Resin flow through fiber beds during composite manufacturing processes. Part I: Review of newtonian flow through fiber beds

Abstract

A critical part of any master model used to simulate or control a composite material manufacturing process is the description of resin flow through the fiber bed. We present here a review of both theoretical and experimental studies of fluid flow through porous media, including fiber beds. For the practical porosity range of interest in continuous fiber composites processing (0.3< ϵ < 0.6), the permeability cannot be accurately described using the Blake‐Kozeny‐Carman equation, even though the flow is Newtonian at very low Reynold's number. For aligned fiber situations, the Kozeny constant, k, deviates radically from theory, depends on bed nonuniformities, and is only constant over very narrow porosity ranges. Thus, one cannot experimentally determine k at high porosities and use this value to describe low porosity situations. Theoretical attempts, based on perfectly spaced and aligned arrays of cylinders, adequately describe the transverse permeability of ideal fiber beds in the high porosity range, but do not succeed at porosities below 0.6. For axial flow through aligned fiber beds, the theory yields permeabilities much lower than are experimentally observed throughout the entire porosity range. For randomly arranged fibers, random cylinder theory also predicts permeabilities that are significantly lower than are measured.

Flow of non-Newtonian polymeric solutions through fibrous media

“…Figure 5 compares the values of the Kozeny constant k as predicted by the present analysis and the experimental values derived from the flow in fibrous beds as compiled in the literature. 13,14 Excellent agreement is seen to exist between the present analysis and the experimental results. Similarly, several other empirical expressions 29 -32 are available in the literature to represent the flow resistance for the creeping flow of Newtonian fluids in fibrous beds.…”

“…Based on the detailed comparisons presented in the literature, it is perhaps fair to state that satisfactory methods of estimating the resistance to flow of Newtonian fluids in such model fibrous media are now available in the literature (e.g., see refs. 13,14). In contrast to this, much less is known about the analogous flow of non-Newtonian fluids in this flow geometry, and the present study represents a step in the direction of bridging this gap in the existing literature.…”

“…13,14 As far as known to us, there have been only three theoretical analyses reported in the literature. Skartsis et al 15 have numerically studied the flow of power law fluids normal to square arrays of different spacing (characterized in terms of an overall mean value of voidage) composed of long cylinders and they reported fair agreement with the predicted and experimental values of the resistance to flow expressed in terms of a dimensionless Kozeny coefficient, for the limited range of conditions of porosity and power law index studied.…”

“…Consequently, a wealth of information is now available relating to the flow of Newtonian fluids, which has been reviewed by several authors. 1,13 Clearly, the estimation of the fluid dynamic resistance to the flow of a fluid represents one of the most important design parameters. This information is conveniently expressed in terms of either a permeability of the system or a drag coefficient or in terms of a friction factor.…”

Permeability calculations in three-dimensional isotropic and oriented fiber networks

“…The study of creeping flow in fibrous media is of considerable interest in a wide variety of applications such as paper production, 1-3 filtration, 4 fibrous beds for manufacturing processes, 5 and transport in biological systems. [6][7][8][9][10] The most common measure used to characterize such flows is the hydraulic permeability k, which for an isotropic medium is defined by Darcy's law as 11…”