements are impregnated with liquid resin systems. To assess the risk of dry spot formation and predict cycle times, the impregnation process is frequently modelled as flow of a viscous liquid through a porous medium, i.e. a network of interconnected hydraulic ducts. Since the fibre volume fraction, which significantly affects the mechanical properties of finished composite components, is a parameter commonly used for material specification, it is useful to describe the dependence of the permeability of fibrous reinforcements on the fibre volume fraction. The Kozeny-Carman equation [2], which was originally derived for the permeability of porous media consisting of spherical particles, is sometimes used successfully for description of this dependence, albeit with adapted geometrical constants [3]. The frequently cited equations derived by Gebart [4] describe the permeability as a function of the fibre volume fraction for parallel and transverse flow in media with uniform periodic
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